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Image Analysis and Mathematical Morphology
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Slope transforms: theory and application to nonlinear signalprocessing
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CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
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Rank-convolutions have important applications in a variety of areas such as signal processing and computer vision. We define a mask as a function taking only values zero and infinity. Rank-convolutions with masks are of special interest to image processing. We show how to compute the rank-k convolution of a function over an interval of length n with an arbitrary mask of length m in O(n&sqrt;m log m) time. The result generalizes to the d-dimensional case. Previously no algorithm performing significantly better than the brute-force O(nm) bound was known. Our algorithm seems to perform well in practice. We describe an implementation, illustrating its application to a problem in image processing. Already on relatively small images, our experiments show a signficant speedup compared to brute force.