A new stereo matching algorithm is developed and applied to natural scenes. The algorithm is based on a recent approach to matching multiple, multidimensional signals that have been deformed with respect to one another.' The goal is to optimally recover the deformation map, which in this case represents the stereoscopic disparity between the left and right images. The problem is formulated as the minimization of an energy measure that combines a similarity functional with a controlled-continuity constraint. Applying the continuation method, this nonlinear, nonconvex minimization problem is solved by a deterministic dynamic system governed by a set of coupled, first-order differential equations. The system finds an optimal approximation at a coarse scale, then tracks it continuously to a fine scale, thus avoiding bad local minima. The stereo algorithm succinctly unifies the notions of matching as constrained optimization, of coarse-to-fine search, and of variational surface reconstruction.