On the geometry of a surface and its singular profiles
Image and Vision Computing
Solid shape
New feature points based on geometric invariants for 3D image registration
International Journal of Computer Vision
Topological Numbers and Singularities in Scalar Images: Scale-Space Evolution Properties
Journal of Mathematical Imaging and Vision
Shock Graphs and Shape Matching
International Journal of Computer Vision
Non-rigid Registration by Geometry-Constrained Diffusion
MICCAI '99 Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
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Koenderink characterizes the local shape of 2D surfaces in 3D in terms of the shape index and the local curvedness. The index characterizes the local type of surface point: concave, hyperbolic, or convex. The curvedness expresses how articulated the local shape is, from flat towards very peaked. In this paper we define corner points as point on a shape of locally maximal Koenderink curvedness. These points can be detected very robustly based on integration indices. This is not the case for other natural corner points like extremal points. Umbilici can likewise be detected robustly by integral expressions, but does not correspond to intuitive corners of a shape. Furthermore, we show that Koenderink corner points do not generically coincide with other well-known shape features such as umbilici, ridges, parabolic lines, sub-parabolic lines, or extremal points. This is formalized through the co-dimension of intersection of the different structures.