This is my expected output.
But, I am getting the following output.
What is wrong with my source code?
Source Code
main.m
clear_all();
I = gray_imread('woman.png');
d0 = 1;
d1 = 100;
n = 20;
J = butter_bandpass(I, d0, d1,n);
J = histeq(J);
K = {I, J};
imshowpair(I, J, 'montage');
butter_bandpass.m
function output_image = butter_bandpass(I, dL, dH,n)
I_double = double(I);
[Height, Width] = size(I_double);
I_double = uint8(I_double);
I_fft = fft2(I_double,2*Height-1,2*Width-1);
I_fft = fftshift(I_fft);
LowPass = ones(2*Height-1,2*Width-1);
HighPass = ones(2*Height-1,2*Width-1);
Kernel = ones(2*Height-1,2*Width-1);
for i = 1:2*Height-1
for j =1:2*Width-1
D = ((i-(Height+1))^2 + (j-(Width+1))^2)^.5;
LowPass(i,j)= 1/(1 + (D/dH)^(2*n));
HighPass(i,j)= 1 - (1/(1 + (D/dL)^(2*n)));
% Create Butterworth filter.
Kernel(i,j) = LowPass(i,j).*HighPass(i,j);
end
end
% apply filter to image
output_image = I_fft + Kernel.*I_fft;
% revert the image to spatial domain
output_image = ifftshift(output_image);
output_image = ifft2(output_image,2*Height-1,2*Width-1);
output_image = real(output_image(1:Height,1:Width));
output_image = uint8(output_image);
end
I have solved this problem.
Output
Refer to this low-pass-filter, and this high-pass-filter source codes.
Since, we know that BPF(band-pass-filter) = LPF * HPF, we can implement a bandpass filter as follows,
Source Code
main.m
clear_all();
I = gray_imread('woman.png');
Dl = 70;
Dh = 70;
n = 1;
[J, K] = butterworth_bpf(I, Dh, Dl, n);
J = histeq(J);
imshowpair(I, J, 'montage');
butter_bp_kernel.m
function k = butter_bp_kernel(I, Dh, Dl, n)
hp_kernel = butter_hp_kernel(I, Dh, n);
lp_kernel = butter_lp_kernel(I, Dl, n);
k = hp_kernel.*lp_kernel; % here is the multiplication
butterworth_bpf.m
function [out1, out2] = butterworth_bpf(I, Dh, Dl, n)
Kernel = butter_bp_kernel(I, Dh, Dl, n);
I_ffted_shifted = fftshift(fft2(I));
I_ffted_shifted_filtered = I_ffted_shifted.*Kernel;
out1 = ifftshow(ifft2(I_ffted_shifted_filtered));
out2 = ifft2(ifftshift(I_ffted_shifted_filtered));
end