Motion and surface recovery using curvature and motion consistency

Akey problem in the recovery of scene descriptions from multiple views is the fusion of information from di erent vantage points. The contribution of this paper is a set of algorithms for reconstructing surfaces obtained from overlapping range images in a common frame of reference. Surfaces are assumed to be piecewise-smooth but not necessarily rigid. Motion parameters, rotations and translations that describe correspondence between views, are recovered locally under the assumption that the curvature structure at a point ona surface varies slowly under transformation. The recovery problem can thus be posed as nding the set of motion parameters that preserves curvature across two views. We show that an appropriate similarity functional can be devised that is convex in the vicinity of the true motion parameters. This leads to an e cient local algorithm that recovers motion parameters in gradient descent fashion. Fusion of information from di erent viewpoints is accomplished by applying local motion estimates to map data points between frames. However, because these estimates are determined locally, they are subject to the usual e ects of noise and quantization error. To increase the robustness of this reconstruction procedure the additional constraint of motion consistency is introduced, that variations in the velocities of adjacent regions are also piecewise-smooth. This is cast as a second local minimization problem which seeks to nd the set of motion parameters that minimizes di erences in the relative positions and orientations at adjacent points. The resulting algorithm serves to smooth out local perturbations and blend adjacent surface patches. In contrast to global rigid body motion approaches, our procedure for reconstructing surfaces from di erent viewpoints is tolerant of local errors in correspondence and can accommodate objects that are articulated