Frequency domain analysis of general planar rigid motion with finite duration

We present the frequency domain analysis of the most general model of plana r rigid motion, i.e., motion under the joint effects of translations and ro tations with polynomial-type time dependence. We show that in the frequency domain the contribution of the object's shape and texture is separate from that of the motion parameters in this general framework. Special attention is devoted to the case of translations and rotations with constant velocit y and constant acceleration, which are the most likely candidates for model ing motion in practical contexts. This work also focuses on the distinction between the effects of the motion parameters and those of time duration, a distinction that is necessary for a clear assessment of the effects of acc eleration in the frequency domain. The results presented belong to the fiel d of signal theory and may serve as a theoretical basis in the various appl ications of motion models in the frequency domain, which include pattern re cognition, television, image registration, image sequence analysis, and cla ssification and neural modeling of motion perception. (C) 1999 Optical Soci ety of America [S0740-3232(99)00606-7].