init

.gitignore

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+
+# Created by https://www.gitignore.io/api/julia,jupyternotebook,jupyternotebooks,latex,python,tex,vim
+# Edit at https://www.gitignore.io/?templates=julia,jupyternotebook,jupyternotebooks,latex,python,tex,vim
+
+### Julia ###
+# Files generated by invoking Julia with --code-coverage
+*.jl.cov
+*.jl.*.cov
+
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+
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+Manifest.toml
+
+### JupyterNotebook ###
+.ipynb_checkpoints
+*/.ipynb_checkpoints/*
+
+# Remove previous ipynb_checkpoints
+#   git rm -r .ipynb_checkpoints/
+#
+
+### JupyterNotebooks ###
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+
+
+# Remove previous ipynb_checkpoints
+#   git rm -r .ipynb_checkpoints/
+
+### LaTeX ###
+## Core latex/pdflatex auxiliary files:
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+*.lof
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+.*.lb
+
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+latex.out/
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+
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+
+# gnuplottex
+*-gnuplottex-*
+
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+*.gaux
+*.gtex
+
+# htlatex
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+*.4tc
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+*.trc
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+
+# hyperref
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+
+# knitr
+*-concordance.tex
+# TODO Comment the next line if you want to keep your tikz graphics files
+*.tikz
+*-tikzDictionary
+
+# listings
+*.lol
+
+# luatexja-ruby
+*.ltjruby
+
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+*.ilg
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+*.ist
+
+# minitoc
+*.maf
+*.mlf
+*.mlt
+*.mtc[0-9]*
+*.slf[0-9]*
+*.slt[0-9]*
+*.stc[0-9]*
+
+# minted
+_minted*
+*.pyg
+
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+
+# nomencl
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+*.nlo
+*.nls
+
+# pax
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+
+# scrwfile
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+
+# sympy
+*.sout
+*.sympy
+sympy-plots-for-*.tex/
+
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+
+# pythontex
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+pythontex-files-*/
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+
+## Editors:
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+### LaTeX Patch ###
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+
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+# Byte-compiled / optimized / DLL files
+__pycache__/
+*.py[cod]
+*$py.class
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+.installed.cfg
+*.egg
+MANIFEST
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+#   According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
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+*.sage.py
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+env/
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+venv.bak/
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+/site
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+.mypy_cache/
+.dmypy.json
+dmypy.json
+
+# Pyre type checker
+.pyre/
+
+### TeX ###
+
+# these rules might exclude image files for figures etc.
+# *.ps
+# *.eps
+# *.pdf
+
+
+
+
+# latexrun
+
+# algorithms
+
+# achemso
+
+# amsthm
+
+# beamer
+
+# changes
+
+# comment
+
+# cprotect
+
+# elsarticle (documentclass of Elsevier journals)
+
+# endnotes
+
+# fixme
+
+# feynmf/feynmp
+
+
+# glossaries
+
+# gnuplottex
+
+# gregoriotex
+
+# htlatex
+
+# hyperref
+
+# knitr
+# TODO Comment the next line if you want to keep your tikz graphics files
+
+# listings
+
+# luatexja-ruby
+
+# makeidx
+
+# minitoc
+
+# minted
+
+# morewrites
+
+# nomencl
+
+# pax
+
+# pdfpcnotes
+
+# sagetex
+
+# scrwfile
+
+# sympy
+
+# pdfcomment
+
+# pythontex
+
+# tcolorbox
+
+# thmtools
+
+# TikZ & PGF
+
+# todonotes
+
+# vhistory
+
+# easy-todo
+
+# xcolor
+
+# xmpincl
+
+# xindy
+
+# xypic precompiled matrices
+
+# endfloat
+
+# Latexian
+
+# WinEdt
+
+# Texpad
+
+# LyX
+
+# Kile
+
+# KBibTeX
+
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+
+# expex forward references with \gathertags
+
+# standalone packages
+
+### TeX Patch ###
+# glossaries
+
+### Vim ###
+# Swap
+[._]*.s[a-v][a-z]
+[._]*.sw[a-p]
+[._]s[a-rt-v][a-z]
+[._]ss[a-gi-z]
+[._]sw[a-p]
+
+# Session
+Session.vim
+
+# Temporary
+.netrwhist
+*~
+# Auto-generated tag files
+tags
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+[._]*.un~
+
+# End of https://www.gitignore.io/api/julia,jupyternotebook,jupyternotebooks,latex,python,tex,vim

julia_notebook/1611617_NGUYEN_ANH_KHOA_new.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "using Formatting\n",
+    "using StatsBase\n",
+    "using FFTW\n",
+    "using Plots"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Histogram normalized\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "5×5 Array{Int64,2}:\n",
+       " 7  1  1  3  5\n",
+       " 5  3  7  3  5\n",
+       " 8  3  7  3  5\n",
+       " 8  6  7  6  5\n",
+       " 8  3  8  3  5"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[0.08, 0.28, 0.16, 0.08, 0.08, 0.16, 0.04, 0.12]\n",
+      "Cumsum Histogram normalized\n",
+      "[0.08, 0.36, 0.52, 0.6, 0.68, 0.84, 0.88, 1.0]\n",
+      "Prefered Histogram\n",
+      "[0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]\n",
+      "Cumsum Prefered Histogram\n",
+      "[0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1.0]\n",
+      "out hist\n",
+      "[0.125, 0.375, 0.625, 0.625, 0.75, 0.875, 1.0, 1.0]\n",
+      "out color\n",
+      "[0, 1, 2, 3, 4, 5, 6, 7]\n",
+      "[1.0, 3.0, 5.0, 5.0, 6.0, 7.0, 8.0, 8.0]\n",
+      "\n",
+      "New Histogram\n",
+      "[2, 0, 7, 0, 6, 2, 4, 4]\n",
+      "New Histogram normalized\n",
+      "[0.08, 0.0, 0.28, 0.0, 0.24, 0.08, 0.16, 0.16]\n",
+      "New Cumsum Histogram normalized\n",
+      "[0.08, 0.08, 0.36, 0.36, 0.6, 0.68, 0.84, 1.0]\n"
+     ]
+    }
+   ],
+   "source": [
+    "  I_cau1 = [\n",
+    "    5 0 0 1 2\n",
+    "    2 1 5 1 2\n",
+    "    7 1 5 1 2\n",
+    "    7 4 5 4 3\n",
+    "    7 1 6 1 3\n",
+    "  ]\n",
+    "\n",
+    "  hist = fit(Histogram, reshape(I_cau1, (length(I_cau1))), nbins=8).weights\n",
+    "  normalized_hist = hist ./ sum(hist)\n",
+    "  cumsum_normalized_hist = cumsum(normalized_hist)\n",
+    "\n",
+    "  println(\"Histogram normalized\")\n",
+    "  println(normalized_hist)\n",
+    "  println(\"Cumsum Histogram normalized\")\n",
+    "  println(cumsum_normalized_hist)\n",
+    "\n",
+    "  prefered_hist = fit(Histogram, 0:7, nbins=8).weights\n",
+    "  normalized_prefered_hist = prefered_hist ./ sum(prefered_hist)\n",
+    "  cumsum_normalized_prefered_hist = cumsum(normalized_prefered_hist)\n",
+    "\n",
+    "  println(\"Prefered Histogram\")\n",
+    "  println(normalized_prefered_hist)\n",
+    "  println(\"Cumsum Prefered Histogram\")\n",
+    "  println(cumsum_normalized_prefered_hist)\n",
+    "\n",
+    "  # https://dsp.stackexchange.com/questions/16166/histogram-matching-of-two-images-using-cdf\n",
+    "  out_hist = zeros(8)\n",
+    "  out_color = zeros(8)\n",
+    "\n",
+    "  for i in 1:length(out_color)\n",
+    "    for k in 1:length(cumsum_normalized_prefered_hist)\n",
+    "      if cumsum_normalized_prefered_hist[k] - cumsum_normalized_hist[i] < 0\n",
+    "        continue\n",
+    "      end\n",
+    "      out_hist[i] = cumsum_normalized_prefered_hist[k]\n",
+    "      out_color[i] = k\n",
+    "      break\n",
+    "    end\n",
+    "  end\n",
+    "\n",
+    "  println(\"out hist\")\n",
+    "  println(out_hist)\n",
+    "  println(\"out color\")\n",
+    "  println([i for i=0:7])\n",
+    "  println(out_color)\n",
+    "\n",
+    "  for idx in CartesianIndices(I_cau1)\n",
+    "    newcolor = out_color[I_cau1[idx] + 1]\n",
+    "    I_cau1[idx] = newcolor\n",
+    "  end\n",
+    "\n",
+    "  display(I_cau1)\n",
+    "  println()\n",
+    "  hist = fit(Histogram, reshape(I_cau1, (length(I_cau1))), nbins=8).weights\n",
+    "  normalized_hist = hist ./ sum(hist)\n",
+    "  cumsum_normalized_hist = cumsum(normalized_hist)\n",
+    "\n",
+    "  println(\"New Histogram\")\n",
+    "  println(hist)\n",
+    "  println(\"New Histogram normalized\")\n",
+    "  println(normalized_hist)\n",
+    "  println(\"New Cumsum Histogram normalized\")\n",
+    "  println(cumsum_normalized_hist)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
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+       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 97.2505, 1087.25)\" x=\"97.2505\" y=\"1087.25\">2</text>\n",
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+       "<g clip-path=\"url(#clip8700)\">\n",
+       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 97.2505, 302.216)\" x=\"97.2505\" y=\"302.216\">6</text>\n",
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+       "<polyline clip-path=\"url(#clip8702)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
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+       "<polyline clip-path=\"url(#clip8702)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
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+       "<polyline clip-path=\"url(#clip8702)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
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+       "  \" fill=\"#009af9\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
+       "<polyline clip-path=\"url(#clip8702)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
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+       "  \" fill=\"#009af9\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
+       "<polyline clip-path=\"url(#clip8702)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
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+       "  \" fill=\"#009af9\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
+       "<polyline clip-path=\"url(#clip8702)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
+       "  1748.41,677.231 1748.41,1462.26 1949.23,1462.26 1949.23,677.231 1748.41,677.231 \n",
+       "  \"/>\n",
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+       "<polyline clip-path=\"url(#clip8702)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
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+       "<polyline clip-path=\"url(#clip8700)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
+       "  1958.43,251.724 2249.26,251.724 2249.26,130.764 1958.43,130.764 1958.43,251.724 \n",
+       "  \"/>\n",
+       "<polygon clip-path=\"url(#clip8700)\" points=\"\n",
+       "1982.43,215.436 2126.43,215.436 2126.43,167.052 1982.43,167.052 1982.43,215.436 \n",
+       "  \" fill=\"#009af9\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
+       "<polyline clip-path=\"url(#clip8700)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
+       "  1982.43,215.436 2126.43,215.436 2126.43,167.052 1982.43,167.052 1982.43,215.436 \n",
+       "  \"/>\n",
+       "<g clip-path=\"url(#clip8700)\">\n",
+       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2150.43, 208.744)\" x=\"2150.43\" y=\"208.744\">y1</text>\n",
+       "</g>\n",
+       "</svg>\n"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# h = fit(Histogram, reshape(I_cau1, (length(I_cau1))), nbins=8)\n",
+    "bar(0:length(hist)-1, hist)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
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+       "<g clip-path=\"url(#clip9100)\">\n",
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+       "<g clip-path=\"url(#clip9100)\">\n",
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+       "<polyline clip-path=\"url(#clip9102)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
+       "  1765.83,88.4582 1765.83,1462.26 1960.54,1462.26 1960.54,88.4582 1765.83,88.4582 \n",
+       "  \"/>\n",
+       "<polygon clip-path=\"url(#clip9102)\" points=\"\n",
+       "2009.22,88.4582 2009.22,1462.26 2203.94,1462.26 2203.94,88.4582 2009.22,88.4582 2009.22,88.4582 \n",
+       "  \" fill=\"#009af9\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
+       "<polyline clip-path=\"url(#clip9102)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
+       "  2009.22,88.4582 2009.22,1462.26 2203.94,1462.26 2203.94,88.4582 2009.22,88.4582 \n",
+       "  \"/>\n",
+       "<polygon clip-path=\"url(#clip9100)\" points=\"\n",
+       "1958.43,251.724 2249.26,251.724 2249.26,130.764 1958.43,130.764 \n",
+       "  \" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
+       "<polyline clip-path=\"url(#clip9100)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
+       "  1958.43,251.724 2249.26,251.724 2249.26,130.764 1958.43,130.764 1958.43,251.724 \n",
+       "  \"/>\n",
+       "<polygon clip-path=\"url(#clip9100)\" points=\"\n",
+       "1982.43,215.436 2126.43,215.436 2126.43,167.052 1982.43,167.052 1982.43,215.436 \n",
+       "  \" fill=\"#009af9\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
+       "<polyline clip-path=\"url(#clip9100)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
+       "  1982.43,215.436 2126.43,215.436 2126.43,167.052 1982.43,167.052 1982.43,215.436 \n",
+       "  \"/>\n",
+       "<g clip-path=\"url(#clip9100)\">\n",
+       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2150.43, 208.744)\" x=\"2150.43\" y=\"208.744\">y1</text>\n",
+       "</g>\n",
+       "</svg>\n"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "bar(0:length(prefered_hist)-1, prefered_hist)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Julia 1.2.0-DEV",
+   "language": "julia",
+   "name": "julia-1.2"
+  },
+  "language_info": {
+   "file_extension": ".jl",
+   "mimetype": "application/julia",
+   "name": "julia",
+   "version": "1.2.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

julia_notebook/dct.ipynb

@@ -0,0 +1,150 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "using FFTW"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "dct (generic function with 1 method)"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "function dct(f)\n",
+    "  function a(u, N)\n",
+    "    if u == 0\n",
+    "      sqrt(1/N)\n",
+    "    else\n",
+    "      sqrt(2/N)\n",
+    "    end\n",
+    "  end\n",
+    "\n",
+    "  if ndims(f) == 1\n",
+    "    N = length(f)\n",
+    "    [a(u, N) * sum([x * cos(pi * u * (2i - 1)/ (2N)) for (i, x) in enumerate(f)]) for u=0:N - 1]\n",
+    "  elseif ndims(f) == 2\n",
+    "    N, M = size(f)\n",
+    "    [a(u, N) * a(v, M) * sum([f[x+1, y+1] * cos(pi * u * (2x + 1)/ (2N)) * cos(pi * v * (2y + 1) / (2M)) for x=0:N-1, y=0:M-1]) for u=0:N - 1, v=0:M-1]\n",
+    "  else\n",
+    "    error(\"What the hell man?\")\n",
+    "  end\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "8-element Array{Float64,1}:\n",
+       " 12.727922061357857     \n",
+       " -6.4423230227051365    \n",
+       " -1.3322676295501878e-15\n",
+       " -0.6734548009039396    \n",
+       "  0.0                   \n",
+       " -0.20090290373599107   \n",
+       " -2.6645352591003757e-15\n",
+       " -0.05070232275964859   "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "8-element Array{Float64,1}:\n",
+       " 12.727922061357857   \n",
+       " -6.442323022705137   \n",
+       "  0.0                 \n",
+       " -0.6734548009039407  \n",
+       "  0.0                 \n",
+       " -0.20090290373599654 \n",
+       "  0.0                 \n",
+       " -0.050702322759645924"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "8×8 Array{Float64,2}:\n",
+       "  260.0          -18.2216       -3.51701e-14  …  -4.89869e-14  -0.143408   \n",
+       " -145.773         -3.55271e-15  -1.77636e-15      3.01981e-14   1.02141e-14\n",
+       "   -4.14504e-14    5.32907e-15   0.0              0.0           1.77636e-15\n",
+       "  -15.2385        -3.55271e-15   3.55271e-15     -7.10543e-15   0.0        \n",
+       "    1.6329e-14    -1.77636e-15   3.55271e-15     -8.88178e-16   9.76996e-15\n",
+       "   -4.54591       -5.32907e-15   0.0          …   0.0           5.9952e-15 \n",
+       "   -5.33831e-14    1.15463e-14  -6.21725e-15     -4.44089e-16  -1.33227e-15\n",
+       "   -1.14726       -2.66454e-15  -4.44089e-15     -2.22045e-15   2.66454e-15"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "8×8 Array{Float64,2}:\n",
+       "  260.0      -18.2216  0.0  -1.90482  0.0  -0.568239  0.0  -0.143408\n",
+       " -145.773      0.0     0.0   0.0      0.0   0.0       0.0   0.0     \n",
+       "    0.0        0.0     0.0   0.0      0.0   0.0       0.0   0.0     \n",
+       "  -15.2385     0.0     0.0   0.0      0.0   0.0       0.0   0.0     \n",
+       "    0.0        0.0     0.0   0.0      0.0   0.0       0.0   0.0     \n",
+       "   -4.54591    0.0     0.0   0.0      0.0   0.0       0.0   0.0     \n",
+       "    0.0        0.0     0.0   0.0      0.0   0.0       0.0   0.0     \n",
+       "   -1.14726    0.0     0.0   0.0      0.0   0.0       0.0   0.0     "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "display(dct(1:8))\n",
+    "\n",
+    "display(FFTW.dct(1:8))\n",
+    "\n",
+    "display(dct([(i-1)*8 + j for i=1:8, j=1:8]))\n",
+    "\n",
+    "display(FFTW.dct([(i-1)*8 + j for i=1:8,j=1:8]))\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Julia 1.2.0-DEV",
+   "language": "julia",
+   "name": "julia-1.2"
+  },
+  "language_info": {
+   "file_extension": ".jl",
+   "mimetype": "application/julia",
+   "name": "julia",
+   "version": "1.2.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

julia_notebook/dft_fft.ipynb

@@ -0,0 +1,211 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "using FFTW"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "dft (generic function with 1 method)"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "function dft(f)\n",
+    "    if ndims(f) == 1\n",
+    "        M = length(f)\n",
+    "        [sum([x * exp(-2im*pi*u * (idx - 1) / M ) for (idx, x) in enumerate(f)]) for u=0:M-1]\n",
+    "    elseif ndims(f) == 2\n",
+    "        M, N = size(f)\n",
+    "        [sum([f[x+1, y+1] * exp(-2im*pi*(u*x/M + v*y/M)) for x=0:M-1, y=0:N-1]) for u=0:M-1, v=0:N-1]\n",
+    "    else\n",
+    "        error(\"Wrong dimension\")\n",
+    "    end\n",
+    "end        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "fft2d (generic function with 1 method)"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "function fft1d(array)\n",
+    "  #= https://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm\n",
+    "  #\n",
+    "  # Xk = Ek + e^(-2pi*i/N * k) * Ok\n",
+    "  #\n",
+    "  # Ek = Event DFT\n",
+    "  # Ok = Odd DFT\n",
+    "  #\n",
+    "  =#\n",
+    "  N = size(array)[1]\n",
+    "  if N == 1\n",
+    "    return array\n",
+    "  elseif N % 2 != 0\n",
+    "    error(\"Wrong dimension\")\n",
+    "  end\n",
+    "\n",
+    "  # people count from zero while julia counts from 1\n",
+    "  # either way, it should be the same name\n",
+    "  even = fft1d(array[1:2:end])\n",
+    "  odd = fft1d(array[2:2:end])\n",
+    "  w = exp.(-2im * pi / N * [i for i=0:N/2-1])\n",
+    "  half1 = even .+ (odd .* w)\n",
+    "  half2 = even .- (odd .* w)\n",
+    "  vcat(half1,half2)\n",
+    "end\n",
+    "\n",
+    "function fft2d(matrix)\n",
+    "  if ndims(matrix) != 2\n",
+    "    error(\"I dont handle other than 2 dimension matrix\")\n",
+    "  end\n",
+    "  matrix_fft1 = hcat(fft1d.(eachrow(matrix))...)\n",
+    "  hcat(fft1d.(eachrow(matrix_fft1))...)\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "8-element Array{Complex{Float64},1}:\n",
+       " 36.0 + 0.0im               \n",
+       " -4.0 + 9.65685424949238im  \n",
+       " -4.0 + 4.0im               \n",
+       " -4.0 + 1.6568542494923806im\n",
+       " -4.0 + 0.0im               \n",
+       " -4.0 - 1.6568542494923806im\n",
+       " -4.0 - 4.0im               \n",
+       " -4.0 - 9.65685424949238im  "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "8-element Array{Complex{Float64},1}:\n",
+       "                36.0 - 0.0im               \n",
+       "                -4.0 + 9.65685424949238im  \n",
+       "                -4.0 + 4.0im               \n",
+       "                -4.0 + 1.6568542494923797im\n",
+       "                -4.0 + 0.0im               \n",
+       " -3.9999999999999996 - 1.6568542494923797im\n",
+       " -3.9999999999999996 - 4.0im               \n",
+       " -3.9999999999999987 - 9.65685424949238im  "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "8-element Array{Complex{Float64},1}:\n",
+       "                36.0 - 0.0im                 \n",
+       "  -4.000000000000003 + 9.65685424949238im    \n",
+       "  -4.000000000000002 + 3.9999999999999982im  \n",
+       "                -4.0 + 1.656854249492386im   \n",
+       "                -4.0 - 3.91886975727153e-15im\n",
+       " -4.0000000000000115 - 1.6568542494923912im  \n",
+       "  -4.000000000000018 - 4.000000000000005im   \n",
+       " -3.9999999999999725 - 9.656854249492369im   "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "2×8 Array{Complex{Float64},2}:\n",
+       " 72.0+0.0im  -8.0+19.3137im  -8.0+8.0im  …  -8.0-8.0im  -8.0-19.3137im\n",
+       "  0.0+0.0im   0.0+0.0im       0.0+0.0im      0.0+0.0im   0.0+0.0im    "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "2×8 Array{Complex{Float64},2}:\n",
+       " 72.0-0.0im  -8.0+19.3137im  -8.0+8.0im  …  -8.0-8.0im  -8.0-19.3137im\n",
+       "  0.0+0.0im   0.0+0.0im       0.0+0.0im      0.0+0.0im   0.0+0.0im    "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "2×8 Array{Complex{Float64},2}:\n",
+       " 72.0-0.0im          -8.0-7.83774e-15im  …  -8.0-3.39081e-13im\n",
+       "  0.0-4.40873e-15im   0.0+4.89859e-16im      0.0-1.87804e-13im"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "display(fft(1:8))\n",
+    "display(fft1d(1:8))\n",
+    "display(dft(1:8))\n",
+    "\n",
+    "\n",
+    "display(fft([[1:8...] [1:8...]]'))\n",
+    "display(fft2d([[1:8...] [1:8...]]'))\n",
+    "display(dft([[1:8...] [1:8...]]'))\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Julia 1.2.0-DEV",
+   "language": "julia",
+   "name": "julia-1.2"
+  },
+  "language_info": {
+   "file_extension": ".jl",
+   "mimetype": "application/julia",
+   "name": "julia",
+   "version": "1.2.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

julia_notebook/jpeg.ipynb

@@ -0,0 +1,409 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "using Images\n",
+    "using FFTW\n",
+    "using Formatting"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "8×8 Array{Int64,2}:\n",
+       "  1   2   6   7  15  16  28  29\n",
+       "  3   5   8  14  17  27  30  43\n",
+       "  4   9  13  18  26  31  42  44\n",
+       " 10  12  19  25  32  41  45  54\n",
+       " 11  20  24  33  40  46  53  55\n",
+       " 21  23  34  39  47  52  56  61\n",
+       " 22  35  38  48  51  57  60  62\n",
+       " 36  37  49  50  58  59  63  64"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "LUMINANCE_QUANTIZATION_TABLE = [\n",
+    "    16  11  10  16  24   40   51   61   \n",
+    "    12  12  14  19  26   58   60   55   \n",
+    "    14  13  16  24  40   57   69   56   \n",
+    "    14  17  22  29  51   87   80   62   \n",
+    "    18  22  37  56  68   109  103  77   \n",
+    "    24  35  55  64  81   104  113  92   \n",
+    "    49  64  78  87  103  121  120  101  \n",
+    "    72  92  95  98  112  100  103  99   \n",
+    "  ]\n",
+    "\n",
+    "ZIGZAG = [\n",
+    "    0   1   5   6  14  15  27  28\n",
+    "    2   4   7  13  16  26  29  42\n",
+    "    3   8  12  17  25  30  41  43\n",
+    "    9  11  18  24  31  40  44  53\n",
+    "    10  19  23  32  39  45  52  54\n",
+    "    20  22  33  38  46  51  55  60\n",
+    "    21  34  37  47  50  56  59  61\n",
+    "    35  36  48  49  57  58  62  63\n",
+    "   ] .+ 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "to_zigzag (generic function with 1 method)"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "function to_zigzag(block)\n",
+    "  out_block = zeros(eltype(block), size(ZIGZAG))\n",
+    "  for idx in CartesianIndices(ZIGZAG)\n",
+    "    out_block[ZIGZAG[idx]] = block[idx]\n",
+    "    # display(out_block)\n",
+    "  end\n",
+    "  reshape(out_block, (1,64))\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "720×1280 Array{Float32,2}:\n",
+       " 39.2166  39.4639  39.4639  39.0577  …  37.4843  37.4843  37.4843  37.4843\n",
+       " 39.4639  39.4639  39.0577  39.0577     37.4843  37.4843  37.4843  37.4843\n",
+       " 39.4639  39.0577  39.0577  39.0577     37.4843  37.4843  37.4843  37.4843\n",
+       " 39.0577  39.0577  39.0577  39.9165     38.0348  37.4843  37.4843  37.4843\n",
+       " 39.0577  39.9165  39.9165  39.9165     38.0348  37.176   37.4843  37.4843\n",
+       " 39.9165  39.9165  39.9165  40.1639  …  38.0348  38.0348  37.4843  37.4843\n",
+       " 39.9165  39.9165  39.9165  40.1639     38.0348  38.0348  37.4843  37.4843\n",
+       " 39.9165  39.9165  39.9165  40.1639     38.1327  38.0348  38.3432  37.4843\n",
+       " 39.4639  39.4639  39.9165  40.1639     39.4493  38.3432  38.0348  38.5484\n",
+       " 39.4639  39.4639  39.0577  40.1639     39.4493  38.3432  38.0348  38.5484\n",
+       " 39.4639  39.4639  39.0577  40.1639  …  39.4493  38.5905  38.0348  38.0348\n",
+       " 39.4639  39.0577  39.0577  40.1639     39.1925  39.4493  38.5905  38.0348\n",
+       " 39.0577  39.0577  39.0577  40.1639     39.1925  39.4493  38.5905  38.5905\n",
+       "  ⋮                                  ⋱                                    \n",
+       " 30.5854  31.1969  31.7105  32.261      37.663   37.663   37.663   37.663 \n",
+       " 31.3927  31.3927  31.4021  31.3927     38.2135  38.2135  38.2135  38.4608\n",
+       " 31.64    31.64    31.64    30.5244  …  38.4608  38.4608  39.3196  39.3196\n",
+       " 31.3738  30.515   30.515   29.6562     38.4608  38.4608  39.3196  39.3196\n",
+       " 28.751   30.7666  30.7202  27.99       39.3196  39.3196  39.3196  39.3196\n",
+       " 29.049   31.4253  28.8394  30.0572     38.4608  38.4608  38.4608  38.4608\n",
+       " 29.6141  29.3899  26.2063  32.4233     38.2135  38.2135  38.2135  38.2135\n",
+       " 29.7077  29.1984  33.8936  25.0958  …  37.663   37.663   37.663   37.663 \n",
+       " 28.7364  32.2369  29.0447  29.6003     37.663   37.663   37.663   37.663 \n",
+       " 32.5504  24.4422  29.8614  31.7749     37.663   37.663   37.663   37.663 \n",
+       " 29.876   31.5507  29.8468  28.1386     37.3546  37.3546  37.3546  37.3546\n",
+       " 31.5645  30.7108  31.397   29.6708     38.2135  38.2135  38.2135  37.3546"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "8×8 Array{Float32,2}:\n",
+       " 55.4277  55.736   54.8772  54.8772  55.736   55.736   55.736   55.736 \n",
+       " 56.2866  56.2866  57.4537  57.4537  56.5949  55.736   55.736   55.736 \n",
+       " 57.9948  57.9948  57.1359  56.0813  55.2225  55.2225  55.736   56.5949\n",
+       " 58.2421  58.2421  58.2421  58.2421  58.2421  58.0463  56.9401  56.9401\n",
+       " 57.3833  58.4894  61.0659  62.7836  63.6424  61.6774  57.7989  55.2225\n",
+       " 58.4894  58.4894  58.9326  60.6502  61.5091  61.0659  58.2421  56.0813\n",
+       " 61.0659  59.6935  59.7914  59.1799  58.9326  58.0832  58.2421  57.7989\n",
+       " 61.0659  62.27    64.0855  64.0246  62.3679  59.8009  58.2421  56.9401"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "8×8 Array{Float32,2}:\n",
+       " -71.5723  -71.264   -72.1228  -72.1228  …  -71.264   -71.264   -71.264 \n",
+       " -70.7134  -70.7134  -69.5463  -69.5463     -71.264   -71.264   -71.264 \n",
+       " -69.0052  -69.0052  -69.8641  -70.9187     -71.7775  -71.264   -70.4051\n",
+       " -68.7579  -68.7579  -68.7579  -68.7579     -68.9537  -70.0599  -70.0599\n",
+       " -69.6167  -68.5106  -65.9341  -64.2164     -65.3226  -69.2011  -71.7775\n",
+       " -68.5106  -68.5106  -68.0674  -66.3498  …  -65.9341  -68.7579  -70.9187\n",
+       " -65.9341  -67.3065  -67.2086  -67.8201     -68.9168  -68.7579  -69.2011\n",
+       " -65.9341  -64.73    -62.9145  -62.9754     -67.1991  -68.7579  -70.0599"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "8×8 Array{Float32,2}:\n",
+       " -550.578        4.7784      …   0.00653681   0.205445    0.212533 \n",
+       "  -13.5756      -2.92463        -0.472033    -0.130214   -0.218505 \n",
+       "   -1.48771      1.21404         0.279535    -0.391432    0.330444 \n",
+       "   -0.673342    -2.97597        -0.222817    -0.0539551  -0.0560064\n",
+       "    3.04324      0.102968       -0.474424    -0.0202312   0.0131407\n",
+       "   -3.61937     -0.509858    …  -0.253103    -0.123185   -0.0314786\n",
+       "   -0.353786     0.00731296     -0.460769    -0.278703   -0.466107 \n",
+       "   -0.00664318   0.52792        -0.0775939   -0.022749    0.307393 "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "8×8 Array{Int32,2}:\n",
+       " -34  0  -1  0  0  0  0  0\n",
+       "  -1  0   0  0  0  0  0  0\n",
+       "   0  0   0  0  0  0  0  0\n",
+       "   0  0   0  0  0  0  0  0\n",
+       "   0  0   0  0  0  0  0  0\n",
+       "   0  0   0  0  0  0  0  0\n",
+       "   0  0   0  0  0  0  0  0\n",
+       "   0  0   0  0  0  0  0  0"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "1×64 Array{Int32,2}:\n",
+       " -34  0  -1  0  0  -1  0  0  0  0  0  …  0  0  0  0  0  0  0  0  0  0  0  0"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "14400-element Array{Any,1}:\n",
+       " -44\n",
+       " -43\n",
+       " -43\n",
+       " -42\n",
+       " -42\n",
+       " -42\n",
+       " -41\n",
+       " -41\n",
+       " -41\n",
+       " -41\n",
+       " -40\n",
+       " -40\n",
+       " -39\n",
+       "   ⋮\n",
+       " -42\n",
+       " -41\n",
+       " -41\n",
+       " -41\n",
+       " -41\n",
+       " -42\n",
+       " -43\n",
+       " -43\n",
+       " -44\n",
+       " -44\n",
+       " -44\n",
+       " -45"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "14400-element Array{Any,1}:\n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " ⋮                                                                    \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[-1, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[1, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \n",
+       " Int32[0, 0, 0, 0, 0, 0, 0, 0, 0, 0  …  0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "720×1280 Array{Float32,2}:\n",
+       " 141.368  141.226  141.226  141.956  …  143.855  143.855  143.855  143.855\n",
+       " 141.226  141.226  141.956  141.956     143.855  143.855  143.855  143.855\n",
+       " 141.226  141.956  141.956  141.956     143.855  143.855  143.855  143.855\n",
+       " 141.956  141.956  141.956  141.956     145.025  143.855  143.855  143.855\n",
+       " 141.956  141.956  141.956  141.956     145.025  145.025  143.855  143.855\n",
+       " 141.956  141.956  141.956  141.813  …  145.025  145.025  143.855  143.855\n",
+       " 141.956  141.956  141.956  141.813     145.025  145.025  143.855  143.855\n",
+       " 141.956  141.956  141.956  141.813     145.464  145.025  143.855  143.855\n",
+       " 141.226  141.226  141.956  141.813     143.713  143.855  145.025  144.728\n",
+       " 141.226  141.226  141.956  141.813     143.713  143.855  145.025  144.728\n",
+       " 141.226  141.226  141.956  141.813  …  143.713  143.713  145.025  145.025\n",
+       " 141.226  141.956  141.956  141.813     143.861  143.713  143.713  145.025\n",
+       " 141.956  141.956  141.956  141.813     143.861  143.713  143.713  143.713\n",
+       "   ⋮                                 ⋱                                    \n",
+       " 130.487  130.63   130.333  131.503     138.299  138.299  138.299  138.299\n",
+       " 131.508  131.508  131.503  131.508     139.469  139.469  139.469  139.326\n",
+       " 131.366  131.366  131.366  131.514  …  139.326  139.326  139.326  139.326\n",
+       " 131.519  131.519  131.519  131.519     139.326  139.326  139.326  139.326\n",
+       " 130.059  133.853  132.392  130.498     139.326  139.326  139.326  139.326\n",
+       " 133.853  130.498  130.503  133.271     139.326  139.326  139.326  139.326\n",
+       " 132.535  131.673  134.006  134.879     139.469  139.469  139.469  139.469\n",
+       " 130.498  133.271  135.022  131.673  …  138.299  138.299  138.299  138.299\n",
+       " 132.546  133.995  131.376  130.064     138.299  138.299  138.299  138.299\n",
+       " 130.344  132.546  132.392  133.271     138.299  138.299  138.299  138.299\n",
+       " 129.905  132.409  134.879  134.874     139.469  139.469  139.469  139.469\n",
+       " 134.879  132.398  130.514  129.032     139.469  139.469  139.469  139.469"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "720×1280 Array{Float32,2}:\n",
+       " 115.448  114.641  114.641  114.938  …  115.459  115.459  115.459  115.459\n",
+       " 114.641  114.641  114.938  114.938     115.459  115.459  115.459  115.459\n",
+       " 114.641  114.938  114.938  114.938     115.459  115.459  115.459  115.459\n",
+       " 114.938  114.938  114.938  114.938     115.684  115.459  115.459  115.459\n",
+       " 114.938  114.938  114.938  114.938     115.684  115.684  115.459  115.459\n",
+       " 114.938  114.938  114.938  114.131  …  115.684  115.684  115.459  115.459\n",
+       " 114.938  114.938  114.938  114.131     115.684  115.684  115.459  115.459\n",
+       " 114.938  114.938  114.938  114.131     115.612  115.684  115.459  115.459\n",
+       " 114.641  114.641  114.938  114.131     114.652  115.459  115.684  116.562\n",
+       " 114.641  114.641  114.938  114.131     114.652  115.459  115.684  116.562\n",
+       " 114.641  114.641  114.938  114.131  …  114.652  114.652  115.684  115.684\n",
+       " 114.641  114.938  114.938  114.131     114.213  114.652  114.652  115.684\n",
+       " 114.938  114.938  114.938  114.131     114.213  114.652  114.652  114.652\n",
+       "   ⋮                                 ⋱                                    \n",
+       " 128.011  128.818  129.696  129.921     114.702  114.702  114.702  114.702\n",
+       " 128.675  128.675  129.921  128.675     114.927  114.927  114.927  114.12 \n",
+       " 127.868  127.868  127.868  127.429  …  114.12   114.12   114.12   114.12 \n",
+       " 126.182  126.182  126.182  126.182     114.12   114.12   114.12   114.12 \n",
+       " 125.59   127.878  127.286  125.518     114.12   114.12   114.12   114.12 \n",
+       " 127.878  125.518  124.272  127.143     114.12   114.12   114.12   114.12 \n",
+       " 128.093  124.497  126.193  127.296     114.927  114.927  114.927  114.927\n",
+       " 125.518  127.143  128.103  124.497  …  114.702  114.702  114.702  114.702\n",
+       " 125.6    128.685  125.375  124.343     114.702  114.702  114.702  114.702\n",
+       " 127.204  125.6    127.286  127.143     114.702  114.702  114.702  114.702\n",
+       " 127.275  123.547  127.296  128.543     114.927  114.927  114.927  114.927\n",
+       " 127.296  126.04   121.78   126.172     114.927  114.927  114.927  114.927"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "img = load(\"../images/f124074.jpg\")\n",
+    "img_ycbcr = channelview(YCbCr.(img))\n",
+    "\n",
+    "for c in 1:3\n",
+    "    channel = img_ycbcr[c,:,:]\n",
+    "    row, col = size(channel)\n",
+    "\n",
+    "    display(channel)\n",
+    "    \n",
+    "    DC = []\n",
+    "    AC = []\n",
+    "\n",
+    "    for i in 1:8:row\n",
+    "      for j in 1:8:col\n",
+    "        block = channel[i:i+7, j:j+7]\n",
+    "\n",
+    "        block_shifted = block .- 127\n",
+    "        block_dct = FFTW.dct(block_shifted)\n",
+    "\n",
+    "        block_quantization = round.(Int32, block_dct ./ LUMINANCE_QUANTIZATION_TABLE)\n",
+    "        # block_quantization = block_dct ./ LUMINANCE_QUANTIZATION_TABLE\n",
+    "        block_zigzag = to_zigzag(block_quantization)\n",
+    "\n",
+    "        if c == 1 && i == 1 + 8*10 && j == 1 + 8*3\n",
+    "          display(block)\n",
+    "          display(block_shifted)\n",
+    "          display(block_dct)\n",
+    "          display(block_quantization)\n",
+    "          display(block_zigzag)\n",
+    "        end\n",
+    "\n",
+    "        # block_zigzag = collect(block_zigzag)\n",
+    "        push!(DC, block_zigzag[1])\n",
+    "        push!(AC, block_zigzag[2:end])\n",
+    "      end\n",
+    "    end\n",
+    "\n",
+    "    if c == 1\n",
+    "        display(DC)\n",
+    "        display(AC)\n",
+    "    end\n",
+    "end\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Julia 1.2.0-DEV",
+   "language": "julia",
+   "name": "julia-1.2"
+  },
+  "language_info": {
+   "file_extension": ".jl",
+   "mimetype": "application/julia",
+   "name": "julia",
+   "version": "1.2.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

julia_scripts/1611617_NguyenAnhKhoa.jl

@@ -0,0 +1,285 @@
+using Images
+using Formatting
+using StatsBase
+using FFTW
+
+function genMatrix(what, params...)
+  params = map(x->parse(Float32, x), params)
+  M = zeros(Float32, (3,3))
+  M[3, 3] = 1
+
+  if what == "scale"
+    if length(params) < 2
+      error("Scale requires two parameter (x, y)")
+    end
+    x, y = params
+    printfmt("Scale with x = {}; y = {}\n", x, y)
+    M[1, 1] = x
+    M[2, 2] = y
+  elseif what == "translate"
+    if length(params) < 2
+      error("Translate requires two parameter (dx, dy)")
+    end
+    dx, dy = params
+    M[1, 1] = 1
+    M[2, 2] = 1
+    M[1, 3] = dx
+    M[2, 3] = dy
+  elseif what == "rotate"
+    if length(params) < 1
+      error("Rotate requires one parameter (theta, isRadian: true)")
+    end
+    theta = params[1]
+    isRadian = 1
+    if length(params) >= 2
+      isRadian = params[2]
+    end
+
+    if isRadian == 1
+      M[1, 1] =  cos(theta)
+      M[1, 2] =  -sin(theta)
+      M[2, 1] =  sin(theta)
+      M[2, 2] =  cos(theta)
+    else
+      M[1, 1] =  cosd(theta)
+      M[1, 2] =  -sind(theta)
+      M[2, 1] =  sind(theta)
+      M[2, 2] =  cosd(theta)
+    end
+  elseif what == "shear"
+    if length(params) < 4
+      error("Rotate requires four parameter (a, b, c, d)")
+    end
+    a,b,c,d = params
+    M[1, 1] = a
+    M[1, 2] = b
+    M[2, 1] = c
+    M[2, 2] = d
+  else
+    error(printfmt("Matrix of {} is unknown\n", what))
+  end
+  M
+end
+
+function conv(in, kernel)
+
+  row, col = size(in)
+  krow, kcol = size(kernel)
+  rowPad, colPad = round(Int32, krow/2, RoundDown),round(Int32, kcol/2, RoundDown)
+
+  # feature_maps = zeros(eltype(in), (row + rowPad * 2, col + colPad * 2))
+  feature_maps = [
+    5 5 0 0 1 2 2 
+    5 5 0 0 1 2 2 
+    2 2 1 5 1 2 2 
+    7 7 1 5 1 2 2 
+    7 7 4 5 4 3 3 
+    7 7 1 6 1 3 3 
+    7 7 1 6 1 3 3
+  ]
+  out = zeros(eltype(in), size(in))
+
+  colStartIdx = colPad + 1
+  colEndIdx = colPad + col
+  rowStartIdx = rowPad + 1
+  rowEndIdx = rowPad + row
+
+  # setup feature map and kernel
+  feature_maps[rowStartIdx:rowEndIdx, colStartIdx:colEndIdx] = in
+  kernel = rot180(kernel)
+
+  for i in rowStartIdx:rowEndIdx
+    for j in colStartIdx:colEndIdx
+      part = feature_maps[i-rowPad:i-rowPad+krow-1, j-colPad:j-colPad+kcol-1]
+      v = sum(part .* kernel)
+      if (v < 0)
+        v = 0
+      elseif (v > 1)
+        v = 1
+      end
+      out[i-rowPad,j-colPad] = v
+    end
+  end
+  # TODO: normalize output
+  out ./ maximum(out)
+end
+if abspath(PROGRAM_FILE) == @__FILE__
+  I_cau1 = [
+    5 0 0 1 2
+    2 1 5 1 2
+    7 1 5 1 2
+    7 4 5 4 3
+    7 1 6 1 3
+  ]
+
+  sobel_x_kernel = [
+      -1 0 1
+      -2 0 2
+      -1 0 1
+  ]
+  sobel_y_kernel = rotl90(sobel_x_kernel)
+
+  # I_Gx = imfilter(I_cau1, centered(reflect(sobel_x_kernel)), "reflect")
+  # I_Gy = imfilter(I_cau1, centered(reflect(sobel_y_kernel)), "reflect")
+  I_Gx = conv(I_cau1, sobel_x_kernel)
+  I_Gy = conv(I_cau1, sobel_y_kernel)
+  # I_G = round.(Int32, sqrt.((I_Gx .^ 2) .* (I_Gy .^ 2)))
+
+  printfmtln("Vector G(0,0) = ({}, {})", I_Gx[1,1], I_Gy[1,1])
+  printfmtln("Vector G(1,1) = ({}, {})", I_Gx[2,2], I_Gy[2,2])
+  printfmtln("Vector G(0,3) = ({}, {})", I_Gx[1,4], I_Gy[1,4])
+
+  hist = fit(Histogram, reshape(I_cau1, (length(I_cau1))), nbins=8).weights
+  normalized_hist = hist ./ sum(hist)
+  cumsum_normalized_hist = cumsum(normalized_hist)
+
+  println("Histogram normalized")
+  println(normalized_hist)
+  println("Cumsum Histogram normalized")
+  println(cumsum_normalized_hist)
+
+  prefered_hist = fit(Histogram, 0:7, nbins=8).weights
+  normalized_prefered_hist = prefered_hist ./ sum(prefered_hist)
+  cumsum_normalized_prefered_hist = cumsum(normalized_prefered_hist)
+
+  println("Prefered Histogram")
+  println(normalized_prefered_hist)
+  println("Cumsum Prefered Histogram")
+  println(cumsum_normalized_prefered_hist)
+
+  # https://dsp.stackexchange.com/questions/16166/histogram-matching-of-two-images-using-cdf
+  out_hist = zeros(8)
+  out_color = zeros(8)
+
+  for i in 1:length(out_color)
+    for k in 1:length(cumsum_normalized_prefered_hist)
+      if cumsum_normalized_prefered_hist[k] - cumsum_normalized_hist[i] < 0
+        continue
+      end
+      out_hist[i] = cumsum_normalized_prefered_hist[k]
+      out_color[i] = k
+      break
+    end
+  end
+
+  println("out hist")
+  println(out_hist)
+  println("out color")
+  println([i for i=0:7])
+  println(out_color)
+
+  for idx in CartesianIndices(I_cau1)
+    newcolor = out_color[I_cau1[idx] + 1]
+    I_cau1[idx] = newcolor
+  end
+
+  display(I_cau1)
+  println()
+  hist = fit(Histogram, reshape(I_cau1, (length(I_cau1))), nbins=8).weights
+  normalized_hist = hist ./ sum(hist)
+  cumsum_normalized_hist = cumsum(normalized_hist)
+
+  println("New Histogram normalized")
+  println(normalized_hist)
+  println("New Cumsum Histogram normalized")
+  println(cumsum_normalized_hist)
+
+  println("==============================")
+
+  fx = [1 3]
+  N = length(fx)
+  dft_fx = [exp(-2im*pi*u*x / N) for u=0:N-1, x=0:N-1]
+  fx_dft = dft_fx * fx'
+
+  println("Ma tran he co dft")
+  display(dft_fx)
+  println()
+  println("Bien doi fft cua fx = [1, 3]")
+  println(fx_dft)
+
+  println("==============================")
+
+  function alpha(u, N)
+    if u == 0
+      sqrt(1/N)
+    else
+      sqrt(2/N)
+    end
+  end
+
+  fx = [1 0 1 0] # pad with 0
+  N = 4
+  dct_fx = [alpha(u, N) * cos((2*x + 1) * u * pi / (2N)) for u=0:N-1, x=0:N - 1]
+  fx_dct = dct_fx * fx'
+
+  println("Ma tran he co dct voi N = 4 tren fx")
+  display(dct_fx)
+  println()
+  println("Bien doi dct 4 diem cua fx = [1, 0, 1]")
+  println(fx_dct)
+
+  println("==============================")
+
+  M_move_00 = genMatrix("translate", "-3", "-3")
+  M_rotate_25 = genMatrix("rotate", "45", "0")
+  M_move_33 = genMatrix("translate", "3", "3")
+
+  M = M_move_33 * M_rotate_25 * M_move_00
+
+  println("Ma tran M de xoay hinh xung quanh (3,3)")
+  display(M)
+  println()
+
+  new_idx = round.(Int32, inv(M) * [2 3 1]')
+  printfmtln("Toa do Io(2, 3) co gia tri bang voi I({}, {})", new_idx[1:2]...)
+
+end
+
+
+# SAMPLE OUTPUT
+#=
+
+Vector G(0,0) = (0.0, 0.0)
+Vector G(1,1) = (1.0, 1.0)
+Vector G(0,3) = (1.0, 0.0)
+Histogram
+Dict{Int64,Float64} with 8 entries:
+  0 => 0.08
+  4 => 0.08
+  7 => 0.12
+  2 => 0.16
+  3 => 0.08
+  5 => 0.16
+  6 => 0.04
+  1 => 0.28
+==============================
+Ma tran he co dft
+2×2 Array{Complex{Float64},2}:
+ 1.0-0.0im   1.0-0.0im        
+ 1.0-0.0im  -1.0-1.22465e-16im
+Bien doi fft cua fx = [1, 3]
+2×1 Array{Complex{Float64},2}:
+  4.0 + 0.0im                   
+ -2.0 - 3.6739403974420594e-16im
+==============================
+Ma tran he co dct voi N = 4 tren fx
+4×3 Array{Float64,2}:
+ 0.5        0.5        0.5     
+ 0.653281   0.270598  -0.270598
+ 0.5       -0.5       -0.5     
+ 0.270598  -0.653281   0.653281
+Bien doi dct 4 diem cua fx = [1, 0, 1]
+4×1 Array{Float64,2}:
+ 1.0               
+ 0.3826834323650898
+ 0.0               
+ 0.9238795325112867
+==============================
+Ma tran M de xoay hinh xung quanh (3,3)
+3×3 Array{Float32,2}:
+ 0.707107  -0.707107   3.0    
+ 0.707107   0.707107  -1.24264
+ 0.0        0.0        1.0    
+Toa do Io(2, 3) co gia tri bang voi I(2, 4)
+
+=#

julia_scripts/convolution.jl

@@ -0,0 +1,77 @@
+module Convole
+using Formatting
+
+export conv
+
+function padSize(kernelSize)
+  row, col = kernelSize
+  round(Int32, row/2, RoundDown),round(Int32, col/2, RoundDown)
+end
+
+function conv(in, kernel)
+
+  row, col = size(in)
+  krow, kcol = size(kernel)
+  rowPad, colPad = padSize(size(kernel))
+
+  feature_maps = zeros(eltype(in), (row + rowPad * 2, col + colPad * 2))
+  out = zeros(eltype(in), size(in))
+
+  colStartIdx = colPad + 1
+  colEndIdx = colPad + col
+  rowStartIdx = rowPad + 1
+  rowEndIdx = rowPad + row
+
+  # setup feature map and kernel
+  feature_maps[rowStartIdx:rowEndIdx, colStartIdx:colEndIdx] = in
+  kernel = rot180(kernel)
+
+  for i in rowStartIdx:rowEndIdx
+    for j in colStartIdx:colEndIdx
+      part = feature_maps[i-rowPad:i-rowPad+krow-1, j-colPad:j-colPad+kcol-1]
+      v = sum(part .* kernel)
+      if (v < 0)
+        v = 0
+      elseif (v > 1)
+        v = 1
+      end
+      out[i-rowPad,j-colPad] = v
+    end
+  end
+  # TODO: normalize output
+  out ./ maximum(out)
+end
+
+end
+
+if abspath(PROGRAM_FILE) == @__FILE__
+  using .Convole
+  in = [1 2 3; 4 5 6; 7 8 9]
+  kernel = [-1 -2 -1; 0 0 0; 1 2 1]
+  println("Input")
+  display(in)
+  println()
+  println("Kernel")
+  display(kernel)
+  println()
+  println("Output")
+  display(conv(in, kernel))
+  println()
+
+  if (length(ARGS) < 1)
+    return
+  end
+
+  println("image convolution")
+  gaussian_kernel = [
+      1 4 7 4 1
+      4 16 26 16 4
+      7 26 41 26 7
+      4 16 26 16 4
+      1 4 7 4 1
+    ] ./ 273
+  img = load(ARGS[1])
+  img_gray = Gray.(img)
+  img_blur = conv(img_gray, gaussian_kernel)
+  save("img_blur_convole.jpg", img_blur)
+end

julia_scripts/dct.jl

@@ -0,0 +1,33 @@
+using FFTW
+
+function dct(f)
+  function a(u, N)
+    if u == 0
+      sqrt(1/N)
+    else
+      sqrt(2/N)
+    end
+  end
+
+  if ndims(f) == 1
+    N = length(f)
+    [a(u, N) * sum([x * cos(pi * u * (2i - 1)/ (2N)) for (i, x) in enumerate(f)]) for u=0:N - 1]
+  elseif ndims(f) == 2
+    N, M = size(f)
+    [a(u, N) * a(v, M) * sum([f[x+1, y+1] * cos(pi * u * (2x + 1)/ (2N)) * cos(pi * v * (2y + 1) / (2M)) for x=0:N-1, y=0:M-1]) for u=0:N - 1, v=0:M-1]
+  else
+    error("What the hell man?")
+  end
+end
+
+if abspath(PROGRAM_FILE) == @__FILE__
+  display(dct(1:8))
+  println()
+  display(FFTW.dct(1:8))
+  println()
+
+  display(dct([(i-1)*8 + j for i=1:8, j=1:8]))
+  println()
+  display(FFTW.dct([(i-1)*8 + j for i=1:8,j=1:8]))
+  println()
+end

julia_scripts/fft.jl

@@ -0,0 +1,93 @@
+include("showpicture.jl")
+
+using FFTW
+using Images
+using ImageView
+using Plots
+
+using .Showpicture
+
+function dft(f)
+  if ndims(f) == 1
+    M = length(f) 
+    [sum([x * exp(-2im*pi*u * (idx - 1) / M ) for (idx, x) in enumerate(f)]) for u=0:M-1]
+  elseif ndims(f) == 2
+    M, N = size(f)
+    [sum([f[x+1, y+1] * exp(-2im*pi*(u*x/M + v*y/M)) for x=0:M-1, y=0:N-1]) for u=0:M-1, v=0:N-1]
+  else
+    error("Wrong dimension")
+  end
+
+  # mesh = [i * j for i=0:N-1, j=0:N-1]
+  # W = exp.(-2im * pi * mesh / N)
+  # W * f
+
+end
+
+function fft1d(array)
+  #= https://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm
+  #
+  # Xk = Ek + e^(-2pi*i/N * k) * Ok
+  #
+  # Ek = Event DFT
+  # Ok = Odd DFT
+  #
+  =#
+  N = size(array)[1]
+  if N == 1
+    return array
+  elseif N % 2 != 0
+    error("Wrong dimension")
+  end
+
+  # people count from zero while julia counts from 1
+  # either way, it should be the same name
+  even = fft1d(array[1:2:end])
+  odd = fft1d(array[2:2:end])
+  w = exp.(-2im * pi / N * [i for i=0:N/2-1])
+  half1 = even .+ (odd .* w)
+  half2 = even .- (odd .* w)
+  vcat(half1,half2)
+end
+
+function fft2d(matrix)
+  if ndims(matrix) != 2
+    error("I dont handle other than 2 dimension matrix")
+  end
+  matrix_fft1 = hcat(fft1d.(eachrow(matrix))...)
+  hcat(fft1d.(eachrow(matrix_fft1))...)
+end
+
+if abspath(PROGRAM_FILE) == @__FILE__
+  if (length(ARGS) < 1)
+    println("fft library")
+    display(fft(1:8))
+    println()
+    println("fft own implemenation")
+    display(fft1d(1:8))
+    println()
+    println("DFT1D")
+    display(dft(1:8))
+    println()
+
+    println("====================")
+
+    println("fft2d library")
+    display(fft([[1:8...] [1:8...]]'))
+    println()
+    println("fft2d own implemenation")
+    display(fft2d([[1:8...] [1:8...]]'))
+    println()
+    println("DFT2D")
+    display(dft([[1:8...] [1:8...]]'))
+    println()
+  else
+    img = load(ARGS[1])
+    img_gray = Float32.(Gray.(img))
+
+    # img_fft = fft2d(Gray.(img))
+    img_fft = fftshift(fft(img_gray))
+    normalize = log.(abs.(img_fft)) .+ 1
+    showpicture(normalize)
+  end
+end

julia_scripts/filter.jl

@@ -0,0 +1,68 @@
+using FileIO
+using Images, ImageView
+using Colors
+using Formatting
+using FFTW
+
+function idealFilter(r, isLow, threshold)
+  if isLow
+    r .<= threshold
+  else
+    r .> threshold
+  end
+end
+
+function gaussianFilter(r, isLow, threshold)
+  if isLow
+    exp.(-(r.^2) ./ 2*(threshold^2))
+  else
+    1 .- exp.(-(r.^2) ./ 2*(threshold^2))
+  end
+end
+
+function butterworthFilter(r, isLow, threshold, n)
+  if isLow
+    1 ./ (1 .+ (r ./ threshold) .^ (2 * n))
+  else
+    1 ./ (1 .+ (threshold ./ r) .^ (2 * n))
+  end
+end
+
+function laplacianFilter(r, isLow, threshold)
+  -r.^2
+end
+
+function filterFactory(name, shape, isLow, threshold, other)
+  n, m = shape
+  r = sqrt.([i^2 + j^2 for i=-n/2:n/2-1, j=-m/2:m/2-1])
+
+  if name == "Ideal"
+    idealFilter(r, isLow, threshold)
+  elseif name == "Gaussian"
+    gaussianFilter(r, isLow, threshold)
+  elseif name == "Butterworth"
+    butterworthFilter(r, isLow, threshold, other)
+  elseif name == "Laplacian"
+    laplacianFilter(r, isLow, threshold)
+  else
+    error("Filter not found")
+  end
+end
+
+if abspath(PROGRAM_FILE) == @__FILE__
+  imagePath = ARGS[1]
+  filterName = ARGS[2]
+  filterLow = ARGS[3] .== "true"
+  filterThreshold = parse(UInt32, ARGS[4])
+  filterOther = parse(UInt32, ARGS[5])
+
+  img = load(imagePath)
+  img_gray = Float32.(Gray.(img))
+  filter = filterFactory(filterName, size(img_gray), filterLow, filterThreshold, filterOther)
+  #= display(filter) =#
+  #= println() =#
+  img_fft = fftshift(fft(img_gray))
+  out = abs.(real.(ifft(img_fft .* filter)))
+  filename = format("filter_{}_{}_{}_{}.png", imagePath, filterName, filterLow, filterThreshold)
+  save(filename, out)
+end

julia_scripts/geometric.jl

@@ -0,0 +1,173 @@
+using FileIO
+using Images, ImageView
+using Formatting
+
+function roundAround(x, low, high)
+  if x < low
+    low
+  elseif x > high
+    high
+  else
+    round(Int32, x)
+  end
+end
+
+function forwardTransform(M, P)
+  n, m = size(P)
+  out = zeros(eltype(P), n, m)
+  for index in CartesianIndices(P)
+    x, y = Tuple(index)
+    newindex = M * [x; y; 1]
+    x1 = roundAround(newindex[1], 1, n)
+    y1 = roundAround(newindex[2], 1, m)
+    out[x1, y1] = P[x, y]
+  end
+  out
+end
+
+function backwardTransform(algo, M, P)
+  M = inv(M)
+  n, m = size(P)
+  out = zeros(eltype(P), n, m)
+  for index in CartesianIndices(out)
+    x, y = Tuple(index)
+    sourceIndex = M * [x; y; 1]
+    sourceIndex ./= sourceIndex[3]
+    x1 = round(Int32, sourceIndex[1])
+    y1 = round(Int32, sourceIndex[2])
+    #= if ((x == 1 && y == 1) || =#
+    #=     (x == 1 && y == m) || =#
+    #=     (x == n && y == 1) || =#
+    #=     (x == n && y == m)) =#
+    #=   println("AAAAAAAAAAA") =#
+    #=   display([x; y; 1]) =#
+    #=   println() =#
+    #=   display(sourceIndex) =#
+    #=   println() =#
+    #= end =#
+    if (x1 < 1 || y1 < 1 || x1 > n || y1 > m)
+      continue
+    end
+    if (sourceIndex[1] > n || sourceIndex[2] > m)
+      continue
+    end
+    out[x, y] = P[x1, y1]
+  end
+  out
+end
+
+function genMatrix(what, params...)
+  params = map(x->parse(Float32, x), params)
+  M = zeros(Float32, (3,3))
+  M[3, 3] = 1
+
+  if what == "scale"
+    if length(params) < 2
+      error("Scale requires two parameter (x, y)")
+    end
+    x, y = params
+    printfmt("Scale with x = {}; y = {}\n", x, y)
+    M[1, 1] = x
+    M[2, 2] = y
+  elseif what == "translate"
+    if length(params) < 2
+      error("Translate requires two parameter (dx, dy)")
+    end
+    dx, dy = params
+    M[1, 1] = 1
+    M[2, 2] = 1
+    M[1, 3] = dx
+    M[2, 3] = dy
+  elseif what == "rotate"
+    if length(params) < 1
+      error("Rotate requires one parameter (theta, isRadian: true)")
+    end
+    theta = params[1]
+    isRadian = 1
+    if length(params) >= 2
+      isRadian = params[2]
+    end
+
+    if isRadian == 1
+      M[1, 1] =  cos(theta)
+      M[1, 2] =  -sin(theta)
+      M[2, 1] =  sin(theta)
+      M[2, 2] =  cos(theta)
+    else
+      M[1, 1] =  cosd(theta)
+      M[1, 2] =  -sind(theta)
+      M[2, 1] =  sind(theta)
+      M[2, 2] =  cosd(theta)
+    end
+  elseif what == "shear"
+    if length(params) < 4
+      error("Rotate requires four parameter (a, b, c, d)")
+    end
+    a,b,c,d = params
+    M[1, 1] = a
+    M[1, 2] = b
+    M[2, 1] = c
+    M[2, 2] = d
+  else
+    error(printfmt("Matrix of {} is unknown\n", what))
+  end
+  M
+end
+
+function projectiveTransform(picture, points)
+  if length(points) != 4
+    error("Not correct number of point")
+  end
+
+  A = zeros(Int64, 2*length(points), 8)
+  B = zeros(Int64, 2*length(points), 1)
+  for i in 1:length(points)
+    x, y, x1, y1 = points[i]
+    A[2*i - 1,:] = [x y 1 0 0 0 -x*x1 -x1*y]
+    A[2*i,:] = [0 0 0 x y 1 -x*y1 -y*y1]
+    B[2*i - 1] = x1
+    B[2*i] = y1
+  end
+  H = vcat(A\B, 1)
+  M = reshape(H, (3,3))'
+
+  println("Matrix M = reshape([A\\B, 1], (3,3))")
+  display(M)
+  println()
+
+  backwardTransform("zero", M, picture)
+end
+
+if abspath(PROGRAM_FILE) == @__FILE__
+  what = ARGS[1]
+  img = load(ARGS[2])
+
+  if what == "transform"
+    # M = [[cosd(25) -sind(25) 0]; [sind(25) cosd(25) 0]; [0 0 1]]
+    # M = genMatrix("rotate", 25, false)
+
+    M = genMatrix(ARGS[3], ARGS[4:end]...)
+
+    forward = forwardTransform(M, img)
+    save("forward.png", forward)
+
+    backward = backwardTransform("zero", M, img)
+    save("backward.png", backward)
+  elseif what == "multitransform"
+  elseif what == "projective"
+    row, col = size(img)
+    out = projectiveTransform(img,
+      [
+        # [x y x1 y1],
+        [55 187 1 1],
+        [1276 619 1295 1],
+        [1447 1761 1295 1635],
+        [166 1819 1 1635]
+      ]
+    )
+    save("projective.png", out)
+  else
+    println("Do what? transform/projective")
+  end
+
+end

julia_scripts/histogram.jl

@@ -0,0 +1,3 @@
+
+if abspath(PROGRAM_FILE) == @__FILE__
+end

julia_scripts/hough.jl

@@ -0,0 +1,99 @@
+include("convolution.jl")
+
+using Images
+using TestImages
+using FileIO
+using Colors
+using ImageFeatures
+using Formatting
+
+using .Convole
+
+function hough(img, thetaRange=100, rhoRange=100)
+  r, c = size(img)
+  D = sqrt(r * r + c * c)
+  rho_min = -D
+  rho_max = D
+  L_rho = 2*D
+  rho_step = L_rho / rhoRange
+
+  theta_min = -pi/2
+  theta_max = pi/2
+  L_theta = pi
+  theta_step = L_theta / thetaRange
+
+  function dcm_rho(idx)
+    rho_min + ((idx) * rho_step) + (rho_step / 2)
+  end
+  function cdm_rho(rho)
+    round(Int32, (rho - rho_min) / rho_step)
+  end
+  function dcm_theta(idx)
+    theta_min + ((idx) * theta_step) + (theta_step / 2)
+  end
+  function cdm_theta(theta)
+    round(Int32, (theta - theta_min) / theta_step)
+  end
+
+  accumulator = zeros(Int32, rhoRange, thetaRange)
+  #= display(accumulator) =#
+  #= println() =#
+  for index in CartesianIndices(img)
+    x, y = Tuple(index)
+    for k in 1:thetaRange
+      theta = dcm_theta(k)
+      rho = x * cos(theta) + y * sin(theta)
+      i = cdm_rho(rho)
+      accumulator[i, k] += 1  # simple delta(x,y)
+    end
+  end
+
+  rho_idx, theta_idx = Tuple(argmax(accumulator))
+  rho, theta = dcm_rho(rho_idx), dcm_theta(theta_idx)
+  (rho, theta)
+end
+
+if abspath(PROGRAM_FILE) == @__FILE__
+  #= img = zeros(Bool,10,10) =#
+  #= for i in 1:10 =#
+  #=   img[2,i] = img[i,2] = img[7,i] = img[i,9] = true =#
+  #= end =#
+  #= lines = hough_transform_standard(img) =#
+  #=  =#
+  #= display(img) =#
+  #= println() =#
+  #= for line in lines =#
+  #=   r, t = line =#
+  #=   printfmt("x * cos({}π) + y * sin({}π) = {}\n", t/π, t/π, r) =#
+  #= end =#
+
+  gaussian_kernel = [
+      1 4 7 4 1
+      4 16 26 16 4
+      7 26 41 26 7
+      4 16 26 16 4
+      1 4 7 4 1
+    ] ./ 273
+  laplacian_kernel = [
+      -1 -1 -1
+      -1  8 -1
+      -1 -1 -1
+    ]
+  sobel_x_kernel = [
+      -1 0 1
+      -2 0 2
+      -1 0 1
+  ]
+  sobel_y_kernel = rotl90(sobel_x_kernel)
+
+  img = load(ARGS[1])
+  img_gray = Gray.(img)
+  img_blur = conv(img_gray, gaussian_kernel)
+  img_edge_x = conv(img_blur, sobel_x_kernel)
+  img_edge_y = conv(img_blur, sobel_y_kernel)
+  img_edge = Gray.(round.(Int32, sqrt.((img_edge_x .^ 2) .* (img_edge_y .^ 2))))
+  save("hough_edge.jpg", img_edge)
+  r, t = hough(img_gray)
+  printfmt("x * cos({}π) + y * sin({}π) = {}\n", t/π, t/π, r)
+end
+ 

julia_scripts/jpeg.jl

@@ -0,0 +1,98 @@
+using Images
+using FFTW
+using Formatting
+
+
+LUMINANCE_QUANTIZATION_TABLE = [
+    16  11  10  16  24   40   51   61   
+    12  12  14  19  26   58   60   55   
+    14  13  16  24  40   57   69   56   
+    14  17  22  29  51   87   80   62   
+    18  22  37  56  68   109  103  77   
+    24  35  55  64  81   104  113  92   
+    49  64  78  87  103  121  120  101  
+    72  92  95  98  112  100  103  99   
+  ]
+
+ZIGZAG = [
+    0   1   5   6  14  15  27  28
+    2   4   7  13  16  26  29  42
+    3   8  12  17  25  30  41  43
+    9  11  18  24  31  40  44  53
+    10  19  23  32  39  45  52  54
+    20  22  33  38  46  51  55  60
+    21  34  37  47  50  56  59  61
+    35  36  48  49  57  58  62  63
+   ] .+ 1
+
+function to_zigzag(block)
+  out_block = zeros(eltype(block), size(ZIGZAG))
+  for idx in CartesianIndices(ZIGZAG)
+    out_block[ZIGZAG[idx]] = block[idx]
+    # display(out_block)
+  end
+  reshape(out_block, (1,64))
+end
+
+
+
+function RLC(block)
+  codes = Tuple{Int32, Int32, Int32}[]
+  leadingZeros = 0
+  for idx in CartesianIndices(ZIGZAG)
+    if (idx == CartesianIndex(1, 1))
+      DC = 0
+      push!(codes, (0, DC, block[idx]))
+    elseif (block[idx] == 0)
+      leadingZeros += 1
+    else
+      push!(codes, (leadingZeros, log(2, block[idx]), block[idx]))
+      leadingZeros = 0
+    end
+  end
+  push!(codes, (0, 0, 0))
+  codes
+end
+
+if abspath(PROGRAM_FILE) == @__FILE__
+  img = load(ARGS[1])
+  img_ycbcr = channelview(YCbCr.(img))
+
+  for c in 1:3
+    channel = img_ycbcr[c,:,:]
+    row, col = size(channel)
+
+    printfmt("{} {}\n", row, col)
+    printfmt("{} {}\n", row % 8, col % 8)
+
+    for i in 1:8:row
+      for j in 1:8:col
+        # printfmt("{} {}\n", i, j)
+        block = channel[i:i+7, j:j+7]
+
+        block_shifted = block .- 127
+        block_dct = FFTW.dct(block_shifted)
+
+        block_quantization = round.(Int32, block_dct ./ LUMINANCE_QUANTIZATION_TABLE)
+        block_zigzag = to_zigzag(block_quantization)
+
+        if i == 1 && j == 9
+          display(block)
+          println()
+          display(block_shifted)
+          println()
+          display(block_dct)
+          println()
+          display(block_quantization)
+          println()
+          display(block_zigzag)
+          println()
+        end
+
+        # block_zigzag = collect(block_zigzag)
+        DC = block_zigzag[1]
+        AC = block_zigzag[2:end]
+      end
+    end
+  end
+end

julia_scripts/point.jl

@@ -0,0 +1,35 @@
+using Images
+using FileIO
+using Colors
+
+function transform(img, what, params...)
+  if length(params) < 2
+    error("Transform requires two parameter (a, b)")
+  end
+  a, b = params
+  out = zeros(eltype(img), size(img))
+  if what == "linear"
+    out = a .* img .+ b
+  elseif what == "log"
+    out = a .* log.(1 .+ img) .+ b
+  elseif what == "exp"
+    out = a .* exp.(img) .+ b
+  elseif what == "pow"
+    if length(params) < 3
+      error("Power transform requires three parameter (a, b, gamma)")
+    end
+    gamma = params[3]
+    out = a .* (img .^ gamma) .+ b
+  else
+    error("What the hell man?")
+  end
+  # TODO: Scale to 255
+  out
+end
+
+if abspath(PROGRAM_FILE) == @__FILE__
+  what = ARGS[1]
+  img = Gray.(load(ARGS[2]))
+  out = transform(img, what, ARGS[3:end]...)
+  save("point.png", out)
+end

julia_scripts/showpicture.jl

@@ -0,0 +1,24 @@
+module Showpicture
+
+using Images, ImageView, Gtk.ShortNames
+
+export showpicture
+
+function showpicture(img)
+
+  guidict = imshow(img);
+  #If we are not in a REPL
+  if (!isinteractive())
+    c = Condition()
+    # Get the window
+    win = guidict["gui"]["window"]
+    # Notify the condition object when the window closes
+    signal_connect(win, :destroy) do widget
+        notify(c)
+    end
+    # Wait for the notification before proceeding ...
+    wait(c)
+  end
+end
+
+end

markdown/1611743_NguyenQuangHoangLam.md

@@ -0,0 +1,165 @@
+```{.python .input  n=84}
+import numpy as np
+from scipy import signal
+from scipy import fftpack
+import matplotlib.pyplot as plt 
+
+
+print("Question 1: ")
+### Question 1
+print("a/")
+##a 
+
+I1 = np.array([
+    [5,0,0,1,2],
+    [2,1,5,1,2],
+    [7,1,5,1,2],
+    [7,4,5,4,3],
+    [7,1,6,1,3]
+])
+
+
+H_sobel_x = np.array([[-1,0,1],[-2,0,2],[-1,0,1]])
+H_sobel_y = np.array([[-1,-2,-1],[0,0,0],[1,2,1]])
+
+grad_x = signal.convolve2d(I1,H_sobel_x,boundary='symm',mode ='same')
+grad_y = signal.convolve2d(I1,H_sobel_y,boundary='symm',mode = 'same')
+
+
+print(f"Gradient of (0,0) according to x and y: {grad_x[0,0]} {grad_y[0,0]}")
+print(f"Gradient of (1,1) according to x and y: {grad_x[1,1]} {grad_y[1,1]}")
+print(f"Gradient of (0,3) according to x and y: {grad_x[0,3]} {grad_y[0,3]}")
+
+##b
+print("b/")
+n = I1.size
+hist1 = np.bincount(I1.flatten())/n
+print("Normalized Histogram of I1: ")
+print(hist1)
+
+##c
+print("c/")
+hist2 = np.array([1/8 for i in range(8)])
+cdf1 = np.cumsum(hist1)
+cdf2 = np.cumsum(hist2)
+
+## equalize 
+print("I2: ")
+I2 = np.zeros((N,N))
+N = I1.shape[0]
+for i in range(N):
+  for j in range(N):
+    x = I1[i,j]
+    c_x = cdf1[x]
+    for k in range(len(cdf2)):
+      if cdf2[k] == c_x:
+        I2[i,j] = k
+        
+print(I2.astype(np.int))
+
+print("Histogram of I2: ")
+plt.hist(I2.flatten(),8,[0,8])
+plt.show()
+
+    
+### Question 2 
+print("Question 2: ")
+#a
+print("a/")
+f = np.array([1,2])
+
+A = np.arange(2).reshape((1,2))
+
+M = A.reshape((2,1)).dot(A)
+
+M_dft = np.round(np.exp(1)**(-2j*(np.pi/2)*M))
+
+print("Based vectors after DFT: ")
+i=0
+for e in M_dft:
+  print(f"e{i}: {e}")
+  i+=1
+  
+#b 
+print("b/")
+M = 4
+u = np.arange(M).reshape((M,1))
+x = 2*u+1
+W_dct = np.dot(u,x.T)
+W_dct = np.cos(np.pi*W_dct/(2*M))
+for _ in range(M):
+  if _ == 0:
+    W_dct[_,:]*= np.sqrt(1/M)
+  else:
+    W_dct[_,:]*= np.sqrt(2/M)
+
+print("Based vectors after DCT for 4 dims: ")
+i=0
+for e in W_dct:
+  print(f"e{i}: {e}")
+  i+=1
+  
+IW = np.round(W_dct.dot(W_dct.T)).astype(np.int32)
+print(f"W_dct.dot(W_dct.T): \n {IW}")
+
+if(np.array_equal(IW,np.eye(4))):
+  print("W is orthor")
+
+
+fx = np.array([1,0,1])
+
+fx_dct = fftpack.dct(fx)
+
+print(f"dct of fx: {fx_dct}")
+
+### Question 3:
+
+print("Question 3: ")
+print("a/")
+phi = np.pi/4
+H2 = np.array([[np.cos(phi),-np.sin(phi),0],[np.sin(phi),np.cos(phi),0],[0,0,1]])
+H1 = np.array([[1,0,-3],[0,1,-3],[0,0,1]])
+H3 = np.array([[1,0,3],[0,1,3],[0,0,1]])
+
+print(f"Translate -3: \n{H1}")
+print(f"Rotate : \n {H2}")
+print(f"Translate 3: \n{H3}")
+H = H3.dot(H2).dot(H1)
+
+print(f"Matrix to rotate the image around (3,3): \n {H}")
+
+print("b/")
+
+Io = np.array((2,3,1)).reshape((3,1))
+I = np.linalg.pinv(H).dot(Io)
+
+x,y=I[0:2,:].flatten()
+print(f"x, y after zero order: {np.round(x).astype(np.int32)},{np.round(y).astype(np.int32)}")
+
+
+```
+
+```{.json .output n=84}
+[
+ {
+  "name": "stdout",
+  "output_type": "stream",
+  "text": "Question 1: \na/\nGradient of (0,0) according to x and y: 16 8\nGradient of (1,1) according to x and y: 1 -9\nGradient of (0,3) according to x and y: -3 -5\nb/\nNormalized Histogram of I1: \n[0.08 0.28 0.16 0.08 0.08 0.16 0.04 0.12]\nc/\nI2: \n[[0 0 0 0 0]\n [0 0 0 0 0]\n [7 0 0 0 0]\n [7 0 0 0 0]\n [7 0 0 0 0]]\nHistogram of I2: \n"
+ },
+ {
+  "data": {
+   "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD8CAYAAABn919SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
+   "text/plain": "<Figure size 432x288 with 1 Axes>"
+  },
+  "metadata": {
+   "tags": []
+  },
+  "output_type": "display_data"
+ },
+ {
+  "name": "stdout",
+  "output_type": "stream",
+  "text": "Question 2: \na/\nBased vectors after DFT: \ne0: [1.+0.j 1.+0.j]\ne1: [ 1.+0.j -1.-0.j]\nb/\nBased vectors after DCT for 4 dims: \ne0: [0.5 0.5 0.5 0.5]\ne1: [ 0.65328148  0.27059805 -0.27059805 -0.65328148]\ne2: [ 0.5 -0.5 -0.5  0.5]\ne3: [ 0.27059805 -0.65328148  0.65328148 -0.27059805]\nW_dct.dot(W_dct.T): \n [[1 0 0 0]\n [0 1 0 0]\n [0 0 1 0]\n [0 0 0 1]]\nW is orthor\ndct of fx: [4. 0. 2.]\nQuestion 3: \na/\nTranslate -3: \n[[ 1  0 -3]\n [ 0  1 -3]\n [ 0  0  1]]\nRotate : \n [[ 0.70710678 -0.70710678  0.        ]\n [ 0.70710678  0.70710678  0.        ]\n [ 0.          0.          1.        ]]\nTranslate 3: \n[[1 0 3]\n [0 1 3]\n [0 0 1]]\nMatrix to rotate the image around (3,3): \n [[ 0.70710678 -0.70710678  3.        ]\n [ 0.70710678  0.70710678 -1.24264069]\n [ 0.          0.          1.        ]]\nb/\nx, y after zero order: 2,4\n"
+ }
+]
+```

python_notebook/hough.ipynb

@@ -0,0 +1,136 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import imageio\n",
+    "import math"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def rgb2gray(rgb):\n",
+    "    return np.dot(rgb[..., :3], [0.299, 0.587, 0.114]).astype(np.uint8)\n",
+    "\n",
+    "\n",
+    "def hough_line(img, angle_step=1, lines_are_white=True, value_threshold=5):\n",
+    "    \"\"\"\n",
+    "    Hough transform for lines\n",
+    "\n",
+    "    Input:\n",
+    "    img - 2D binary image with nonzeros representing edges\n",
+    "    angle_step - Spacing between angles to use every n-th angle\n",
+    "                 between -90 and 90 degrees. Default step is 1.\n",
+    "    lines_are_white - boolean indicating whether lines to be detected are white\n",
+    "    value_threshold - Pixel values above or below the value_threshold are edges\n",
+    "\n",
+    "    Returns:\n",
+    "    accumulator - 2D array of the hough transform accumulator\n",
+    "    theta - array of angles used in computation, in radians.\n",
+    "    rhos - array of rho values. Max size is 2 times the diagonal\n",
+    "           distance of the input image.\n",
+    "    \"\"\"\n",
+    "    # Rho and Theta ranges\n",
+    "    thetas = np.deg2rad(np.arange(-90.0, 90.0, angle_step))\n",
+    "    width, height = img.shape\n",
+    "    diag_len = int(round(math.sqrt(width * width + height * height)))\n",
+    "    rhos = np.linspace(-diag_len, diag_len, diag_len * 2)\n",
+    "\n",
+    "    # Cache some resuable values\n",
+    "    cos_t = np.cos(thetas)\n",
+    "    sin_t = np.sin(thetas)\n",
+    "    num_thetas = len(thetas)\n",
+    "\n",
+    "    # Hough accumulator array of theta vs rho\n",
+    "    accumulator = np.zeros((2 * diag_len, num_thetas), dtype=np.uint8)\n",
+    "    # (row, col) indexes to edges\n",
+    "    are_edges = img > value_threshold if lines_are_white else img < value_threshold\n",
+    "    y_idxs, x_idxs = np.nonzero(are_edges)\n",
+    "\n",
+    "    # Vote in the hough accumulator\n",
+    "    for i in range(len(x_idxs)):\n",
+    "        x = x_idxs[i]\n",
+    "        y = y_idxs[i]\n",
+    "\n",
+    "        for t_idx in range(num_thetas):\n",
+    "            # Calculate rho. diag_len is added for a positive index\n",
+    "            rho = diag_len + int(round(x * cos_t[t_idx] + y * sin_t[t_idx]))\n",
+    "            accumulator[rho, t_idx] += 1\n",
+    "\n",
+    "    return accumulator, thetas, rhos"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def show_hough_line(img, accumulator, thetas, rhos, save_path=None):\n",
+    "    import matplotlib.pyplot as plt\n",
+    "\n",
+    "    fig, ax = plt.subplots(1, 2, figsize=(10, 10))\n",
+    "\n",
+    "    ax[0].imshow(img, cmap=plt.cm.gray)\n",
+    "    ax[0].set_title('Input image')\n",
+    "    ax[0].axis('image')\n",
+    "\n",
+    "    ax[1].imshow(\n",
+    "        accumulator, cmap='jet',\n",
+    "        extent=[np.rad2deg(thetas[-1]), np.rad2deg(thetas[0]), rhos[-1], rhos[0]])\n",
+    "    ax[1].set_aspect('equal', adjustable='box')\n",
+    "    ax[1].set_title('Hough transform')\n",
+    "    ax[1].set_xlabel('Angles (degrees)')\n",
+    "    ax[1].set_ylabel('Distance (pixels)')\n",
+    "    ax[1].axis('image')\n",
+    "\n",
+    "    # plt.axis('off')\n",
+    "    if save_path is not None:\n",
+    "        plt.savefig(save_path, bbox_inches='tight')\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "imgpath = '../images/bangdiem.png'\n",
+    "img = imageio.imread(imgpath)\n",
+    "if img.ndim == 3:\n",
+    "    img = rgb2gray(img)\n",
+    "accumulator, thetas, rhos = hough_line(img)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

python_scripts/1612143_TruongPhuongNam.py

@@ -0,0 +1,134 @@
+import cv2 as cv
+import numpy as np
+from numpy import fft
+import matplotlib.pyplot as plt
+from scipy import ndimage
+from scipy import signal
+from scipy import fftpack
+
+def create_histogram(img):
+	size = img.shape[0]*img.shape[1]
+	hist = np.zeros(8, dtype=np.float)
+	for row in range(img.shape[0]):
+		for col in range(img.shape[1]):
+			hist[img[row][col]] += 1
+	return hist/size
+
+def create_sum_histogram(hist):
+	sum_hist = np.zeros(8,dtype=np.float)
+	sum_hist[0] = hist[0]
+	for x in range(1,8):
+		sum_hist[x] = sum_hist[x-1] + hist[x]
+	return sum_hist
+
+def dft(signal):
+	N = len(signal)
+	x = np.array(range(N))
+	x = np.tile(x,(N,1))
+	u = x.copy().T
+	M = np.exp((-1j*2*np.pi*x*u)/N)
+	return np.matmul(M,signal)
+
+def show_dft_vector(N):
+	x = np.array(range(N))
+	x = np.tile(x,(N,1))
+	u = x.copy().T
+	M = np.exp((-1j*2*np.pi*x*u)/N)
+	print(M)
+
+def dct(signal):
+	N = len(signal)
+	x = np.array(range(N))
+	x = np.tile(x,(N,1))
+	u = x.copy().T
+	M = np.cos((2*x+1)*u*np.pi/(2*N))
+	a1 = [np.sqrt(1/N)]
+	a2 = np.repeat(np.array([np.sqrt(2/N)]),N-1)
+	a = np.concatenate((a1,a2),axis = 0)
+	return np.matmul(M,signal)*a
+
+def show_dct(N):
+	x = np.array(range(N))
+	x = np.tile(x,(N,1))
+	u = x.copy().T
+	M = np.cos((2*x+1)*u*np.pi/(2*N))
+	a1 = [np.sqrt(1/N)]
+	a2 = np.repeat(np.array([np.sqrt(2/N)]),N-1)
+	a = np.concatenate((a1,a2),axis = 0)
+	a = np.repeat(a,4)
+	a = np.reshape(a,(4,4))
+	return M*a
+
+
+def bai1():
+	I = np.array([[5,0,0,1,2],
+				[2,1,5,1,2],
+				[7,1,5,1,2],
+				[7,4,5,4,3],
+				[7,1,6,1,3]])
+	Kx = np.array([[-1,0,1],
+				[-2,0,2],
+				[-1,0,1]])
+	Ky = Kx.T
+	Gx = ndimage.convolve(I,Kx,mode='reflect')
+	Gy = ndimage.convolve(I,Ky,mode='reflect')
+	print('Gradient vector at (0,0): (' + str(Gx[0,0]) + ',' + str(Gy[0,0]) +')')
+	print('Gradient vector at (1,1): (' + str(Gx[1,1]) + ',' + str(Gy[1,1]) +')')
+	print('Gradient vector at (0,3): (' + str(Gx[0,3]) + ',' + str(Gy[0,3]) +')')
+
+	h = create_histogram(I)
+	plt.plot(h,color = 'b')
+	plt.xlim([0,7])
+	plt.show()
+	sumhist = create_sum_histogram(h)
+
+	new_I = I.copy()
+	for x in range(I.shape[0]):
+		for y in range(I.shape[1]):
+			new_I[x][y] = int(np.round(sumhist[I[x][y]]*7))
+	new_h = create_histogram(new_I)
+	new_h_sum = create_sum_histogram(new_h)
+	plt.plot(sumhist,color = 'r')
+	plt.plot(new_h_sum,color = 'b')
+	plt.xlim([0,7])
+	plt.show()
+
+	print(new_I)
+
+
+def bai2():
+	# a)
+	print('Cau 2a)')
+	show_dft_vector(2)
+	print(dft([1,3]))
+	# b)
+	print('Cau b)')
+	fx = np.array([1,3])
+	fu = dft(fx)
+	print(fu)
+	print('Chung minh truc giao chuan:')
+	base_vector = show_dct(4)
+	for v in base_vector:
+		print(np.sum(v**2))
+	for x in range(base_vector.shape[0]):
+		for y in range(x,base_vector.shape[0]):
+			if x == y:
+				continue
+			print(np.dot(base_vector[x],base_vector[y]))
+
+	fx = np.array([1,0,1])
+	fxx = np.array([1,0,1,0])
+	print(dct(fxx))
+
+
+def bai3():
+	A = np.array([[1/np.sqrt(2),-1/np.sqrt(2),3],
+				[1/np.sqrt(2),1/np.sqrt(2),-3*2**0.5+3],
+				[0,0,1]])
+	P1 = np.array([2,3,1])
+	pixel = np.round(np.matmul(np.linalg.inv(A),P1))
+	print(pixel)
+
+bai1()
+bai2()
+bai3()

python_scripts/1614096_NguyenLeQuocViet.py

@@ -0,0 +1,107 @@
+from skimage.exposure import rescale_intensity
+import numpy as np
+import cv2 as cv
+import matplotlib.pyplot as plt
+import math
+def convolve(image, kernel):
+	(iH, iW) = image.shape[:2]
+	(kH, kW) = kernel.shape[:2]
+	kernel = kernel[::-1]
+	pad = (kW - 1) // 2
+	image = cv.copyMakeBorder(image, pad, pad, pad, pad, cv.BORDER_REPLICATE)
+	output = np.zeros((iH,iW), dtype="float32")
+
+	for y in np.arange(pad, iH + pad):
+		for x in np.arange(pad, iW + pad):
+			roi = image[y - pad:y+pad+1, x - pad:x + pad + 1]
+			k =(roi * kernel).sum()
+			output[y - pad, x - pad] = k
+		
+	output = rescale_intensity(output, in_range=(0,255))
+	output = (output * 255).astype("uint8")
+	return output
+
+I = np.array([  [5,0,0,1,2],
+                [2,1,5,1,2],
+                [7,1,5,1,2],
+                [7,4,5,4,3],
+                [7,1,6,1,3] ])
+    
+sobelX = np.array((
+	[-1,0,1],
+	[-2,0,2],
+	[-1,0,1]), dtype="int")
+
+sobelY = np.array((
+	[-1,-1,-1],
+	[-2, 0, 2],
+	[-1, 0, 1]), dtype="int")
+
+H,W = I.shape
+D_x = convolve(I,sobelX)
+D_y = convolve(I,sobelY)
+result_a = []
+for i in range(H):
+    temp = []
+    for j in range(W):
+        temp += [(D_x[i,j],D_y[i,j])]
+    result_a.append(temp)
+print("1A\n",result_a)
+
+def create_histogram(img):
+    assert len(img.shape) == 2
+    H,W = img.shape
+    sum = H * W
+    histogram = np.zeros(shape=(8,), dtype = float)
+    for row in range(img.shape[0]):
+        for col in range(img.shape[1]):
+            histogram[img[row,col]] += 1 / sum
+    return histogram
+
+
+def visualize_histogram(histogram, name):
+    index = np.arange(len(histogram))
+    plt.bar(index,histogram)
+    plt.xlabel('Intensity', fontsize = 5)
+    plt.ylabel('Frequency', fontsize = 5)
+    plt.title(name)
+    plt.show()
+
+def histogram_equation(histogram, img):
+    c = np.cumsum(histogram)
+    print(c)
+    m_table = np.array([]).astype(np.uint8)
+    m_table = c * 7
+    for row in range(img.shape[0]):
+        for col in range(img.shape[1]):
+            img[row,col] = m_table[img[row,col]]
+    return img
+
+
+visualize_histogram(create_histogram(I),"1B")
+
+print("1C\n",histogram_equation(create_histogram(I),I))
+
+def DFT1D(array):
+    N = array.shape[0]
+    # (a[x, y], b[x, y]) = (x, y)
+    a = np.tile(np.arange(0, N), (N, 1))
+    b = a.copy().T
+    W = np.exp(-2j*np.pi/N*a*b)
+    return np.around(np.dot(W, array), 2)
+
+def DCT1D(array):
+    N = array.shape[0]
+    factor = math.pi / N
+    C = np.zeros((N, N), dtype = np.float32)
+    for x in range(N):
+        C[0][x] = math.sqrt(1/N) * math.cos((x + 0.5) * 0 * factor)
+    for u in range(N)[1:]:
+        for x in range(N):
+            C[u][x] = math.sqrt(2/N) * math.cos((x + 0.5) * u * factor)
+    return C, np.matmul(C, array)
+
+print("2A\n",DFT1D(np.array([1,3])))
+C, F = DCT1D(np.array([1,0,1,0]))
+print("2B\nC=\n", C)
+print("F=",F)

python_scripts/FTs.py

@@ -0,0 +1,84 @@
+import numpy as np
+import scipy.ndimage as ndi
+import matplotlib.pyplot as plt
+
+
+def imshow(img, cap=None):
+    if np.amax(img) > 255:
+        img = img / (np.amax(img)) * 255
+    img.astype(np.uint8)
+    fig = plt.figure(figsize=(4, 4))
+    if cap is not None:
+        plt.title(cap)
+    plt.imshow(img, cmap="gray")
+    plt.axis("off")
+    plt.show()
+
+
+def shift(array):
+    n = array.shape[0]
+    t = array[0:int(n / 2), 0:int(n / 2)].copy()
+    array[0:int(n / 2), 0:int(n / 2)] = array[int(n / 2):n, int(n / 2):n]
+    array[int(n / 2):n, int(n / 2):n] = t
+    t = array[0:int(n / 2), int(n / 2):n].copy()
+    array[0:int(n / 2), int(n / 2):n] = array[int(n / 2):n, 0:int(n / 2)]
+    array[int(n / 2):n, 0:int(n / 2)] = t
+    return array
+
+
+def padding(img):
+    s = 2**np.ceil(np.log2(np.amax(img.shape))).astype(np.int32)
+    height = s - img.shape[0]
+    width = s - img.shape[1]
+    left = width // 2
+    right = width - left
+    top = height // 2
+    down = height - top
+    shape_ = [[top, down], [left, right]]
+    return np.pad(img, shape_, 'constant')
+
+
+def dft1d(array):
+    N = array.shape[0]
+    # (a[x, y], b[x, y]) = (x, y)
+    a = np.tile(np.arange(0, N), (N, 1))
+    b = a.copy().T
+    W = np.exp(-2j * np.pi / N * a * b)
+    return np.around(np.dot(W, array), 2)
+
+
+def idft1d(array):
+    N = array.shape[0]
+    # (a[x, y], b[x, y]) = (x, y)
+    a = np.tile(np.arange(0, N), (N, 1))
+    b = a.copy().T
+    W = np.exp(2j * np.pi / N * a * b) / N
+    return np.around(np.dot(W, array), 2)
+
+
+def fft1d(array):
+    m = array.shape[0]
+    if m == 1:
+        return array
+    elif m % 2 == 0:
+        even = fft1d(array[::2])
+        odd = fft1d(array[1::2])
+        Wm = np.exp(-2j * np.pi / m * np.arange(int(m / 2)))
+        half1 = even + odd * Wm
+        half2 = even - odd * Wm
+        return np.concatenate([half1, half2])
+    else:
+        raise ValueError("Wrong dimension")
+
+
+def fft(array):
+    n = array.shape[0]
+    if np.log2(n) % 1 != 0:
+        return dft1d(array)
+    else:
+        return np.around(fft1d(array), 2)
+
+
+def fft2d(matrix):
+    temp = np.array([fft(x) for x in matrix]).T
+    return np.around(np.array([fft(x) for x in temp]).T, 2)

python_scripts/Filters.py

@@ -0,0 +1,114 @@
+import cv2
+import numpy as np
+import scipy.ndimage as ndi
+import matplotlib.pyplot as plt
+
+# customized imshow function
+
+
+def imshow(img, cap=None):
+    if np.amax(img) > 255:
+        img = img / (np.amax(img)) * 255
+    img.astype(np.uint8)
+    fig = plt.figure(figsize=(4, 4))
+    if cap is not None:
+        plt.title(cap)
+    plt.imshow(img, cmap="gray")
+    plt.axis("off")
+    plt.show()
+
+
+def apply(img, ker):
+    return np.abs(np.fft.ifft2(np.fft.fftshift(np.fft.fft2(img)) * ker).real)
+
+################################################################
+
+# Ideal LowPass Filter kernel
+
+
+def ilpf(m, n, r):
+    a = np.tile(np.arange(-n / 2, n / 2), (m, 1))
+    b = np.tile(np.arange(-m / 2, m / 2), (n, 1)).T
+    return (a * a + b * b < r * r).astype(np.uint8)
+
+# Print ILPF Result
+
+
+def apply_ilpf(img, r):
+    row, col = img.shape
+    imshow(img(*ilpf(row, col, r)), 'Ideal LowPass Filter\nwith r = ' + str(r))
+
+
+img = cv2.imread("C:/Users/NGPD/Desktop/2.jpg", cv2.IMREAD_GRAYSCALE)
+imshow(img, 'Loaded Image')
+apply_ilpf(img, 5)
+apply_ilpf(img, 15)
+apply_ilpf(img, 30)
+apply_ilpf(img, 80)
+
+################################################################
+
+# Butterworth LPF kernel
+
+
+def blpf(m, n, N, r):
+    a = np.tile(np.arange(-n / 2, n / 2), (m, 1))
+    b = np.tile(np.arange(-m / 2, m / 2), (n, 1)).T
+    return (1 / (1 + ((a * a + b * b) / (r * r))**N))
+
+# Print BLPF Result
+
+
+def apply_blpf(img, N, r):
+    row, col = img.shape
+    imshow(img(*blpf(row, col, N, r)),
+           'Butterworth LowPass Filter\nwith r = ' + str(r) + ' and n = ' + str(N))
+
+
+img = cv2.imread("C:/Users/NGPD/Desktop/2.jpg", cv2.IMREAD_GRAYSCALE)
+imshow(img, 'Loaded Image')
+n = 2
+apply_blpf(img, n, 5)
+apply_blpf(img, n, 15)
+apply_blpf(img, n, 30)
+apply_blpf(img, n, 80)
+
+################################################################
+
+# Gaussian LPF kernel
+
+
+def glpf(m, n, r):
+    a = np.tile(np.arange(-n / 2, n / 2), (m, 1))
+    b = np.tile(np.arange(-m / 2, m / 2), (n, 1)).T
+    return np.exp(-(a * a + b * b) / (2 * r * r))
+
+# Print GLPF Result
+
+
+def apply_glpf(img, r):
+    row, col = img.shape
+    imshow(img(*glpf(row, col, r)), 'Gaussian LowPass Filter\nwith r = ' + str(r))
+
+
+img = cv2.imread("C:/Users/NGPD/Desktop/2.jpg", cv2.IMREAD_GRAYSCALE)
+imshow(img, 'Loaded Image')
+apply_glpf(img, 5)
+apply_glpf(img, 15)
+apply_glpf(img, 30)
+apply_glpf(img, 80)
+
+################################################################
+
+img = cv2.imread("C:/Users/NGPD/Desktop/2.jpg", cv2.IMREAD_GRAYSCALE)
+
+m, n = img.shape
+a = np.tile(np.arange(-n / 2, n / 2), (m, 1))
+b = np.tile(np.arange(-m / 2, m / 2), (n, 1)).T
+lap = img(*-(a * a + b * b))
+if np.amax(lap) > 255:
+    lap = lap / (np.amax(lap)) * 255
+
+imshow(img, 'Loaded Image')
+imshow(lap, 'Laplacian Filter')
+imshow(img - lap, 'g(x, y)')

python_scripts/chessboard.py

@@ -0,0 +1,46 @@
+import cv2
+import numpy as np
+import scipy.ndimage as ndi
+import matplotlib.pyplot as plt
+
+# customized imshow function
+
+
+def imshow(img, cap=None):
+    if np.amax(img) > 255:
+        img = img / (np.amax(img)) * 255
+    img.astype(np.uint8)
+    fig = plt.figure(figsize=(4, 4))
+    if cap is not None:
+        plt.title(cap)
+    plt.imshow(img, cmap="gray")
+    plt.axis("off")
+    plt.show()
+
+
+def ilpf(m, n, r):
+    a = np.tile(np.arange(-n / 2, n / 2), (m, 1))
+    b = np.tile(np.arange(-m / 2, m / 2), (n, 1)).T
+    return (a * a + b * b < r * r).astype(np.uint8)
+
+
+def apply(img, ker):
+    return np.abs(np.fft.ifft2(np.fft.fftshift(np.fft.fft2(img)) * ker).real)
+
+
+# generate chess board with size NxN
+N = 64
+a = np.tile(np.array(1), (int(N / 4), int(N / 4)))
+b = np.tile(np.array(0), (int(N / 4), int(N / 4)))
+img1 = np.concatenate([a, b], axis=0)
+img2 = np.concatenate([b, a], axis=0)
+img = np.concatenate([img1, img2], axis=1)
+img = np.tile(img, (4, 4))
+
+r, c = img.shape
+ker = ilpf(r, c, 30)
+res = img(*ker)
+
+imshow(img, 'Created Image')
+imshow(ker, 'ILPF Kernel')
+imshow(res, 'ILPF Result')

python_scripts/hough.py

@@ -0,0 +1,90 @@
+import numpy as np
+import imageio
+import math
+
+def rgb2gray(rgb):
+    return np.dot(rgb[..., :3], [0.299, 0.587, 0.114]).astype(np.uint8)
+
+
+def hough_line(img, angle_step=1, lines_are_white=True, value_threshold=5):
+    """
+    Hough transform for lines
+
+    Input:
+    img - 2D binary image with nonzeros representing edges
+    angle_step - Spacing between angles to use every n-th angle
+                 between -90 and 90 degrees. Default step is 1.
+    lines_are_white - boolean indicating whether lines to be detected are white
+    value_threshold - Pixel values above or below the value_threshold are edges
+
+    Returns:
+    accumulator - 2D array of the hough transform accumulator
+    theta - array of angles used in computation, in radians.
+    rhos - array of rho values. Max size is 2 times the diagonal
+           distance of the input image.
+    """
+    # Rho and Theta ranges
+    thetas = np.deg2rad(np.arange(-90.0, 90.0, angle_step))
+    width, height = img.shape
+    diag_len = int(round(math.sqrt(width * width + height * height)))
+    rhos = np.linspace(-diag_len, diag_len, diag_len * 2)
+
+    # Cache some resuable values
+    cos_t = np.cos(thetas)
+    sin_t = np.sin(thetas)
+    num_thetas = len(thetas)
+
+    # Hough accumulator array of theta vs rho
+    accumulator = np.zeros((2 * diag_len, num_thetas), dtype=np.uint8)
+    # (row, col) indexes to edges
+    are_edges = img > value_threshold if lines_are_white else img < value_threshold
+    y_idxs, x_idxs = np.nonzero(are_edges)
+
+    # Vote in the hough accumulator
+    for i in range(len(x_idxs)):
+        x = x_idxs[i]
+        y = y_idxs[i]
+
+        for t_idx in range(num_thetas):
+            # Calculate rho. diag_len is added for a positive index
+            rho = diag_len + int(round(x * cos_t[t_idx] + y * sin_t[t_idx]))
+            accumulator[rho, t_idx] += 1
+
+    return accumulator, thetas, rhos
+
+
+def show_hough_line(img, accumulator, thetas, rhos, save_path=None):
+    import matplotlib.pyplot as plt
+
+    fig, ax = plt.subplots(1, 2, figsize=(10, 10))
+
+    ax[0].imshow(img, cmap=plt.cm.gray)
+    ax[0].set_title('Input image')
+    ax[0].axis('image')
+
+    ax[1].imshow(
+        accumulator, cmap='jet',
+        extent=[np.rad2deg(thetas[-1]), np.rad2deg(thetas[0]), rhos[-1], rhos[0]])
+    ax[1].set_aspect('equal', adjustable='box')
+    ax[1].set_title('Hough transform')
+    ax[1].set_xlabel('Angles (degrees)')
+    ax[1].set_ylabel('Distance (pixels)')
+    ax[1].axis('image')
+
+    # plt.axis('off')
+    if save_path is not None:
+        plt.savefig(save_path, bbox_inches='tight')
+    plt.show()
+
+
+if __name__ == '__main__':
+    imgpath = '../images/bangdiem.png'
+    img = imageio.imread(imgpath)
+    if img.ndim == 3:
+        img = rgb2gray(img)
+    accumulator, thetas, rhos = hough_line(img)
+    idx = np.argmax(accumulator)
+    rho = rhos[idx / accumulator.shape[1]]
+    theta = thetas[idx % accumulator.shape[1]]
+    print ("rho={0:.2f}, theta={1:.0f}".format(rho, np.rad2deg(theta)))
+    # show_hough_line(img, accumulator, save_path='imgs/output.png')

resource/Sources/Decription/dsa-style.tex

@@ -0,0 +1,236 @@
+% Copyright 2007 by Till Tantau
+%
+% This file may be distributed and/or modified
+%
+% 1. under the LaTeX Project Public License and/or
+% 2. under the GNU Public License.
+%
+% See the file doc/licenses/LICENSE for more details.
+
+
+% Common packages
+\usepackage[utf8x]{inputenc}
+\usepackage[vietnam,english]{babel}
+\usepackage[utf8]{vietnam}
+%\usepackage{times}
+\usefonttheme[onlymath]{serif}
+\usecolortheme{default}
+\usepackage{booktabs}
+\usepackage{mathpartir}
+\usepackage{listings}
+\usepackage{listingsutf8}
+
+\usepackage{pbox}
+\mprset{flushleft}
+\mode<article>
+{
+  \usepackage{times}
+  \usepackage{mathptmx}
+  \usepackage[left=1.5cm,right=6cm,top=1.5cm,bottom=3cm]{geometry}
+}
+
+\usepackage{hyperref}
+\usepackage{tikz}
+\usetikzlibrary{arrows,backgrounds}
+%\tikzstyle{mnode}=[circle, draw, fill=black, inner sep=0pt, minimum width=4pt]
+\usepackage{colortbl}
+%\usepackage{yfonts}
+\usepackage{translator} % comment this, if not available
+
+
+% Common settings for all lectures in this course
+
+\def\lecturename{Image Processing and Computer Vision}
+
+\title{\insertlecture}
+
+\author{\textbf{LE Thanh Sach}}
+
+\institute
+{
+  \textit{Faculty of Computer Science and Engineering}\\
+  \textit{Ho Chi Minh University of Technology, VNU-HCM}
+}
+
+\subject{Lecturer \lecturename}
+
+% Beamer version theme settings
+
+\useoutertheme[height=0pt,width=2cm,right]{sidebar}
+\usecolortheme{rose,sidebartab}
+\useinnertheme{circles}
+\usefonttheme[only large]{structurebold}
+
+\setbeamercolor{sidebar right}{bg=black!15}
+\setbeamercolor{structure}{fg=blue}
+\setbeamercolor{author}{parent=structure}
+
+\setbeamerfont{title}{series=\normalfont,size=\LARGE}
+\setbeamerfont{title in sidebar}{series=\bfseries}
+\setbeamerfont{author in sidebar}{series=\bfseries}
+\setbeamerfont*{item}{series=}
+\setbeamerfont{frametitle}{size=}
+\setbeamerfont{block title}{size=\small}
+\setbeamerfont{subtitle}{size=\normalsize,series=\normalfont}
+
+\setbeamertemplate{navigation symbols}{}
+\setbeamertemplate{bibliography item}[book]
+\setbeamertemplate{sidebar right}
+{
+  {\usebeamerfont{title in sidebar}%
+    \vskip1.5em%
+    \hskip3pt%
+    \usebeamercolor[fg]{title in sidebar}%
+    \insertshorttitle[width=2cm,center,respectlinebreaks]\par%
+    \vskip1.25em%
+  }%
+  {%
+    \hskip3pt%
+    \usebeamercolor[fg]{author in sidebar}%
+    \usebeamerfont{author in sidebar}%
+    \insertshortauthor[width=2cm,center,respectlinebreaks]\par%
+    \vskip1.25em%
+  }%
+  \hbox to2cm{\hss\insertlogo\hss}
+  \vskip1.25em%
+  \insertverticalnavigation{2cm}%
+  \vfill
+  \hbox to 2cm{\hfill\usebeamerfont{subsection in
+      sidebar}\strut\usebeamercolor[fg]{subsection in
+      sidebar}\insertshortlecture.\insertframenumber\hskip5pt}%
+  \vskip3pt%
+}%
+
+\setbeamertemplate{title page}
+{
+  \vbox{}
+  \vskip1em
+  {\huge Chapter \insertshortlecture\par}
+  {\usebeamercolor[fg]{title}\usebeamerfont{title}\inserttitle\par}%
+  \ifx\insertsubtitle\@empty%
+  \else%
+    \vskip0.25em%
+    {\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}%
+  \fi%     
+  \vskip1em\par
+  \emph{\lecturename}\ 
+  %on \insertdate\par
+  \vskip3em\par
+
+  \leftskip=0pt plus1fill\insertauthor\par
+  \insertinstitute\vskip1em
+}
+
+\logo{\includegraphics[width=1.5cm]{hcmut.png}}
+
+
+
+% Article version layout settings
+
+\mode<article>
+
+\makeatletter
+\def\@listI{\leftmargin\leftmargini
+  \parsep 0pt
+  \topsep 5\p@   \@plus3\p@ \@minus5\p@
+  \itemsep0pt}
+\let\@listi=\@listI
+
+
+\setbeamertemplate{frametitle}{\paragraph*{\insertframetitle\
+    \ \small\insertframesubtitle}\ \par
+}
+\setbeamertemplate{frame end}{%
+  \marginpar{\scriptsize\hbox to 1cm{\sffamily%
+      \hfill\strut\insertshortlecture.\insertframenumber}\hrule height .2pt}}
+\setlength{\marginparwidth}{1cm}
+\setlength{\marginparsep}{4.5cm}
+
+\def\@maketitle{\makechapter}
+
+\def\makechapter{
+  \newpage
+  \null
+  \vskip 2em%
+  {%
+    \parindent=0pt
+    \raggedright
+    \sffamily
+    \vskip8pt
+    {\fontsize{36pt}{36pt}\selectfont Chapter \insertshortlecture \par\vskip2pt}
+    {\fontsize{24pt}{28pt}\selectfont \color{blue!50!black} \insertlecture\par\vskip4pt}
+    {\Large\selectfont \color{blue!50!black} \insertsubtitle\par}
+    \vskip10pt
+
+    \normalsize\selectfont Print version of
+    Lecturer \emph{\lecturename} of \@date\par\vskip1.5em
+    \hfill Le Thanh Sach and Luong The Nhan, Faculty of CSE, HCMC University of Technology
+  }
+  \par
+  \vskip 1.5em%
+}
+
+\let\origstartsection=\@startsection
+\def\@startsection#1#2#3#4#5#6{%
+  \origstartsection{#1}{#2}{#3}{#4}{#5}{#6\normalfont\sffamily\color{blue!50!black}\selectfont}}
+
+\makeatother
+
+\mode
+<all>
+
+
+
+
+% Typesetting Listings
+
+\usepackage{listings}
+\lstset{language=Java}
+
+\alt<presentation>
+{\lstset{%
+  basicstyle=\footnotesize\ttfamily,
+  commentstyle=\slshape\color{green!50!black},
+  keywordstyle=\bfseries\color{blue!50!black},
+  identifierstyle=\color{blue},
+  stringstyle=\color{orange},
+  escapechar=\#,
+  emphstyle=\color{red}}
+}
+{
+  \lstset{%
+    basicstyle=\ttfamily,
+    keywordstyle=\bfseries,
+    commentstyle=\itshape,
+    escapechar=\#,
+    emphstyle=\bfseries\color{red}
+  }
+}
+
+
+
+% Common theorem-like environments
+
+\theoremstyle{example}
+\newtheorem{exercise}[theorem]{\translate{Exercise}}
+
+
+% New useful definitions:
+
+\newbox\mytempbox
+\newdimen\mytempdimen
+
+\newcommand\includegraphicscopyright[3][]{%
+  \leavevmode\vbox{\vskip3pt\raggedright\setbox\mytempbox=\hbox{\includegraphics[#1]{#2}}%
+    \mytempdimen=\wd\mytempbox\box\mytempbox\par\vskip1pt%
+    \fontsize{3}{3.5}\selectfont{\color{black!25}{\vbox{\hsize=\mytempdimen#3}}}\vskip3pt%
+}}
+
+\newenvironment{colortabular}[1]{\medskip\rowcolors[]{1}{blue!20}{blue!10}\tabular{#1}\rowcolor{blue!40}}{\endtabular\medskip}
+
+\def\equad{\leavevmode\hbox{}\quad}
+
+\newenvironment{greencolortabular}[1]
+{\medskip\rowcolors[]{1}{green!50!black!20}{green!50!black!10}%
+  \tabular{#1}\rowcolor{green!50!black!40}}%
+{\endtabular\medskip}

resource/Sources/Decription/mathpartir.sty

@@ -0,0 +1,446 @@
+%  Mathpartir --- Math Paragraph for Typesetting Inference Rules
+%
+%  Copyright (C) 2001, 2002, 2003, 2004, 2005 Didier Rémy
+%
+%  Author         : Didier Remy 
+%  Version        : 1.2.0
+%  Bug Reports    : to author
+%  Web Site       : http://pauillac.inria.fr/~remy/latex/
+% 
+%  Mathpartir is free software; you can redistribute it and/or modify
+%  it under the terms of the GNU General Public License as published by
+%  the Free Software Foundation; either version 2, or (at your option)
+%  any later version.
+%  
+%  Mathpartir is distributed in the hope that it will be useful,
+%  but WITHOUT ANY WARRANTY; without even the implied warranty of
+%  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+%  GNU General Public License for more details 
+%  (http://pauillac.inria.fr/~remy/license/GPL).
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%  File mathpartir.sty (LaTeX macros)
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{mathpartir}
+    [2005/12/20 version 1.2.0 Math Paragraph for Typesetting Inference Rules]
+
+%%
+
+%% Identification
+%% Preliminary declarations
+
+\RequirePackage {keyval}
+
+%% Options
+%% More declarations
+
+%% PART I: Typesetting maths in paragraphe mode
+
+%% \newdimen \mpr@tmpdim
+%% Dimens are a precious ressource. Uses seems to be local.
+\let \mpr@tmpdim \@tempdima
+
+% To ensure hevea \hva compatibility, \hva should expands to nothing 
+% in mathpar or in inferrule
+\let \mpr@hva \empty
+
+%% normal paragraph parametters, should rather be taken dynamically
+\def \mpr@savepar {%
+  \edef \MathparNormalpar
+     {\noexpand \lineskiplimit \the\lineskiplimit
+      \noexpand \lineskip \the\lineskip}%
+  }
+
+\def \mpr@rulelineskip {\lineskiplimit=0.3em\lineskip=0.2em plus 0.1em}
+\def \mpr@lesslineskip {\lineskiplimit=0.6em\lineskip=0.5em plus 0.2em}
+\def \mpr@lineskip  {\lineskiplimit=1.2em\lineskip=1.2em plus 0.2em}
+\let \MathparLineskip \mpr@lineskip
+\def \mpr@paroptions {\MathparLineskip}
+\let \mpr@prebindings \relax
+
+\newskip \mpr@andskip \mpr@andskip 2em plus 0.5fil minus 0.5em
+
+\def \mpr@goodbreakand
+   {\hskip -\mpr@andskip  \penalty -1000\hskip \mpr@andskip}
+\def \mpr@and {\hskip \mpr@andskip}
+\def \mpr@andcr {\penalty 50\mpr@and}
+\def \mpr@cr {\penalty -10000\mpr@and}
+\def \mpr@eqno #1{\mpr@andcr #1\hskip 0em plus -1fil \penalty 10}
+
+\def \mpr@bindings {%
+  \let \and \mpr@andcr
+  \let \par \mpr@andcr
+  \let \\\mpr@cr
+  \let \eqno \mpr@eqno
+  \let \hva \mpr@hva
+  } 
+\let \MathparBindings \mpr@bindings
+
+% \@ifundefined {ignorespacesafterend}
+%    {\def \ignorespacesafterend {\aftergroup \ignorespaces}
+
+\newenvironment{mathpar}[1][]
+  {$$\mpr@savepar \parskip 0em \hsize \linewidth \centering
+     \vbox \bgroup \mpr@prebindings \mpr@paroptions #1\ifmmode $\else
+     \noindent $\displaystyle\fi
+     \MathparBindings}
+  {\unskip \ifmmode $\fi\egroup $$\ignorespacesafterend}
+
+\newenvironment{mathparpagebreakable}[1][]
+  {\begingroup 
+   \par
+   \mpr@savepar \parskip 0em \hsize \linewidth \centering
+      \mpr@prebindings \mpr@paroptions #1%
+      \vskip \abovedisplayskip \vskip -\lineskip%
+     \ifmmode  \else  $\displaystyle\fi
+     \MathparBindings
+  }
+  {\unskip
+   \ifmmode $\fi \par\endgroup
+   \vskip \belowdisplayskip
+   \noindent
+  \ignorespacesafterend}
+
+% \def \math@mathpar #1{\setbox0 \hbox {$\displaystyle #1$}\ifnum
+%     \wd0 < \hsize  $$\box0$$\else \bmathpar #1\emathpar \fi}
+
+%%% HOV BOXES
+
+\def \mathvbox@ #1{\hbox \bgroup \mpr@normallineskip 
+  \vbox \bgroup \tabskip 0em \let \\ \cr
+  \halign \bgroup \hfil $##$\hfil\cr #1\crcr \egroup \egroup
+  \egroup}
+
+\def \mathhvbox@ #1{\setbox0 \hbox {\let \\\qquad $#1$}\ifnum \wd0 < \hsize
+      \box0\else \mathvbox {#1}\fi}
+
+
+%% Part II -- operations on lists
+
+\newtoks \mpr@lista
+\newtoks \mpr@listb
+
+\long \def\mpr@cons #1\mpr@to#2{\mpr@lista {\\{#1}}\mpr@listb \expandafter
+{#2}\edef #2{\the \mpr@lista \the \mpr@listb}}
+
+\long \def\mpr@snoc #1\mpr@to#2{\mpr@lista {\\{#1}}\mpr@listb \expandafter
+{#2}\edef #2{\the \mpr@listb\the\mpr@lista}}
+
+\long \def \mpr@concat#1=#2\mpr@to#3{\mpr@lista \expandafter {#2}\mpr@listb
+\expandafter {#3}\edef #1{\the \mpr@listb\the\mpr@lista}}
+
+\def \mpr@head #1\mpr@to #2{\expandafter \mpr@head@ #1\mpr@head@ #1#2}
+\long \def \mpr@head@ #1#2\mpr@head@ #3#4{\def #4{#1}\def#3{#2}}
+
+\def \mpr@flatten #1\mpr@to #2{\expandafter \mpr@flatten@ #1\mpr@flatten@ #1#2}
+\long \def \mpr@flatten@ \\#1\\#2\mpr@flatten@ #3#4{\def #4{#1}\def #3{\\#2}}
+
+\def \mpr@makelist #1\mpr@to #2{\def \mpr@all {#1}%
+   \mpr@lista {\\}\mpr@listb \expandafter {\mpr@all}\edef \mpr@all {\the
+   \mpr@lista \the \mpr@listb \the \mpr@lista}\let #2\empty 
+   \def \mpr@stripof ##1##2\mpr@stripend{\def \mpr@stripped{##2}}\loop
+     \mpr@flatten \mpr@all \mpr@to \mpr@one
+     \expandafter \mpr@snoc \mpr@one \mpr@to #2\expandafter \mpr@stripof
+     \mpr@all \mpr@stripend  
+     \ifx \mpr@stripped \empty \let \mpr@isempty 0\else \let \mpr@isempty 1\fi
+     \ifx 1\mpr@isempty
+   \repeat
+}
+
+\def \mpr@rev #1\mpr@to #2{\let \mpr@tmp \empty
+   \def \\##1{\mpr@cons ##1\mpr@to \mpr@tmp}#1\let #2\mpr@tmp}
+
+%% Part III -- Type inference rules
+
+\newif \if@premisse
+\newbox \mpr@hlist
+\newbox \mpr@vlist
+\newif \ifmpr@center \mpr@centertrue
+\def \mpr@htovlist {%
+   \setbox \mpr@hlist
+      \hbox {\strut
+             \ifmpr@center \hskip -0.5\wd\mpr@hlist\fi
+             \unhbox \mpr@hlist}%
+   \setbox \mpr@vlist
+      \vbox {\if@premisse  \box \mpr@hlist \unvbox \mpr@vlist
+             \else \unvbox \mpr@vlist \box \mpr@hlist
+             \fi}%
+}
+% OLD version
+% \def \mpr@htovlist {%
+%    \setbox \mpr@hlist
+%       \hbox {\strut \hskip -0.5\wd\mpr@hlist \unhbox \mpr@hlist}%
+%    \setbox \mpr@vlist
+%       \vbox {\if@premisse  \box \mpr@hlist \unvbox \mpr@vlist
+%              \else \unvbox \mpr@vlist \box \mpr@hlist
+%              \fi}%
+% }
+
+\def \mpr@item #1{$\displaystyle #1$}
+\def \mpr@sep{2em}
+\def \mpr@blank { }
+\def \mpr@hovbox #1#2{\hbox
+  \bgroup
+  \ifx #1T\@premissetrue
+  \else \ifx #1B\@premissefalse
+  \else
+     \PackageError{mathpartir}
+       {Premisse orientation should either be T or B}
+       {Fatal error in Package}%
+  \fi \fi
+  \def \@test {#2}\ifx \@test \mpr@blank\else
+  \setbox \mpr@hlist \hbox {}%
+  \setbox \mpr@vlist \vbox {}%
+  \if@premisse \let \snoc \mpr@cons \else \let \snoc \mpr@snoc \fi
+  \let \@hvlist \empty \let \@rev \empty
+  \mpr@tmpdim 0em
+  \expandafter \mpr@makelist #2\mpr@to \mpr@flat
+  \if@premisse \mpr@rev \mpr@flat \mpr@to \@rev \else \let \@rev \mpr@flat \fi
+  \def \\##1{%
+     \def \@test {##1}\ifx \@test \empty
+        \mpr@htovlist
+        \mpr@tmpdim 0em %%% last bug fix not extensively checked
+     \else
+      \setbox0 \hbox{\mpr@item {##1}}\relax
+      \advance \mpr@tmpdim by \wd0
+      %\mpr@tmpdim 1.02\mpr@tmpdim
+      \ifnum \mpr@tmpdim < \hsize
+         \ifnum \wd\mpr@hlist > 0
+           \if@premisse
+             \setbox \mpr@hlist 
+                \hbox {\unhbox0 \hskip \mpr@sep \unhbox \mpr@hlist}%
+           \else
+             \setbox \mpr@hlist
+                \hbox {\unhbox \mpr@hlist  \hskip \mpr@sep \unhbox0}%
+           \fi
+         \else 
+         \setbox \mpr@hlist \hbox {\unhbox0}%
+         \fi
+      \else
+         \ifnum \wd \mpr@hlist > 0
+            \mpr@htovlist 
+            \mpr@tmpdim \wd0
+         \fi
+         \setbox \mpr@hlist \hbox {\unhbox0}%
+      \fi
+      \advance \mpr@tmpdim by \mpr@sep
+   \fi
+   }%
+   \@rev
+   \mpr@htovlist
+   \ifmpr@center \hskip \wd\mpr@vlist\fi \box \mpr@vlist
+   \fi
+   \egroup
+}
+
+%%% INFERENCE RULES
+
+\@ifundefined{@@over}{%
+    \let\@@over\over % fallback if amsmath is not loaded
+    \let\@@overwithdelims\overwithdelims
+    \let\@@atop\atop \let\@@atopwithdelims\atopwithdelims
+    \let\@@above\above \let\@@abovewithdelims\abovewithdelims
+  }{}
+
+%% The default
+
+\def \mpr@@fraction #1#2{\hbox {\advance \hsize by -0.5em
+    $\displaystyle {#1\mpr@over #2}$}}
+\def \mpr@@nofraction #1#2{\hbox {\advance \hsize by -0.5em
+    $\displaystyle {#1\@@atop #2}$}}
+
+\let \mpr@fraction \mpr@@fraction
+
+%% A generic solution to arrow
+
+\def \mpr@make@fraction #1#2#3#4#5{\hbox {%
+     \def \mpr@tail{#1}%
+     \def \mpr@body{#2}%
+     \def \mpr@head{#3}%
+     \setbox1=\hbox{$#4$}\setbox2=\hbox{$#5$}%
+     \setbox3=\hbox{$\mkern -3mu\mpr@body\mkern -3mu$}%
+     \setbox3=\hbox{$\mkern -3mu \mpr@body\mkern -3mu$}%
+     \dimen0=\dp1\advance\dimen0 by \ht3\relax\dp1\dimen0\relax
+     \dimen0=\ht2\advance\dimen0 by \dp3\relax\ht2\dimen0\relax
+     \setbox0=\hbox {$\box1 \@@atop \box2$}%
+     \dimen0=\wd0\box0
+     \box0 \hskip -\dimen0\relax
+     \hbox to \dimen0 {$%
+       \mathrel{\mpr@tail}\joinrel
+       \xleaders\hbox{\copy3}\hfil\joinrel\mathrel{\mpr@head}%
+     $}}}
+
+%% Old stuff should be removed in next version
+\def \mpr@@nothing #1#2
+    {$\lower 0.01pt \mpr@@nofraction {#1}{#2}$}
+\def \mpr@@reduce #1#2{\hbox
+    {$\lower 0.01pt \mpr@@fraction {#1}{#2}\mkern -15mu\rightarrow$}}
+\def \mpr@@rewrite #1#2#3{\hbox
+    {$\lower 0.01pt \mpr@@fraction {#2}{#3}\mkern -8mu#1$}}
+\def \mpr@infercenter #1{\vcenter {\mpr@hovbox{T}{#1}}}
+
+\def \mpr@empty {}
+\def \mpr@inferrule
+  {\bgroup
+     \ifnum \linewidth<\hsize \hsize \linewidth\fi
+     \mpr@rulelineskip
+     \let \and \qquad
+     \let \hva \mpr@hva
+     \let \@rulename \mpr@empty
+     \let \@rule@options \mpr@empty
+     \let \mpr@over \@@over
+     \mpr@inferrule@}
+\newcommand {\mpr@inferrule@}[3][]
+  {\everymath={\displaystyle}%       
+   \def \@test {#2}\ifx \empty \@test
+      \setbox0 \hbox {$\vcenter {\mpr@hovbox{B}{#3}}$}%
+   \else 
+   \def \@test {#3}\ifx \empty \@test
+      \setbox0 \hbox {$\vcenter {\mpr@hovbox{T}{#2}}$}%
+   \else
+   \setbox0 \mpr@fraction {\mpr@hovbox{T}{#2}}{\mpr@hovbox{B}{#3}}%
+   \fi \fi
+   \def \@test {#1}\ifx \@test\empty \box0
+   \else \vbox 
+%%% Suggestion de Francois pour les etiquettes longues
+%%%   {\hbox to \wd0 {\RefTirName {#1}\hfil}\box0}\fi
+      {\hbox {\RefTirName {#1}}\box0}\fi
+   \egroup}
+
+\def \mpr@vdotfil #1{\vbox to #1{\leaders \hbox{$\cdot$} \vfil}}
+
+% They are two forms
+% \inferrule [label]{[premisses}{conclusions}
+% or
+% \inferrule* [options]{[premisses}{conclusions}
+%
+% Premisses and conclusions are lists of elements separated by \\
+% Each \\ produces a break, attempting horizontal breaks if possible, 
+% and  vertical breaks if needed. 
+% 
+% An empty element obtained by \\\\ produces a vertical break in all cases. 
+%
+% The former rule is aligned on the fraction bar. 
+% The optional label appears on top of the rule
+% The second form to be used in a derivation tree is aligned on the last
+% line of its conclusion
+% 
+% The second form can be parameterized, using the key=val interface. The
+% folloiwng keys are recognized:
+%       
+%  width                set the width of the rule to val
+%  narrower             set the width of the rule to val\hsize
+%  before               execute val at the beginning/left
+%  lab                  put a label [Val] on top of the rule
+%  lskip                add negative skip on the right
+%  left                 put a left label [Val]
+%  Left                 put a left label [Val],  ignoring its width 
+%  right                put a right label [Val]
+%  Right                put a right label [Val], ignoring its width
+%  leftskip             skip negative space on the left-hand side
+%  rightskip            skip negative space on the right-hand side
+%  vdots                lift the rule by val and fill vertical space with dots
+%  after                execute val at the end/right
+%  
+%  Note that most options must come in this order to avoid strange
+%  typesetting (in particular  leftskip must preceed left and Left and
+%  rightskip must follow Right or right; vdots must come last 
+%  or be only followed by rightskip. 
+%  
+
+%% Keys that make sence in all kinds of rules
+\def \mprset #1{\setkeys{mprset}{#1}}
+\define@key {mprset}{andskip}[]{\mpr@andskip=#1}
+\define@key {mprset}{lineskip}[]{\lineskip=#1}
+\define@key {mprset}{flushleft}[]{\mpr@centerfalse}
+\define@key {mprset}{center}[]{\mpr@centertrue}
+\define@key {mprset}{rewrite}[]{\let \mpr@fraction \mpr@@rewrite}
+\define@key {mprset}{atop}[]{\let \mpr@fraction \mpr@@nofraction}
+\define@key {mprset}{myfraction}[]{\let \mpr@fraction #1}
+\define@key {mprset}{fraction}[]{\def \mpr@fraction {\mpr@make@fraction #1}}
+\define@key {mprset}{sep}{\def\mpr@sep{#1}}
+
+\newbox \mpr@right
+\define@key {mpr}{flushleft}[]{\mpr@centerfalse}
+\define@key {mpr}{center}[]{\mpr@centertrue}
+\define@key {mpr}{rewrite}[]{\let \mpr@fraction \mpr@@rewrite}
+\define@key {mpr}{myfraction}[]{\let \mpr@fraction #1}
+\define@key {mpr}{fraction}[]{\def \mpr@fraction {\mpr@make@fraction #1}}
+\define@key {mpr}{left}{\setbox0 \hbox {$\TirName {#1}\;$}\relax
+     \advance \hsize by -\wd0\box0}
+\define@key {mpr}{width}{\hsize #1}
+\define@key {mpr}{sep}{\def\mpr@sep{#1}}
+\define@key {mpr}{before}{#1}
+\define@key {mpr}{lab}{\let \RefTirName \TirName \def \mpr@rulename {#1}}
+\define@key {mpr}{Lab}{\let \RefTirName \TirName \def \mpr@rulename {#1}}
+\define@key {mpr}{narrower}{\hsize #1\hsize}
+\define@key {mpr}{leftskip}{\hskip -#1}
+\define@key {mpr}{reduce}[]{\let \mpr@fraction \mpr@@reduce}
+\define@key {mpr}{rightskip}
+  {\setbox \mpr@right \hbox {\unhbox \mpr@right \hskip -#1}}
+\define@key {mpr}{LEFT}{\setbox0 \hbox {$#1$}\relax
+     \advance \hsize by -\wd0\box0}
+\define@key {mpr}{left}{\setbox0 \hbox {$\TirName {#1}\;$}\relax
+     \advance \hsize by -\wd0\box0}
+\define@key {mpr}{Left}{\llap{$\TirName {#1}\;$}}
+\define@key {mpr}{right}
+  {\setbox0 \hbox {$\;\TirName {#1}$}\relax \advance \hsize by -\wd0
+   \setbox \mpr@right \hbox {\unhbox \mpr@right \unhbox0}}
+\define@key {mpr}{RIGHT}
+  {\setbox0 \hbox {$#1$}\relax \advance \hsize by -\wd0
+   \setbox \mpr@right \hbox {\unhbox \mpr@right \unhbox0}}
+\define@key {mpr}{Right}
+  {\setbox \mpr@right \hbox {\unhbox \mpr@right \rlap {$\;\TirName {#1}$}}}
+\define@key {mpr}{vdots}{\def \mpr@vdots {\@@atop \mpr@vdotfil{#1}}}
+\define@key {mpr}{after}{\edef \mpr@after {\mpr@after #1}}
+
+\newcommand \mpr@inferstar@ [3][]{\setbox0
+  \hbox {\let \mpr@rulename \mpr@empty \let \mpr@vdots \relax
+         \setbox \mpr@right \hbox{}%
+         $\setkeys{mpr}{#1}%
+          \ifx \mpr@rulename \mpr@empty \mpr@inferrule {#2}{#3}\else
+          \mpr@inferrule [{\mpr@rulename}]{#2}{#3}\fi
+          \box \mpr@right \mpr@vdots$}
+  \setbox1 \hbox {\strut}
+  \@tempdima \dp0 \advance \@tempdima by -\dp1
+  \raise \@tempdima \box0}
+
+\def \mpr@infer {\@ifnextchar *{\mpr@inferstar}{\mpr@inferrule}}
+\newcommand \mpr@err@skipargs[3][]{}
+\def \mpr@inferstar*{\ifmmode 
+    \let \@do \mpr@inferstar@
+  \else 
+    \let \@do \mpr@err@skipargs
+    \PackageError {mathpartir}
+      {\string\inferrule* can only be used in math mode}{}%
+  \fi \@do}
+
+
+%%% Exports
+
+% Envirnonment mathpar
+
+\let \inferrule \mpr@infer
+
+% make a short name \infer is not already defined
+\@ifundefined {infer}{\let \infer \mpr@infer}{}
+
+\def \TirNameStyle #1{\small \textsc{#1}}
+\def \tir@name #1{\hbox {\small \TirNameStyle{#1}}}
+\let \TirName \tir@name
+\let \DefTirName \TirName
+\let \RefTirName \TirName
+
+%%% Other Exports
+
+% \let \listcons \mpr@cons
+% \let \listsnoc \mpr@snoc
+% \let \listhead \mpr@head
+% \let \listmake \mpr@makelist
+
+
+
+
+\endinput

resource/Sources/Decription/mhsetup.sty

@@ -0,0 +1,166 @@
+%%
+%% This is file `mhsetup.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% mhsetup.dtx  (with options: `package')
+%% 
+%% It may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%   http://www.latex-project.org/lppl.txt
+%% and version 1.3 or later is part of all distributions of LaTeX
+%% version 2003/12/01 or later.
+%% 
+%% This work has the LPPL maintenance status "maintained".
+%% 
+%% The Current Maintainer of this work is Morten H\o gholm.
+%% 
+%% This work consists of the files mhsetup.dtx and mhsetup.ins and
+%% the derived file mhsetup.sty.
+%% 
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{mhsetup}
+  [2004/10/10 v1.0b programming setup (MH)]
+\def\MHInternalSyntaxOn{
+  \edef\MHInternalSyntaxOff{%
+  \catcode`\noexpand\~=\the\catcode`\~\relax
+  \catcode`\noexpand\ =\the\catcode`\ \relax
+  \catcode`\noexpand\^^I=\the\catcode`\^^I\relax
+  \catcode`\noexpand\@=\the\catcode`\@\relax
+  \catcode`\noexpand\:=\the\catcode`\:\relax
+  \catcode`\noexpand\_=\the\catcode`\_\relax
+  \endlinechar=\the\endlinechar\relax
+  }%
+  \catcode`\~=10\relax
+  \catcode`\ =9\relax
+  \catcode`\^^I=9\relax
+  \makeatletter
+  \catcode`\_=11\relax
+  \catcode`\:=11\relax
+  \endlinechar=` %
+  \relax
+}
+\MHInternalSyntaxOn
+\AtEndOfPackage{\MHInternalSyntaxOff}
+\let\MH_let:NwN \let
+\def\MH_let:cN #1#2{
+  \expandafter\MH_let:NwN \csname#1\endcsname#2}
+\def\MH_let:cc #1#2{
+  \expandafter\MH_let:NwN\csname#1\expandafter\endcsname
+  \csname#2\endcsname}
+\def\MH_new_boolean:n #1{
+  \expandafter\@ifdefinable\csname if_boolean_#1:\endcsname{
+    \@namedef{boolean_#1_true:}
+      {\MH_let:cN{if_boolean_#1:}\iftrue}
+    \@namedef{boolean_#1_false:}
+      {\MH_let:cN{if_boolean_#1:}\iffalse}
+    \@nameuse{boolean_#1_false:}%
+  }
+}
+\def\MH_set_boolean_F:n #1{ \@nameuse{boolean_#1_false:} }
+\def\MH_set_boolean_T:n #1{ \@nameuse{boolean_#1_true:} }
+\def\MH_if_boolean:nTF #1{
+  \@nameuse{if_boolean_#1:}
+    \expandafter\@firstoftwo
+  \else:
+    \expandafter\@secondoftwo
+  \fi:
+}
+\def\MH_if_boolean:nT #1{
+  \@nameuse{if_boolean_#1:}
+    \expandafter\@firstofone
+  \else:
+    \expandafter\@gobble
+  \fi:
+}
+\def\MH_if_boolean:nF #1{
+  \@nameuse{if_boolean_#1:}
+    \expandafter\@gobble
+  \else:
+    \expandafter\@firstofone
+  \fi:
+}
+\@ifundefined{if:w}{\MH_let:NwN \if:w =\if}{}
+\@ifundefined{if_meaning:NN}{\MH_let:NwN \if_meaning:NN =\ifx}{}
+\@ifundefined{else:}{\MH_let:NwN \else:=\else}{}
+\@ifundefined{fi:}{\MH_let:NwN \fi:=\fi}{}
+\@ifundefined{if_num:w}{\MH_let:NwN \if_num:w =\ifnum}{}
+\@ifundefined{if_dim:w}{\MH_let:NwN \if_dim:w =\ifdim}{}
+\@ifundefined{if_case:w}{\MH_let:NwN \if_case:w =\ifcase}{}
+\@ifundefined{or:}{\MH_let:NwN \or:=\or}{}
+\def\MH_cs_to_str:N {\expandafter\@gobble\string}
+\@ifundefined{eTeXversion}
+  {
+    \MH_let:NwN \MH_protected:\relax
+    \def\MH_setlength:dn{\setlength}
+    \def\MH_addtolength:dn{\addtolength}
+  }
+  {
+    \MH_let:NwN \MH_protected:\protected
+    \def\MH_setlength:dn #1#2{#1=\dimexpr#2\relax\relax}
+    \def\MH_addtolength:dn #1#2{\advance#1 \dimexpr#2\relax\relax}
+  }
+
+\def\MH_keyval_alias_with_addon:nnnn #1#2#3#4{
+  \@namedef{KV@#1@#2}{\@nameuse{KV@#1@#3}#4}
+  \@namedef{KV@#1@#2@default}{\@nameuse{KV@#1@#3@default}#4}}
+\def\MH_keyval_alias:nnn #1#2#3{
+  \MH_keyval_alias_with_addon:nnnn {#1}{#2}{#3}{}}
+\def\MH_use_choice_i:nnnn #1#2#3#4{#1}
+\def\MH_use_choice_ii:nnnn #1#2#3#4{#2}
+\def\MH_use_choice_iii:nnnn #1#2#3#4{#3}
+\def\MH_use_choice_iv:nnnn #1#2#3#4{#4}
+\long\def\MH_nospace_ifnextchar:Nnn #1#2#3{
+  \MH_let:NwN\reserved@d=~#1
+  \def\reserved@a{#2}
+  \def\reserved@b{#3}
+  \futurelet\@let@token\MH_nospace_nextchar:
+}
+\def\MH_nospace_nextchar:{
+  \if_meaning:NN \@let@token\reserved@d
+    \MH_let:NwN \reserved@b\reserved@a
+  \fi:
+  \reserved@b
+}
+\long\def\MH_nospace_testopt:nn #1#2{
+  \MH_nospace_ifnextchar:Nnn[
+    {#1}
+    {#1[{#2}]}
+}
+\def\MH_nospace_protected_testopt:n #1{
+  \if_meaning:NN \protect\@typeset@protect
+    \expandafter\MH_nospace_testopt:nn
+  \else:
+    \@x@protect#1
+  \fi:
+}
+\@ifundefined{kernel@ifnextchar}
+  {\MH_let:NwN \kernel@ifnextchar \@ifnextchar}
+  {}
+\MH_let:NwN \MH_kernel_xargdef:nwwn \@xargdef
+\long\def\MH_nospace_xargdef:nwwn #1[#2][#3]#4{
+  \@ifdefinable#1{
+     \expandafter\def\expandafter#1\expandafter{
+          \expandafter
+          \MH_nospace_protected_testopt:n
+          \expandafter
+          #1
+          \csname\string#1\endcsname
+          {#3}}
+       \expandafter\@yargdef
+          \csname\string#1\endcsname
+           \tw@
+           {#2}
+           {#4}}}
+\providecommand*\MHPrecedingSpacesOff{
+  \MH_let:NwN \@xargdef \MH_nospace_xargdef:nwwn
+}
+\providecommand*\MHPrecedingSpacesOn{
+  \MH_let:NwN \@xargdef \MH_kernel_xargdef:nwwn
+}
+\endinput
+%%
+%% End of file `mhsetup.sty'.