Estimating motion in scenes containing multiple moving objects remains a difficult problem in computer vision yet is solved effortlessly by humans. In this thesis we present a computational investigation of this astonishing performance in human vision. The method we use throughout is to formulate a small number of assumptions and see the extent to which the optimal interpretation given these assumptions corresponds to the human percept.
For scenes containing a single motion we show that a wide range of previously published results are predicted by a Bayesian model that finds the most probable velocity field assuming that (1) images may be noisy and (2) velocity fields are likely to be slow and smooth. The predictions agree qualitatively, and are often in remarkable agreement quantitatively.
For scenes containing multiple motions we introduce the notion of ``smoothness in layers''. The scene is assumed to be composed of a small number of surfaces or layers, and the motion of each layer is assumed to be slow and smooth. We again formalize these assumptions in a Bayesian framework and use the statistical technique of mixture estimation to find the predicted percept. Again, we find a surprisingly wide range of previously published results that are predicted with these simple assumptions. We discuss the shortcomings of these assumptions and show how additional assumptions can be incorporated into the same framework.
Taken together, the first two parts of the thesis suggest that a seemingly complex set of illusions in human motion perception may arise from a single computational strategy that is optimal under reasonable assumptions. The third part of the thesis presents a computer vision algorithm that is based on the same assumptions. We compare the approach to recent developments in motion segmentation and illustrate its performance on real and synthetic image sequences.
The thesis is presented in terms of three self contained papers. However, the three papers are best read in sequence since they form part of a single line of study. In this introduction we make this line of inquiry explicit. We first describe the problem we wish to understand and the rationale for the method of investigation. We then summarize the main results of the three papers.