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 u seful in a number of different contexts ranging from television signal processing to computer vision. This work considers the frequency doma in analysis of a generalization of such simple dynamics, which include s 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. Moti on information in the frequency domain is given by functions character ized by a family of differential equations. Such differential equation s are introduced in the work and their solutions are exemplified in or der to compute the frequency domain motion contributions. For simplici ty, the results are presented for the case of translations, but they a pply equally well to rotations.