Detection of Critical Structures in Scale Space

In this paper we investigate scale space based structural grouping in images. Our strategy is to detect (relative) critical point sets in scale space, which we consider as an extended image representation. In this way the multi-scale behavior of the original image structures is taken into account and automatic scale space grouping and scale selection is possible. We review a constructive and efficient topologically based method to detect the (relative) critical points. The method is presented for arbitrary dimensions. Relative critical point sets in a Hessian vector frame provide us with a generalization of height ridges. Automatic scale selection is accomplished by a proper reparameterization of the scale axis. As the relative critical sets are in general connected submanifolds, it provides a robust method for perceptual grouping with only local measurements.