Decoupling Fourir Components of Dynamic Image Sequences: A Theory of Signal Separation, Image Segmentation, and Optical Flow Estimation

This paper presents a new Fourier-based approach to the separation or decoupling of m additive images from a time-sequence of the sum of these images where at least m−1 images are translating with distinct and unique velocity. A closed-form solution is presented for the case where m=2. A generalization is then presented which extends the theory to embrace situations where the images are not additive but are, instead, formed by the superposition of an occluding object or objects on an occluded background. That is, the approach is generalized to effect a model-free segmentation of objects undergoing translatory fronto-parallel motion in dynamic image sequences. Object velocities of one pixel per frame are sufficient to guarantee segmentation.

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