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.
