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