How to transform a FFT (Fast Fourier Transform) into a Polar Transformation with Python?

Question

I was able to create a FFT Transformation from my image but I don't know how to continue...

I am using this to solve my problem: Align text for OCR

This code was all that worked for me until now:

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

%matplotlib inline

img = cv2.imread(r'test.jpg', cv2.IMREAD_GRAYSCALE)

f = np.fft.fft2(img)
fshift = np.fft.fftshift(f)
magnitude_spectrum = 20 * np.log(np.abs(fshift))

plt.subplot(121), plt.imshow(img, cmap='gray')
plt.title('Input Image'), plt.xticks([]), plt.yticks([])

plt.subplot(122), plt.imshow(magnitude_spectrum, cmap='gray')
plt.title('Magnitude Spectrum'), plt.xticks([]), plt.yticks([])

plt.show()

I need the mean value generated from a Polar Transformation, but I don't know how to transform a FFT to a Polar Transformation in Python.

Answer 1

这大致可以解决您的问题；在一个样本图像上进行了测试，结果看起来是可信的。

# your code goes here... 

def transform_data(m):
    dpix, dpiy = m.shape
    x_c, y_c = np.unravel_index(np.argmax(m), m.shape)
    angles = np.linspace(0, np.pi*2, min(dpix, dpiy))
    mrc = min(abs(x_c - dpix), abs(y_c - dpiy), x_c, y_c)
    radiuses = np.linspace(0, mrc, max(dpix, dpiy))
    A, R = np.meshgrid(angles, radiuses)
    X = R * np.cos(A)
    Y = R * np.sin(A)
    return A, R, m[X.astype(int) + mrc - 1, Y.astype(int) + mrc - 1]

    angles, radiuses, m = transform_data(magnitude_spectrum)

    plt.contourf(angles, radiuses, m)

最后，我们可以得到想要旋转原始图像的角度：

sample_angles = np.linspace(0,  2 * np.pi, len(c.sum(axis=0))) / np.pi*180
turn_angle_in_degrees = 90 - sample_angles[np.argmax(c.sum(axis=0))]

对于我的示例图像，我得到了：

turn_angle_in_degrees = 3.2015810276679844 degrees.

此外，我们可以绘制投影频谱幅度：

plt.plot(sample_angles, c.sum(axis=0))

希望有帮助...