Understanding the behavior of SFM algorithms: a geometric approach

We put forth in this paper a geometrically motivated motion error analysis which is capable of supporting investigation of global e®ect such as inherent ambiguities. This is in contrast with the usual statistical kinds of motion error analyses which can only deal with local e®ect such as noise perturbations, and where much of the results regarding global ambiguities are empirical in nature. The error expression that we derive allows us to predict the exact conditions likely to cause ambiguities and how these ambiguities vary with motion types such as lateral or forward motion. Given the erroneous 3-D motion estimates caused by the inherent ambiguities, it is also important to study the behavior of the resultant distortion in depth recovered under di®erent motion-scene con¯gurations. Such an investigation may alert us to the occurrence of ambiguities under di®erent conditions and be more careful in picking the solution. Our formulation, though geometrically motivated, was also put to use in modeling the e®ect of noise and in revealing the strong in°uence of feature distribution. Experiments on both synthetic and real image sequences were conducted to verify the various theoretical predictions