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Ph.D. Theses

Model selection, merging, and splitting techniques for surface reconstruction

By Kishore Bubna
Advisor: Charles V. Stewart
June 5, 1998

The accurate segmentation and description of sensor data is an important but difficult problem in computer vision applications. Segmentation is generally accomplished using a combination of region growing, splitting, and merging techniques which in turn use model selection and parameter estimation techniques to describe the data in each segment. While advances have been made in parameter estimation and region growing techniques, the associated issues of model selection and merging have received much less attention in computer vision. Yet good solution to these problems are crucial to the performance of segmentation and description algorithms.

Several model selection criteria have been used in the vision literature and many more have been proposed in statistics, but the relative strengths of these criteria have not been analyzed in vision. More importantly, suitable extensions to these criteria must be made to solve problems unique to computer vision. Using the problem of surface reconstruction as the context, this thesis characterizes the behavior of existing criteria using simulations and sensor data, introduces new criteria from statistics, and develops novel bootstrap based criteria capable of handling unknown error distributions and outliers. The thesis extends the model selection criteria to formulate theoretically rigorous and more effective rules for surface merging. The thesis also shows how the new merging rules can be used to develop effective region splitting techniques.

The detailed experimental analysis presented in this thesis shows that the new Bayesian model selection criteria and its bootstrap version perform the best over a wide range of experimental conditions. The new merging rules based on these criteria work well even at small step heights (h = 2 * sigma) and crease discontinuities. The performance of different segmentation and description applications can be substantially improved by substituting heuristics based techniques with new model selection criteria and merging rules developed in this research. The thesis illustrates this by embedding model selection and merging and splitting techniques in the newly developed Domain Bounding M-Estimator.

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