Signal matching through scale space

TLDR: This work formulate the general signal matching problem as the minimization of an energy measure that combines a smoothness term and a similarity term that reduces to a dynamic system governed by a set of coupled, first-order differential equations.

Abstract: Given a collection of similar signals that have been deformed with respect to each other, the general signal matching problem is to recover the deformation. We formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term. The minimization reduces to a dynamic system governed by a set of coupled, first-order differential equations. The dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale. Among the major themes in recent work on visual signal matching have been the notions of matching as constrained optimization, of variational surface reconstruction, and of coarse-to-fine matching. Our solution captures these in a precise, succinct, and unified form. Results are presented for one-dimensional signals, a motion sequence, and a stereo pair.