The topological structure of scale-space images

We investigate the deep structure of a scale-space image. The emphasis is on topology, i.e. we concentrate on critical points-points with vanishing gradient-and top-points-critical points with degenerate Hessian-and monitor their displacements, respectively generic morsifications in scale-space. Relevant parts of catastrophe theory in the context of the scale-space paradigm are briefly reviewed, and subsequently rewritten into coordinate independent form. This enables one to implement topological descriptors using a conveniently defined coordinate system.