2D Convolution - Sobel Filter. What is wrong?

img = imread('Davis_Hall.jpg');
% 'Davis_Hall.jpg':color image

img =double(rgb2gray(img));

Gx = double([-1 0 1;-2 0 2;-1 0 1]);
Gx=rot90(Gx,2);

Gy = double([-1 -2 -1; 0 0 0; 1 2 1]);
Gy=rot90(Gy,2);

I= img;

[r,c]=size(I);  

Fx = zeros(r,c);
Fy = zeros(r,c);

I = padarray(I,[1 1]);

for i=2:r-1
for j=2:c-1
Fx(i,j)=sum(sum(Gx.*I(i-1:i+1,j-1:j+1)));
Fy(i,j)=sum(sum(Gy.*I(i-1:i+1,j-1:j+1)));
end
end


img=uint8(img);
FMag=sqrt(Fx.^2+Fy.^2);


figure(1)
imshow(img);
title('Original Image');

figure(2)
imshow((abs(Fx))./max(max(Fx)));
title('Gradient in X direction');

figure(3)
imshow(abs(Fy)./max(max(Fy)));
title('Gradient in Y direction');

figure(4)
imshow(FMag./max(max(FMag)));
title('Gradient Magnitude');

% IT IS  Not Allowed to use: imfilter,  conv2,  filter2, conv 

Answer 1

[David Wilson]

Here's my (old) code for a sobel filter:

img = imread('Davis_Hall.jpg');
% 'Davis_Hall.jpg':color image
X =double(rgb2gray(img));

%% Start 

Bx = [-1,0,1;-2,0,2;-1,0,1]; % Sobel Gx kernel
By = Bx'; % gradient Gy
Yx = filter2(Bx,X); % convolve in 2d
Yy = filter2(By,X);

G = sqrt(Yy.^2 + Yx.^2); % Find magnitude
Gmin = min(min(G)); dx = max(max(G)) - Gmin; % find range
G = floor((G-Gmin)/dx*255); % normalise from 0 to 255
image(G); axis('image')
colormap gray

Gives the following:

[Nisreen Sulayman]

IT IS Not Allowed to use: imfilter, conv2, filter2, conv

[David Wilson]

Ah, then this is homework?

[Nisreen Sulayman]

It is a graded excercise\online course.

Answer 2

[Nisreen Sulayman]

Here is my results:

[Bruno Luong]

Why you think there is anything wrong?

I see aliasing but it might cause to the way you capture/attach image here.

[Nisreen Sulayman]

It is a graded excercise\online course.

I didn't pass.

[Bruno Luong]

Well sorry the only thing I detect is

Gx=rot90(Gx,2);
Gy=rot90(Gy,2);

That reverse the sign of the gradient. But there is no consequence on edge detection.

[Nisreen Sulayman]

I've tried to follow this:

https://uk.mathworks.com/help/images/what-is-image-filtering-in-the-spatial-domain.html

[Bruno Luong]

I know now what induce you the error. Using CONVOLUTION with flipped the kernel == filter with "straight" kernel.

In your double for-loop you perform filtering (and not convolution), so you must not flip (rotate 180 degree = flip-x/flip-y) Gx, Gy.

[Nisreen Sulayman]

I have commented the rotation ... Still have the error.

[Nisreen Sulayman]

[Bruno Luong]

The second error I spot is the way you deal with padding and boundary

IMO the loop and padding should be (not tested)

[r,c]=size(I);  
Fx = zeros(r,c);
Fy = zeros(r,c);
I = padarray(I,[1 1],'replicate'); % lass abrute than 0
for i=1:r
    for j=1:c
        Fx(i,j)=sum(sum(Gx.*I(i:i+2,j:j+2)));
        Fy(i,j)=sum(sum(Gy.*I(i:i+2,j:j+2)));
        end
end

[Nisreen Sulayman]

Didn't work!!

Maybe there is something wrong related to the "greader"

We have a good results ... still didn't accept the answer!! (even with first code I have a good results!!)

OR THERE is that kind of silly bug which I couldn't spot.

[Nisreen Sulayman]

How to normalize a convolved image?

I have got these messages after running

%read the image
img = imread('Davis_Hall.jpg');
I =double(rgb2gray(img));

%Gx = double([-1 0 1;-2 0 2;-1 0 1]);
Gx=[-1 0 1;-2 0 2;-1 0 1];
Gx=rot90(Gx,2);

%Gy = double([-1 -2 -1; 0 0 0; 1 2 1]);
Gy=[-1 -2 -1; 0 0 0;1 2 1];
Gy=rot90(Gy,2);

[r,c]=size(I);  
Fx = zeros(r,c);
Fy = zeros(r,c);
FMag=zeros(r,c);

I = padarray(I,[1 1],0,'both'); 

for i=2:r-1
    for j=2:c-1
        Fx(i,j)=sum(sum(Gx.*I(i-1:i+1,j-1:j+1)));
        Fy(i,j)=sum(sum(Gy.*I(i-1:i+1,j-1:j+1)));
        FMag(i,j)=sqrt(power(Fx(i,j),2)+power(Fy(i,j),2));
    end
end

Fx=Fx(2:r-1,2:c-1);
Fy=Fy(2:r-1,2:c-1);
FMag=FMag(2:r-1,2:c-1);

img=uint8(img);

figure(1)
imshow(img);
title('Original Image');

figure(2)
imshow((abs(Fx))./max(max(Fx)));
title('Gradient in X direction');

figure(3)
imshow(abs(Fy)./max(max(Fy)));
title('Gradient in Y direction');

figure(4)
imshow(FMag./max(max(FMag)));
title('Gradient Magnitude');

%Fx may have negative values and values which are greater than 255, hence normalize before visualiz

%Fy may have negative values and values which are greater than 255, hence normalize before visualizin

%FMag may have values which are greater than 255, hence normalize before visualizing