# 2D Convolution - Sobel Filter. What is wrong?

241 views (last 30 days)
Nisreen Sulayman on 11 Sep 2019
Commented: Nisreen Sulayman on 20 Sep 2019
% '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);
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)));
figure(3)
imshow(abs(Fy)./max(max(Fy)));
figure(4)
imshow(FMag./max(max(FMag)));
% IT IS Not Allowed to use: imfilter, conv2, filter2, conv

David Wilson on 12 Sep 2019
Here's my (old) code for a sobel filter:
% '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 on 12 Sep 2019
IT IS Not Allowed to use: imfilter, conv2, filter2, conv
David Wilson on 12 Sep 2019
Ah, then this is homework?
Nisreen Sulayman on 12 Sep 2019
It is a graded excercise\online course.

Nisreen Sulayman on 12 Sep 2019
Here is my results:

Bruno Luong on 12 Sep 2019
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 on 13 Sep 2019
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 on 20 Sep 2019
How to normalize a convolved image?
I have got these messages after running
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);
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)));
figure(3)
imshow(abs(Fy)./max(max(Fy)));
figure(4)
imshow(FMag./max(max(FMag)));
%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