Contents List of Figures vi List of Tables ix

Estimation Theoretic Analysis of Motion in Image Sequences by M. Dirk Robinson Estimating the motion (or dynamics) manifested in a set of images or an image sequence is a fundamental problem in both image and video processing and computer vision. From a computer vision perspective, much of what is interpretable in any real-world scene is reflected in the apparent motion. For instance, estimating the apparent motion in a video sequence provides the necessary information for many applications including autonomous navigation, industrial process control, 3-D shape reconstruction, object recognition, robotic motion control, object tracking, and automatic image sequence analysis. In image and video processing, the estimation of motion plays a vital role in video compression as well as multi-frame image enhancement. Disparate as they may seem, these many applications share one common thread: in all such applications, the demand is high for accurate estimates of motion requiring minimal computational cost. In this thesis, we offer an estimation theoretic perspective on the problem of estimating motion from an image sequence. In particular, we focus on the various performance tradeoffs in both accuracy and computational efficiency associated with motion estimation. It is our goal that this work provide a common framework with which to evaluate and understand motion estimation performance. To this end, this thesis offers contributions in three main areas. The first contribution is the proposal of a mechanism to greatly reduce the computational complexity in estimating complex motion vector fields from image sequences. In particular, we develop novel algorithms for estimating motion vector fields using tomographic projections. For example, we show that by incorporating tomographic projections into a multiscale gradient-based algorithms, we may achieve dramatic computational speedups while sacrificing little in the way of estimator accuracy. The second contribution is a thorough analysis of the widely popular class of gradientbased motion estimation algorithms. We derive and analyze the bias for this class of estimators and propose novel methods for optimizing gradient-based estimator performance. The third contribution is the analysis of the fundamental bounds limiting the accuracy of motion estimation. Specifically, we study the Cramér-Rao bounds associated with the problem of estimating translational motion in both aliased and non-aliased images. Finally, we show the intimate relationship between the performance bounds for motion estimation of aliased images and the problem of multi-frame image reconstruction.