The medial feature detector: Stable regions from image boundaries

We present a local feature detector that is able to detect regions of arbitrary scale and shape, without scale space construction. We compute a weighted distance map on image gradient, using our exact linear-time algorithm, a variant of group marching for Euclidean space. We find the weighted medial axis by extending residues, typically used in Voronoi skeletons. We decompose the medial axis into a graph representing image structure in terms of peaks and saddle points. A duality property enables reconstruction of regions using the same marching method. We greedily group regions taking both contrast and shape into account. On the way, we select regions according to our shape fragmentation factor, favoring those well enclosed by boundaries—even incomplete. We achieve state of the art performance in matching and retrieval experiments with reduced memory and computational requirements.