different results using imfilter and conv2

Question

Based on this question and this one I thought that "imfilter" and "conv2" should have the same results. But try this code you will see the differences. What is the problem?

I = imread('tire.tif');  
fil=[1 2 3;4 5 6;7 8 9];  
out1=conv2(double(I),fil,'same');  
out2=uint8(out1);  
out3=imfilter(I,fil,'same');

Answer 1

If you use imfilter(I,fil,'same','conv') then they are the same.

The difference is that imfilter uses correlation to filter images by default, which has some small differences - basically, convolution starts from one side of the image, whereas correlation starts from the other, so there is some small differences in the filter output. If you flip the image first, you get the same output:

out4=fliplr(flipud(imfilter(fliplr(flipud(I)),fil,'same')));

This is exactly equal to out2.

Answer 2

Your answer lies in the explanation of the fourth input argument to imfilter.

• Correlation and convolution

    'corr'       imfilter performs multidimensional filtering using
                 correlation, which is the same way that FILTER2
                 performs filtering.  When no correlation or
                 convolution option is specified, imfilter uses
                 correlation.

    'conv'       imfilter performs multidimensional filtering using
                 convolution.

Try out3=imfilter(I,fil,'same','conv'); and you'll get identical results to conv2.