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

The concepts of structural stability and linear diffusion scale space are reviewed. The possible arrangements and interrelationships 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.

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