Following corners on curves and surfaces in the scale space

Abstract

This paper is devoted to an analytical study of extrema curvature evolution through scale-space. Our analytical study allows to get results which show that, from a qualitative point of view, corner evolution in scale-space has the same behavior for planar curves or surfaces. In particular, this analysis, performed with different corner-shape models, shows that, for a two-corner shape, two curvature maxima exist and merge at a certain scale σ0, depending on the shape. For a two-corner grey-level surface, the evolution of the determinant of hessian (DET) shows a merging point for a certain σ0 independently of contrast, and the evolution of Ganssian Curvature presents the same characteristic but this point evolves with contrast.