How can I create a custom band-pass filter?

Question

In this research paper, in the Section 4.1(Preprocessing), an equation of a Bandpass filter is given:

Where,

Now, I have implemented this like the following:

https://dotnetfiddle.net/ZhucE2

But, this code produces nothing.

Answer 1

You need to create image of your kernel, then to convolve it with your image. fft is used for optimization of convolution for large images. You can use filter2D function to make opencv do everything for you.

Kernel image:

Source image:

Convolution applied:

Trhesholding:

Please see code below:

import cv2
import math
import numpy as np

class Kernel(object):
    def H_Function(self, Dh, Dv, u, v, centerX, centerY, theta, n):
        return 1 / (1 + 0.414 * math.sqrt(math.pow(self.U_Star(u, centerX, centerY, theta) / Dh + self.V_Star(v, centerX, centerY, theta) / Dv, 2 * n)))

    def U_Star(self, u, centerX, centerY, theta):
        return math.cos(theta) * (u + self.Tx(centerX, theta)) + math.sin(theta) * (u + self.Ty(centerY, theta))

    def V_Star(self, u, centerX, centerY, theta):
        return (-math.sin(theta)) * (u + self.Tx(centerX, theta)) + math.cos(theta) * (u + self.Ty(centerY, theta))

    def Tx(self, center, theta):
        return center * math.cos(theta)

    def Ty(self, center, theta):
        return center * math.sin(theta)

K = Kernel()

size = 40, 40
kernel = np.zeros(size, dtype=np.float)
Dh=2
Dv=2
centerX = -size[0] / 2
centerY = -size[1] / 2
theta=0.9
n=4

for u in range(0, size[0]):
    for v in range(0, size[1]):
        kernel[u][v] = K.H_Function(Dh, Dv, u, v, centerX, centerY, theta, n) 
kernelNorm = np.copy(kernel)
cv2.normalize(kernel, kernel, 1.0, 0, cv2.NORM_L1)
cv2.normalize(kernelNorm, kernelNorm, 0, 255, cv2.NORM_MINMAX)
cv2.imwrite("kernel.jpg", kernelNorm)

imgSrc = cv2.imread('src.jpg',0)

convolved = cv2.filter2D(imgSrc,-1,kernel)
cv2.normalize(convolved, convolved, 0, 255, cv2.NORM_MINMAX)
cv2.imwrite("conv.jpg", convolved)
th, thresholded = cv2.threshold(convolved, 100, 255, cv2.THRESH_BINARY)
cv2.imwrite("thresh.jpg", thresholded)