Spatio-temporal moments and generalized spectral analysis of divergent images for motion estimation

This paper addresses the use of transform methods applied to the analysis of dynamic sequences and to the characterization of image motion. It is shown that image motion resulting from arbitrary 3D camera translation is conveniently analyzed in the Mellin transform (MT) domain associated with space as well as time dimensions, resulting in the desired factorization of the generalized spectrum into a structural component corresponding to the spatial MT of the static image and a MT component depending on the image motion itself (a motion support). This has potential applications for the recovery of image motion and time to collision (TTC) from integral image brightness measurements. We study the relationship between TTC to an imaged object on the resulting MT spectral motion support; conversely we study the recovery of TTC from MT spectral analysis along time and space directions. Different cases of Mellin parameters are examined