One-dimensional scale-space preserving filters

We show how graph-morphology processors may be specialized to one dimension and how in this case they amount to parsers of extrema. We compare these scale-space processors on the basis of their performance in additive and replacement noise. Of the filters studied we find that M and TV-filters behave similarly to the recursive median filter and hence inherit their robustness whereas muniscale openings and closings produce much less stable representations.