Puzzle Solving Results

Puzzle solving animated images:

A 4 piece solution can be viewed here.
A 10 piece solution can be viewed here.

Interactive Surface Sculpting Results

Sculpture created from the sculpting system discussed in:

Willis, A. and Speicher, J. and Cooper, D., Surface Sculpting with Stochastic Deformable 3D Surfaces, International Conference on Pattern Recognition (ICPR), Vol. II, pp. 249–252, 2004.

spinous process (link to VRML file)

Past Course Projects

Medical Image Registration via Maximization of the Correlation Ratio
Andrew Willis
Medical Imaging Final Project, May 2000.
Link to HTML report
Link to HTML presentation

Recent advances in computing power have made it possible to use data provided from medical images in new and revolutionary ways.  A crucial aspect of these developments hinge upon coalescing image data provided from different modalities. This is done by image registration.Given two images representing the same or similar structures, we want to automatically determine the transformation which will allow these structures to be superimposed. The complications of this problem has sparked a line research on the topic of image registration.


Baseball Statistics, Bootstrap Methods and the Boston Red Sox
Andrew Willis
Non-Parametric Statistics Final Project, May 2001.
Link to report (270k Adobe Acrobat .pdf format)

This report makes use of various methods of non-parametric statistics to investigate some hypotheses relating to the sport baseball. Sports statistics are computed for almost all popular sports where they are utilized to estimate the success for athletes and entire teams. In sports, statistics are computed at the lowest level for each player. The team statistics are then formed as a function of the statistics of each member of the team. This report will concentrate solely on team statistics. Team sports statistics generally fall into one of 2 categories:
    • Offensive statistics.
    • Defensive statistics.
In baseball, offensive statistics relate to batting where a team has the opportunity to score runs. Defensive statistics relate to pitching and fielding where a team is attempting to prevent runs from scoring. In this case, offensive statistics are well separated from defensive statistics in the sense that for a given team there is no possibility of affecting offensive statistics such as runs scored while on defense and vice-versa. These statistics will be used to investigate 3 major conjectures.
    • What is the best single baseball statistic?
    • Is talent equally distributed in American and National Leagues?
    • How much variability is there in the outcome of a single season?
Two of these conjectures relate to baseball in general. The third uses bootstrapping methods to estimate the variability of the
 possible outcomes for a given season. Throughout the report we will concentrate on the win statistic for a team: W. The win statistic is the number of games won by a baseball team during regular season play (i.e. it does not include playoff games). Since teams play an equal number of games throughout each baseball season, the win statistic directly measures a teams success in winning baseball games. The win statistic will play a pivotal role in analysis of (1), (2) and (3).


The Geometric Heat Equation and Surface Fairing
Andrew Willis
Seminar Course on Shape Statistics Final Project, May 2002.

Link to report (~1.7MB Adobe Acrobat .pdf format)

This paper concentrates on analysis and discussion of the heat equation as it pertains to smoothing of geometric shapes and its relationship to the problem of surface fairing. The geometric heat equation distorts a given shape in order to obtain scale-space representation of a shape. This scale-space provides a complete description of the original shape in terms of small to large scale structures. These structures may then be interrogated by recognition algorithms in an attempt to classify the shape. In computer science, researchers have been working on methods for eliminating noise from mesh data obtained via 3D measurements. In this case one wishes to eliminate the noise present in the surface measurements in order to obtain an improved approximation of the true surface. This process is called surface fairing. These two seemingly different problems actually have many common goals. This report will focus on a generic implementation of the geometric heat equation and a particular implementation of surface fairing suggested by Gabriel Taubin in his SIGGRAPH '95 paper. Each method will be explained and their inter-relationships will be made clear. These relationships will be supported via experimental results obtained from 3D measurements on a set of human faces. The input data consisted of 3D mesh data sets obtained via a 3D laser range scanner, specifically the ShapeGrabber product of Vitana Corporation.