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Computational NotesWhen implementing a convolution or correlation algorithm, there are certain important things you should think about. Firstly, since this a neighbourhood operation, not all pixels in the original image are going to have a complete neighbour (border pixels) so you need a way to deal with these. The most common way is just to ignore them and have an output image slightly smaller than the input. Other techniques include truncating the kernel to process the edge pixels correctly, but this can be complex to implement.The second, most important factor is efficiency. Any programmer will have noticed that the convolution algorithm is naturally costly since it requires retrieval of the neighbourhood, then numerous operations upon that neighbourhood. The most common way to cut down the operation is to take into account the shifting window of operation. You can see that the neighbourhood in the first iteration (left) and the neighbourhood in the second iteration (right) share twothirds of the same values. If the algorithm takes this into account, it is only necessary to make 3 retrievals instead of 9. Savings are even more significant when the kernels are bigger (i.e., for 11x11 kernels, 11 retrievals are made instead of 121!). As always, see Image Analysis Explorer Pro for examples and code.
Submitted: 30/08/2002 Article content copyright © James Matthews, 2002.


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