On topological deep - structure segment i 9 t ’ l 0 n

A hierarchical segmentation model i s obtained by using linear scale evolution of gray-scale images. At each scale segments are generated as Voronoi diagrams wi th a distance measure defined o n the image landscape. T h e set of centers of the Voronoi cells i s the set of local extrema of the gray-scale image. T h i s set i s localized by using the winding number distribution of the gradient vector field. Scale evolution induces hierarchical structure of embedded segments. Objects defined at coarser scales ”decompose” in to sub-objects at f iner scales. T h e process is naturally described in t e r m s of singularity catastrophes within the smooth scale evolution. Alternatively, we present a purely topological segmenta t ion procedure, based on singular isophotes. T h e last are generated by the set of saddle points in the image which are detected also with the topological winding-number method.