Superficial and deep structure in linear diffusion scale space: isophotes, critical points and separatrices

摘要

The concepts of structural stability and linear diffusion scale space are reviewed. The possible arrangements and inter-relationships of isophotes, critical points and separatrices in single structurally stable images are detailed. The behaviour of these structures with changing resolution in a linear diffusion scale space is examined. This behaviour includes not only periods of smooth change, but also four catastrophic changes: shoe surface, balanced saddle, double-saddle isophote and heteroclinic separatrix.