Local Appropriate Scale in Morphological Scale-Space

This paper discusses the problem of selecting appropriate scales for region detection prior to feature localization. We argue that an approach in morphological opening-closing scale-space is better than one in Gaussian scale-space. The proposed operator is based on a new shape decomposition method called morphological band-pass lter that decomposes an image into structures of diierent size and diierent curvature polarity. Local appropriate scale is then deened as the scale that maximizes the response of the band-pass lter at each point. This operator gives constant scale values in a region of constant width, and its zero-crossings coincide with local maxima of the gradient magnitudes. Its usefulness is demonstrated by some examples.