We present the frequency domain analysis of the most general model of planar rigid motion, i.e., motion under the joint effects of translations and rotations 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 velocity and constant acceleration, which are the most likely candidates for modeling 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 acceleration in the frequency domain. The results presented belong to the field of signal theory and may serve as a theoretical basis in the various applications of motion models in the frequency domain, which include pattern recognition, television, image registration, image sequence analysis, and classification and neural modeling of motion perception.
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