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

Abstract

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. We also show how the technique can be applied on a local basis to compute a dense instantaneous optical flow field for the image sequence, even in relatively featureless regions. The technique is evaluated using Otte's and Nagel's benchmark image sequence, for which ground-truth data is available, and results comparable with the ground-truth flow field are achieved. RMS errors of velocity magnitude and direction are computed and reported.