如何使用 opencv python 反演具有幅度的 DFT
How to inverse a DFT with magnitude with opencv python
我是这一切的新手，我想从图像中获取幅度谱，然后从修改后的幅度谱中重建图像。但是现在我正在进行非常暗的重建。
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
你们能帮我看看为什么这么黑吗？
提前致谢:)
编辑
我尝试对图像进行标准化，但没有用。我的图像仍然很暗。
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后的版本重建图像。
您应该在不应用日志的情况下从 cartToPolar() 中提取幅度和相位图像。然后单独做日志只查看频谱，保持其原始形式的大小。然后在进行反 dft 之前根据需要修改原始大小。
另一个问题是往返图像需要重新缩放回 8 位范围和数据类型。我用 cv2.normalize() 来做到这一点。您可以从打印的最小值和最大值中看出这一点。
下面是如何做 dft，得到频谱然后在 Python/OpenCV 中做逆 dft。我从彩色图像开始，但在读入时将其转换为灰度图像。最终返回的往返行程 dft/idft 仍将是灰度图像。
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
# 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("ORIGINAL DFT/IFT ROUND TRIP", img_back)
cv2.waitKey(0)
cv2.destroyAllWindows()
# write result to disk
cv2.imwrite("lena_dft_ift_opencv.png", img_back)
结果：
如果您需要通过将幅度提高到接近 1 的幂来修改幅度（称为系数求根或 alpha 求根），那么它只是使用 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）：
以下是如何使用 Python/OpenCV
在傅立叶域中使用陷波滤波从图像中去除重复图案噪声
- 阅读图片
- 进行 DFT
- 从实部和虚部生成幅度和相位分量
- 根据震级创建频谱
- 对光谱图像进行阈值处理，使蒙版覆盖阈值图像中心的黑色区域
- 将掩码应用于幅度
- 合并新的幅度和原始相位
- 将它们转换为实部和虚部
- 进行 IDFT
- 保存结果
具有重复图案噪声的输入：
import numpy as np
import cv2
# read input as grayscale
img = cv2.imread('clown.jpg', 0)
# get min and max values of img
img_min, img_max = np.amin(img, (0,1)), np.amax(img, (0,1))
print(img_min,img_max)
# 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
spec = np.log(mag) / 20
# create mask from spectrum keeping only the brightest spots as the notches
mask = cv2.normalize(spec, None, alpha=0, beta=1, norm_type=cv2.NORM_MINMAX)
mask = cv2.threshold(mask, 0.65, 1, cv2.THRESH_BINARY)[1]
# dilate mask
kernel = cv2.getStructuringElement(cv2.MORPH_ELLIPSE, (3,3))
mask = cv2.morphologyEx(mask, cv2.MORPH_DILATE, kernel)
# cover center DC component by circle of black leaving only a few white spots on black background
xcenter = mask.shape[1] // 2
ycenter = mask.shape[0] // 2
mask = cv2.circle(mask, (xcenter,ycenter), radius=10, color=0, thickness=cv2.FILLED)
# apply mask to magnitude such that magnitude is made zero where mask is one, ie at spots
mag[mask!=0] = 0
# convert new magnitude and old 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 in range of original
min, max = np.amin(img_back, (0,1)), np.amax(img_back, (0,1))
print(min,max)
notched = cv2.normalize(img_back, None, alpha=img_min, beta=img_max, 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("MASK", mask)
cv2.imshow("NOTCHED", notched)
cv2.waitKey(0)
cv2.destroyAllWindows()
# write result to disk
cv2.imwrite("clown_mask.png", (255*mask).clip(0,255).astype(np.uint8))
cv2.imwrite("clown_notched.png", notched)
频谱：
掩码：
陷波滤波结果（去除噪声）：
动画（使用 Imagemagick 单独创建）：
我是这一切的新手，我想从图像中获取幅度谱，然后从修改后的幅度谱中重建图像。但是现在我正在进行非常暗的重建。
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
你们能帮我看看为什么这么黑吗？
提前致谢:)
编辑
我尝试对图像进行标准化，但没有用。我的图像仍然很暗。
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后的版本重建图像。
您应该在不应用日志的情况下从 cartToPolar() 中提取幅度和相位图像。然后单独做日志只查看频谱，保持其原始形式的大小。然后在进行反 dft 之前根据需要修改原始大小。
另一个问题是往返图像需要重新缩放回 8 位范围和数据类型。我用 cv2.normalize() 来做到这一点。您可以从打印的最小值和最大值中看出这一点。
下面是如何做 dft，得到频谱然后在 Python/OpenCV 中做逆 dft。我从彩色图像开始，但在读入时将其转换为灰度图像。最终返回的往返行程 dft/idft 仍将是灰度图像。
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
# 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("ORIGINAL DFT/IFT ROUND TRIP", img_back)
cv2.waitKey(0)
cv2.destroyAllWindows()
# write result to disk
cv2.imwrite("lena_dft_ift_opencv.png", img_back)
结果：
如果您需要通过将幅度提高到接近 1 的幂来修改幅度（称为系数求根或 alpha 求根），那么它只是使用 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）：
以下是如何使用 Python/OpenCV
在傅立叶域中使用陷波滤波从图像中去除重复图案噪声- 阅读图片
- 进行 DFT
- 从实部和虚部生成幅度和相位分量
- 根据震级创建频谱
- 对光谱图像进行阈值处理，使蒙版覆盖阈值图像中心的黑色区域
- 将掩码应用于幅度
- 合并新的幅度和原始相位
- 将它们转换为实部和虚部
- 进行 IDFT
- 保存结果
具有重复图案噪声的输入：
import numpy as np
import cv2
# read input as grayscale
img = cv2.imread('clown.jpg', 0)
# get min and max values of img
img_min, img_max = np.amin(img, (0,1)), np.amax(img, (0,1))
print(img_min,img_max)
# 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
spec = np.log(mag) / 20
# create mask from spectrum keeping only the brightest spots as the notches
mask = cv2.normalize(spec, None, alpha=0, beta=1, norm_type=cv2.NORM_MINMAX)
mask = cv2.threshold(mask, 0.65, 1, cv2.THRESH_BINARY)[1]
# dilate mask
kernel = cv2.getStructuringElement(cv2.MORPH_ELLIPSE, (3,3))
mask = cv2.morphologyEx(mask, cv2.MORPH_DILATE, kernel)
# cover center DC component by circle of black leaving only a few white spots on black background
xcenter = mask.shape[1] // 2
ycenter = mask.shape[0] // 2
mask = cv2.circle(mask, (xcenter,ycenter), radius=10, color=0, thickness=cv2.FILLED)
# apply mask to magnitude such that magnitude is made zero where mask is one, ie at spots
mag[mask!=0] = 0
# convert new magnitude and old 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 in range of original
min, max = np.amin(img_back, (0,1)), np.amax(img_back, (0,1))
print(min,max)
notched = cv2.normalize(img_back, None, alpha=img_min, beta=img_max, 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("MASK", mask)
cv2.imshow("NOTCHED", notched)
cv2.waitKey(0)
cv2.destroyAllWindows()
# write result to disk
cv2.imwrite("clown_mask.png", (255*mask).clip(0,255).astype(np.uint8))
cv2.imwrite("clown_notched.png", notched)
频谱：
掩码：
陷波滤波结果（去除噪声）：
动画（使用 Imagemagick 单独创建）：