A differential equation approach to the computation of the Fourier transform of the images of translating objects

The frequency domain analysis of constant velocity motion has proven useful in a number of different contexts ranging from television signal processing to computer vision. This work considers the frequency domain analysis of a generalization of such simple dynamics, which includes the effect of acceleration and its time derivatives (of any order). In the frequency domain the contribution due to the object´s shape and the contribution due to translation terms are clearly separated. Motion information in the frequency domain is given by functions characterized by a family of differential equations. Such differential equations are introduced in the work and their solutions are exemplified in order to compute the frequency domain motion contributions. For simplicity; the results are presented for the case of translations, but they apply equally well to rotations