Multiscale image filtering and segmentation by means of adaptive neighborhood mathematical morphology

The purpose of this paper is to extend the theory of mathematical morphology to the paradigm of adaptive neighborhood, dealing with multiscale image processing. The basic idea in this approach is to substitute the extrinsically-defined fixed-shape, fixed-size structuring elements generally used for morphological operators, by intrinsically-defined variable shape, variable size structuring elements. These last ones should fit to the local multiscale features of the image, with respect to a selected criterion such as luminance, contrast, thickness, curvature, etc. The resulting operators, connected with regard to the ´luminance´ criterion, perform a really spatially-adaptive morphological processing. Practically, different multiscale representations by alternating sequential filters with the usual operators, the usual operators by reconstruction and the adaptive operators are first exposed and discussed. In a second time, a hierarchical segmentation is built from adaptive sequential filters.