Hi Georg,
AFAIK there is no correspondence between separability in linear operations, where an outer product can be used to transform a 2D matrix operation into two 1D vector operations, and separability in nonlinear operations such as erosion and dilation (and, by generalization, any rank-order operator).
Right now PCL implements 'brute force' morphological transformations, whose complexity is roughly O((n*N)^2), n being the size of the structuring element and N representing the size of the image. My implementations have the advantage that one can use arbitrary structuring elements; for example, circular and star-like elements, which are very useful to process astronomical images. This confers great flexibility but the problem is that these operations are extremely slow for moderately sized filters.
There exist separable morphological transformations, but AFAIK they are always restricted to square and similar kernels. The most well-known one is the van Herk/Gil-Werman algorithm (Marcel van Herk, A fast algorithm for local minimum and maximum filters on rectangular and octagonal kernels, Pattern Recognition Letters, 13, pp. 517-521, 1992). This algorithm has complexity independent on the size of the structuring element and as the paper title tells it works for rectangular and octogonal SEs. Octogonal is not too far from circular, so it sounds as a quite useful alternative for DS images.
Since your work has shown that we need better/faster morphological transformations, and I need them also for several projects (one of them is a morphological wavelet transform tool that I want to publish this Fall-Winter), I'll try to implement some variants of the van Herk/Gil-Werman algorithm in PCL ASAP.
Looking forward to your code to publish it as a development update.
