GSoC 2013: imerode and imdilate (update #6)

Since I deviated so much from the original project while fixing the image IO functions in Octave core, I decided to only focus on optimizing the imerode and imdilate in the final phase of GSoC. The reason is that these are at the core of many functions in the image package.

On the original project it was planned to do all the work by expanding the __spatial_filtering__ function and that's where I previously started. While doing so, it became evident that a complete rewrite was necessary. The convn() which could be used in most cases of binary images was performing much faster even though it was performing a more complex operation. As such, performing at least as fast as convn() became the target which was achieved:

octave> se = [0 1 0; 1 1 1; 0 1 0];
octave> im = rand (1000) > 0.5;
octave> t = cputime (); for i = 1:100, a = imerode (im, se, "same"); endfor; cputime() - t
ans = 2.1281
octave> t = cputime (); for i = 1:100, a = convn (im, se, "same") == nnz (se); endfor; cputime() - t
ans = 2.7802

This implementation could be reused in __spatial_filtering__ to also speed up functions such as medfilt2, ordfilt2, and ordfiltn but there are specific algorithms for those cases which should be used instead.

I have tested the new implementation of imerode against the last release (version 2.0.0) and the last development version that was still making use of __spatial_filtering__ (cset 6db5e3c6759b). The tests are very simple (test imerode), just random matrices with different number of dimensions. The new implementation seems to perform much faster in all cases, and shows a performance increase between 1.5-30x (output of test imerode). The differences are bigger for grayscale images (since imerode was already using convn for binary cases), and larger structuring elements (SE) with multiple dimensions.

A couple of things:

• in the latest release of the image package (version 2.0.0), there was no erosion for multidimensional binary images (only grayscale);
• both development versions make use of the new strel class. One of the things that it does, its to decompose structuring elements automatically, hence why the tests use a cross rather than a square for SE;
• I'm only testing with the shape "same" since version 2.0.0 only had that one;
• when using binary images I test with different percentages of true values since the new implementation is sensitive to it;
• I do not compare the results since I know the new implementations also fix some bugs, specially related to the border pixels.
• imdilate uses exactly the same code and so I'm assuming that the differences from imerode are the same.