A Virtually Continuous Representation of the Deep Structure of Scale-Space

The deep structure of scale-space of a signal refers to tracking the zero-crossings of differential invariants across scales. In classical approaches, feature tracking is performed by neighbor search between consecutive levels of a discrete collection of scales. Such an approach is prone to noise and tracking errors and provides just a coarse representation of the deep structure. We propose a new approach that allows us to construct a virtually continuous scale-space for scalar functions, supporting reliable tracking and a fine representation of the deep structure of their critical points. Our approach is based on a piecewise-linear approximation of the scale-space, in both space and scale dimensions. We present results on terrain data and range images.