Robust recovery of motion: effects of surface orientation and field of view

Recovering, from two-dimensional images, certain three-dimensional properties of the scene, such as motion and shape of objects in a scene and their spatial arrangement, is one of the primary goals of a machine vision system. Given a textured scene motion can be recovered rather easily if the structure of the scene, usually in the form of a depth map of the scene, is known. In theory, it is also possible to recover shape if the relative motion between the viewer and objects in the scene is known. The authors study the sensitivity of the solution of the first problem to inaccuracies in the knowledge of the depth map of the scene. First a brightness change constraint equation, is used give closed-form solutions for the motion parameters in two cases: known depth, and small depth variations relative to the absolute distance of the scene from the viewer. They then investigate the robustness of the solution for the motion parameters in terms of the scene structure, modeled as piecewise planar patches. They demonstrate the behavior of the solution with the variations of the orientation of the surface patch being viewed and the size of the field of view. Using a quantitative measure, the show the need for a large field of view to recover motion robustly. The eigenvalue-eigenvector decomposition of a 6×6 matrix allows the authors to analyze some well-known ambiguities in recovering motion