Motion analysis from a sequence of range images

The main goal of this work is to demonstrate the feasibility and potential of recovering motion from a sequence of range images as an alternate solution to the complex motion problem. The work presented in this thesis can be divided into two separate parts. The first part describes the long term process, and the second part discusses the short term process. The major problem for the long term process is to reliably find matching features in two or more successive images. An approach is proposed to establish the best match of point features between successive frames using a Hopfield neural network. A model is developed to convert the correspondence problem to the problem of minimizing an energy function, which occurs at the stable state of a Hopfield neural network. After establishing the feature matching, a $\delta$-bound matching concept is introduced to detect the reliable matching features, therefore increase the accuracy of the estimated motion parameters by removing the effect of mismatching features. In this way, the algorithm is tolerant to noise due to feature detection or occlusion. For the short term process, the case of a single rigid moving object is first studied. A simple, yet powerful, algorithm is proposed to estimate motion of a single rigid object. The motion problem is modeled as solving a set of linear equations. A weighted least squares technique has been found to provide the best performance among several other versions of least squares techniques. Theoretical analysis on the necessary and sufficients conditions for the unique interpretation of the motion parameters and on the sensitivity of the estimated motion parameters to noise provides further insight into the behavior of the algorithm. For more complicated motion such as nonrigid motion, the complete process can be viewed in two separate levels: low and high. In this thesis, attention has been paid to the low level processing. A 3D velocity field has been chosen to be the output of the low level stage. We first develop an algorithm which uniquely estimates 3D velocities of points on smooth surfaces by its first and second order partial derivatives, except at parabolic points. The algorithm is very fast and easy to implement in hardware or software. However, it does not provide reliable estimates of velocities near edge points. Hence we propose another algorithm, which is based on the correlation of the local structure of principal curvatures. The advantage of this correlation approach is that it can estimate velocities of both corner points as well as points on smooth curved surfaces, and vernier velocities of line edge points. The disadvantage is that it is computationally intensive compared with the approach for smooth surfaces. Therefore, we suggest that two algorithms should be combined together to give the best performance. Many experimental results on both synthetic and real images are presented in this thesis