index exceeds matrix dimension in image convolution

function y=convolve(Im,H) %#ok<*STOUT,*INUSD>
In=imread(Im);
I=im2double(In);
[rows,columns]=size(I); %#ok<*NOPRT,*ASGLU>
[rowsx,columnsx]=size(H);
C=0;
a=0;
b=0;
rowsy=rows-rowsx+1;
columnsy=columns-columnsx+1;
c=zeros(rowsy,columnsy);
for k=1:1:rowsy-1
  for p=1:1:columnsy-1
      for i=1:1:rowsx
          for j=1:1:columnsx
              T=I(i+a,j+b)*H(i,j);
              C=C+T;
          end
      end
      c(k,p)=C;
      b=b+1;
  end
  a=a+1;
end
y=c;

Hi there, I am trying to code a two dimensional matrix convolution. However when I run this code there is an error: Index exceeds matrix dimensions.

Error in convolve (line 17) T=I(i+a,j+b)*H(i,j); But I cannot find where is wrong, can any one help? Thanks.

Answer 1

[Walter Roberson]

You have

I(i+a,j+b)

when i can be up to size(I,1) and j can be up to numels(I)/size(I,1) . Which, incidentally, is only the same as size(I,2) if I is two dimensional, which in turn implies that I is a grayscale image. Using size() the way you did is wrong for images that can be RGB.

Anyhow, suppose that the image is 2D so i can be up to the number of rows, and j can be up to the number of columns. But when i is equal to the number of rows, then i+a will be past the last row unless a is 0 (or negative), and j+b will be past the last column unless b is 0 (or negative.) But you have b=b+1; so b can become 1. When b does become 1, then as soon as j becomes columnsx, then j+1 would be past the end of I

Convolution with an array or vector produces a result that is larger than the original matrix. Have a look at the documentation for conv2() at the 'full' and 'same' and 'valid' options there, which are three different approaches for dealing with the size of output to be returned.

[mingchuan zhao]

 rowsy=rows-rowsx+1;
columnsy=columns-columnsx+1;
c=zeros(rowsy,columnsy);
for k=1:1:rowsy-1
  for p=1:1:columnsy-1
      for i=1:1:rowsx
          for j=1:1:columnsx
              T=I(i+a,j+b)*H(i,j);
              C=C+T;

I think i,j are for the filter. k,p for the image,so i,j wouldn't change,only a,b change,and I have written rowsy=rows-rowsx+1; columnsy=columns-columnsx+1; so I don't think convolution will produce a result larger than original matix.

[Walter Roberson]

At the command line command

dbstop if error

and run again. When it stops, look at i, a, j, b, and size(I) and size(H)