The Structure of Multiplicative Motions in Natural Imagery

Abstract—A theoretical investigation of the frequency structure of multiplicative image motion signals is presented, e.g., as associated with translucency phenomena. Previous work has claimed that the multiplicative composition of visual signals generally results in the annihilation of oriented structure in the spectral domain. As a result, research has focused on multiplicative signals in highly specialized scenarios where highly structured spectral signatures are prevalent, or introduced a nonlinearity to transform the multiplicative image signal to an additive one. In contrast, in this paper, it is shown that oriented structure is present in multiplicative cases when natural domain constraints are taken into account. This analysis suggests that the various instances of naturally occurring multiple motion structures can be treated in a unified manner. As an example application of the developed theory, a multiple motion estimator previously proposed for translation, additive transparency, and occlusion is adapted to multiplicative image motions. This estimator is shown to yield superior performance over the alternative practice of introducing a nonlinear preprocessing step. Index Terms—Multiplicative motion, translucency, dynamic occlusion, pseudotransparency, non-Fourier motion, spectral analysis, optical flow, multiple motion. Ç