Browse Theses

Motion analysis is the systematic and usually quantitative study of the movements of organisms, humans, particles, and other entitities as recorded on movie film or video tape. Many fields of research employ motion analysis, but existing techniques are often very primitive. The problem of quantitatively analyzing shapes that, through time, undergo complex motions and deformations, is particularly hard, as it is often very costly and time-consuming to acquire the huge amounts of data needed to describe the complex motions.

For the last ten to fifteen years, a great deal of research in computer graphics has been focused on the representation of complex three-dimensional static shape. This thesis establishes a framework for the representation of complex dynamic shape and applies this framework to the application domain of motion analysis.

Our research investigates quantitative representations and algorithms to be used as the foundation of an interactive computer graphics system for the construction of complex dynamic shape descriptions. We critically evaluate various representations of complex dynamic shape by establishing a set of evaluation criteria, and performing a series of experiments aimed at testing each representation with respect to each criterion. The representations we consider are either drawn from the literature or developed within this thesis. We determine our best representation by weighting the criteria, analyzing the experimental results, examining the theoretical considerations, and making, where necessary, justifiable tradeoffs.

Before considering complex dynamic shape, the thesis investigates its basic "building blocks"--possible representations of static shape and moving points. Our criteria for the evaluation of these representations are: generality, accuracy, efficiency, reliability, compactness, and convenience. Our evaluation leads us to adopt a representation based on parametric piecewise hermite cubic polynomials.

We then combine the representations of static shape and moving points to form representations of complex dynamic shape. The criteria we establish for their evaluation are: generality, efficiency, economy of specification, accuracy, convenience, and compactness. Here we select a representation based loosely on the Coons surface representation for three-dimensional objects.

An interactive graphics motion analysis system built upon our research will be significant for two reasons. First, it will be possible to acquire dynamic shape data much faster than with existing manual techniques. Second, the dynamic shape data will be more accurate than data currently being acquired.

In addition, our research makes three major contributions to computer graphics in general. From our static shape research, we present new and efficient representations for hand-drawn curves. As a result of our representations of complex dynamic shape, we present several new and powerful interpolation algorithms for use in computer animation. And finally, from our efforts to determine the best representation, we present a general set of criteria for the evaluation and comparison of static and dynamic shape representations. These evaluation criteria can be applied to application domains other than motion analysis where a representation of static or dynamic shape is required.