CAREER: Shape Model Selection: Theory and Practice

California State University Channel Islands, Camarillo CA

Investigators

Abstract

This project explores shape models that unite human shape perception, computational tractability and mathematical rigor. In particular, it establishes geometry-based selection criteria for skeletal models, defining the best model to be the one that requires the fewest bits to approximate within a specified error tolerance. The goals of the project are to develop theoretical results establishing selection criteria for skeletal models and to apply those results to shape-dependent industrial projects. Skeletal shape models are attractive for shape-based applications because they decompose shapes into salient parts that can be manipulated independently. Their primary downfall for practical applications, a lack of robustness to noises in the shape boundary, has only recently been addressed. In the classical definition of the skeletal model, each shape has a unique skeleton. That uniqueness creates a geometric rigidity that in turn leads to the lack of robustness. A recent generalized skeletal definition relaxes the uniqueness constraint, allowing multiple skeletal models for each shape. Multiple models provide the flexibility to accommodate noisy shape boundaries, but introduce a new problem in selecting the best skeletal model for a given shape. The project engages capable but disadvantaged students who would otherwise be unaware of research as a career in exciting and relevant research. Broader impacts include extensive collaboration between research students and future teachers to develop learning activities for K-12 classrooms, development of course modules to incorporate concepts from digital image analysis into standard sophomore-level mathematics courses, and development of industrial applications in collaboration with students and industrial partners.