A new approach to the formulation and solution of the problem of recovering scene topography from a stereo image pair is presented. The approach circumvents the need to solve the correspondence problem, returning a solution that makes surface interpolation unnecessary. The methodology demonstrates a way of handling image analysis problems that differs from the usual linear-system approach. We exploit the use of nonlinear functions of local image measurements to constrain and infer global solutions that must be consistent with such measurements. Because the solution techniques we present entail certain computational difficulties, significant work still lies ahead before they can be routinely applied to image analysis tasks.