Finding local maxima for 3d matrix - matlab

Question

I am trying to implement Hough transform in Matlab to find circles in a picture.
In the accumulator matrix, the global maximum is 105 at A(32,31,24). So I'm able to get this: max circle
The problem is, how can i find the local maxima to find the rest of the circles?
I wrote this to find A(i,j,k) which is bigger than the 26 adjacent points (26-Connected voxel neighborhood):
[i j k]=find(A~=0) ;
f=0;
for s=1:size(i)
if(i(s)~=100&&j(s)~=100&&k(s)~=141&&i(s)~=1&&j(s)~=1&&k(s)~=1)
if (A(i(s),j(s),k(s))>A(i(s)-1,j(s),k(s))&&A(i(s),j(s),k(s))>A(i(s)+1,j(s),k(s))&&A(i(s),j(s),k(s))>A(i(s),j(s)-1,k(s))&&A(i(s),j(s),k(s))>A(i(s),j(s)+1,k(s))&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)-1,k(s))&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)+1,k(s))&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)+1,k(s))&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)-1,k(s))&&A(i(s),j(s),k(s))>A(i(s),j(s),k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s),k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s),k(s)+1)&&A(i(s),j(s),k(s))>A(i(s),j(s)-1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s),j(s)+1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)-1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)+1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)+1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)-1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s),j(s),k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s),k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s),k(s)-1)&&A(i(s),j(s),k(s))>A(i(s),j(s)-1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s),j(s)+1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)-1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)+1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)+1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)-1,k(s)-1))
f=f+1
i(s)
j(s)
k(s)
end
end
end
Why i never got these correct i,j,k and f is always 0? I think i should at least find (32,31,24) and f=1?
Can anyone help me ?
Thank you so much!
The complete code is here:
im=imread('C:\Users\dell\Desktop\tp-complet\Hough\four.png');
sigma = 0.3;
gausFilter = fspecial('gaussian',[5 5],sigma);
sobelFilter=fspecial('sobel');
img=imfilter(im,gausFilter,'replicate');
ims=edge(img,'sobel');
rmax=size(im,1);
cmax=size(im,2);
radmax=round(sqrt(rmax^2+cmax^2));
for i=1:rmax
for j=1:cmax
for k=1:radmax
A(i,j,k)=0;
end
end
end
[r c]=find(ims==1);
length=size(r);
for k=1:length
for l=1:rmax
for m=1:cmax
if((l~=r(k))&&(m~=c(k)))
x=sqrt((l-r(k))^2+(m-c(k))^2);
x=round(x);
A(l,m,x)=A(l,m,x)+1;
end
end
end
end
[i j k]=find(A~=0) ;
f=0;
for s=1:size(i)
if(i(s)~=100&&j(s)~=100&&k(s)~=141&&i(s)~=1&&j(s)~=1&&k(s)~=1)
if (A(i(s),j(s),k(s))>A(i(s)-1,j(s),k(s))&&A(i(s),j(s),k(s))>A(i(s)+1,j(s),k(s))&&A(i(s),j(s),k(s))>A(i(s),j(s)-1,k(s))&&A(i(s),j(s),k(s))>A(i(s),j(s)+1,k(s))&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)-1,k(s))&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)+1,k(s))&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)+1,k(s))&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)-1,k(s))&&A(i(s),j(s),k(s))>A(i(s),j(s),k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s),k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s),k(s)+1)&&A(i(s),j(s),k(s))>A(i(s),j(s)-1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s),j(s)+1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)-1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)+1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)+1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)-1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s),j(s),k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s),k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s),k(s)-1)&&A(i(s),j(s),k(s))>A(i(s),j(s)-1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s),j(s)+1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)-1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)+1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)+1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)-1,k(s)-1))
f=f+1
i(s)
j(s)
k(s)
end
end
end

Answer 1

I don't have the image processing toolbox, so cannot readily run your code. However, a quick review indicates to me that you're using the find function incorrectly. When provided with 3 outputs (as you have it), find doesn't return the 3D indices, but rather row, column, and a vector of the values. That means that k is just a giant vector of 1's, and so your for loop's if k(s)~=1 statement is never satisfied. You should do something like [i,j,k]=ind2sub(size(A),find(A~=0)) if you instead want the 3D indices.
Also, FYI, this:
for i=1:rmax
for j=1:cmax
for k=1:radmax
A(i,j,k)=0;
end
end
end
Can be replaced with A=zeros(rmax,cmax,radmax);.