python - 如何使用opencv python反转具有幅度的DFT

Question

我对这一切都很陌生，我想从图像中获取幅度谱，然后从修改后的幅度谱重建图像..但现在我得到了一个非常暗的重建。

import numpy as np
import cv2
from matplotlib import pyplot as plt

img = cv2.imread('IMG.jpg',0)

dft = cv2.dft(np.float32(img),flags = cv2.DFT_COMPLEX_OUTPUT)
dft_shift = np.fft.fftshift(dft)

m, a = np.log(cv2.cartToPolar(dft_shift[:,:,0],dft_shift[:,:,1]))

# do somthing with m

x, y = cv2.polarToCart(np.exp(m), a)


back = cv2.merge([x, y])


f_ishift = np.fft.ifftshift(back)
img_back = cv2.idft(f_ishift)
img_back = cv2.magnitude(img_back[:,:,0],img_back[:,:,1])

plt.subplot(131),plt.imshow(img, cmap = 'gray')
plt.title('Input Image'), plt.xticks([]), plt.yticks([])
plt.subplot(132),plt.imshow(m, cmap = 'gray')
plt.title('Magnitude Spectrum'), plt.xticks([]), plt.yticks([])
plt.subplot(133),plt.imshow(img_back, cmap = 'gray')
plt.title('result'), plt.xticks([]), plt.yticks([])
plt.show()

结果



你们能帮我弄清楚为什么这么黑吗？

预先感谢 :)

编辑

我试图标准化图像，但它不起作用。我仍然有一个非常暗的图像。

import numpy as np
import cv2
from matplotlib import pyplot as plt

img = cv2.imread('IMG.jpg',0)

dft = cv2.dft(np.float32(img),flags = cv2.DFT_COMPLEX_OUTPUT)
dft_shift = np.fft.fftshift(dft)

m, a = np.log1p(cv2.cartToPolar(dft_shift[:,:,0],dft_shift[:,:,1]))

# modify m, then use the modify m to reconstruct


x, y = cv2.polarToCart(np.expm1(m), a)


back = cv2.merge([x, y])


f_ishift = np.fft.ifftshift(back)
img_back = cv2.idft(f_ishift, flags=cv2.DFT_SCALE)
img_back = cv2.magnitude(img_back[:,:,0],img_back[:,:,1])


min, max = np.amin(img, (0,1)), np.amax(img, (0,1))
print(min,max)

# re-normalize to 8-bits
min, max = np.amin(img_back, (0,1)), np.amax(img_back, (0,1))
print(min,max)
img_back = cv2.normalize(img_back, None, alpha=0, beta=252, norm_type=cv2.NORM_MINMAX, dtype=cv2.CV_8U)


min, max = np.amin(img_back, (0,1)), np.amax(img_back, (0,1))
print(min,max)


plt.subplot(131),plt.imshow(img, cmap = 'gray')
plt.title('Input Image'), plt.xticks([]), plt.yticks([])
plt.subplot(132),plt.imshow(m, cmap = 'gray')
plt.title('Magnitude Spectrum'), plt.xticks([]), plt.yticks([])
plt.subplot(133),plt.imshow(img_back, cmap = 'gray')
plt.title('result'), plt.xticks([]), plt.yticks([])
plt.show()
cv2.waitKey(0)
cv2.destroyAllWindows()

输出:

0 252
0.36347726 5867.449
0 252

我想修改幅度谱并使用修改版本来重建图像。

Answer 1

如果您需要通过将其提高到接近 1 的幂来修改幅度(称为系数生根或 alpha 生根)，那么这只是使用 Python/OpenCV 对我上面的代码进行的简单修改。在将幅度和相位转换回实部和虚部之前，只需添加 cv2.pow(mag, 1.1)。

输入:

import numpy as np
import cv2

# read input as grayscale
img = cv2.imread('lena.png', 0)

# convert image to floats and do dft saving as complex output
dft = cv2.dft(np.float32(img), flags = cv2.DFT_COMPLEX_OUTPUT)

# apply shift of origin from upper left corner to center of image
dft_shift = np.fft.fftshift(dft)

# extract magnitude and phase images
mag, phase = cv2.cartToPolar(dft_shift[:,:,0], dft_shift[:,:,1])

# get spectrum for viewing only
spec = np.log(mag) / 30

# NEW CODE HERE: raise mag to some power near 1
# values larger than 1 increase contrast; values smaller than 1 decrease contrast
mag = cv2.pow(mag, 1.1)

# convert magnitude and phase into cartesian real and imaginary components
real, imag = cv2.polarToCart(mag, phase)

# combine cartesian components into one complex image
back = cv2.merge([real, imag])

# shift origin from center to upper left corner
back_ishift = np.fft.ifftshift(back)

# do idft saving as complex output
img_back = cv2.idft(back_ishift)

# combine complex components into original image again
img_back = cv2.magnitude(img_back[:,:,0], img_back[:,:,1])

# re-normalize to 8-bits
min, max = np.amin(img_back, (0,1)), np.amax(img_back, (0,1))
print(min,max)
img_back = cv2.normalize(img_back, None, alpha=0, beta=255, norm_type=cv2.NORM_MINMAX, dtype=cv2.CV_8U)

cv2.imshow("ORIGINAL", img)
cv2.imshow("MAG", mag)
cv2.imshow("PHASE", phase)
cv2.imshow("SPECTRUM", spec)
cv2.imshow("REAL", real)
cv2.imshow("IMAGINARY", imag)
cv2.imshow("COEF ROOT", img_back)
cv2.waitKey(0)
cv2.destroyAllWindows()

# write result to disk
cv2.imwrite("lena_grayscale_opencv.png", img)
cv2.imwrite("lena_grayscale_coefroot_opencv.png", img_back)

原始灰度:



系数求根结果:



这是显示差异的动画(使用 ImageMagick 创建):