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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 0, 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 0 independently of contrast, and the evolution of Gaussian Curvature presents the same characteristic but this point evolves with contrast.

Following corners on curves and surfaces in the scale space