在傅里叶域中设计Gabor滤波器组

Question

我正在尝试使用Matlab中的以下代码在傅里叶域中设计一个gabor滤波器组：

for i=1:u
 for j = 1:v
   theta =theta_list(j);
   w_1_x=(centerFreq(1,i)*((m+1)/2)*cos(theta)); % size of filter and image is m-by-n 
   w_1_y=(centerFreq(2,i)*((n+1)/2)*sin(theta));
   w_2_x=(-centerFreq(1,i)*((m+1)/2)*cos(theta));
   w_2_y=(-centerFreq(2,i)*((n+1)/2)*sin(theta));
   sigma=sqrt((w_1_x)^2+(w_1_y)^2);
   sigma_H=sigma/(2*pi);
   gF=fspecial('gaussian', [m,n], sigma_H);
   gFilter1=circshift(gF, [round(w_1_x), round(w_1_y)]);
   gFilter2=circshift(gF, [round(w_2_x), round(w_2_y)]);
   gaborArray1{i,j} = 0.5*gFilter1+0.5*gFilter2;
   gaborArray2{i,j} = 0.5*1i*gFilter1-0.5*1i*gFilter2;
   gaborFilterBank{i,j}=gaborArray1{i,j}+1i.*gaborArray2{i,j};
 end
end

但是，当我使用以下代码将滤镜转换为图像域并可视化滤镜的相位图时：

filter=ifft2(ifftshift(gaborFilterBank{i,j}));
phase=zeros(m, n);
for p=1:m
 for q=1:n
    phase(p,q)=atan(imag(filter(p,q)/real(filter(p,q)));
  end
end
figure, imshow(phase, []);

我在滤镜的中心出现了奇怪的图案（如附图所示）。你能让我知道我的代码有什么问题吗？

Answer 1

我发现了问题。而不是将中心坐标乘以[（m + 1）/ 2，（n + 1）/ 2]，我应该将它们乘以[m，n]。更具体地说，而不是：

w_1_x=(centerFreq(1,i)*((m+1)/2)*cos(theta)); % size of filter and image is m-by-n 
w_1_y=(centerFreq(2,i)*((n+1)/2)*sin(theta));
w_2_x=(-centerFreq(1,i)*((m+1)/2)*cos(theta));
w_2_y=(-centerFreq(2,i)*((n+1)/2)*sin(theta));

应该是：

w_1_x=(centerFreq(1,i)*m*cos(theta)); % size of filter and image is m-by-n 
w_1_y=(centerFreq(2,i)*n*sin(theta));
w_2_x=(-centerFreq(1,i)*m*cos(theta));
w_2_y=(-centerFreq(2,i)*n*sin(theta));