Project Description All work funded by NSF IIS0954256
Background: At the most basic level, images consist of shapes (e.g., a chair) and textures (e.g., the chair's upholstery). To perform automated object recognition, we must understand both shapes and textures. This project focuses on shape. Many mathematical structures model shape well, ranging from the simple, like the area inside the shape, to the extremely sophisticated, like a diffeomorphism of the unit circle. Depending on the application, one or another of these models will be most desirable. One particularly appealing shape model is the Blum medial axis, which gives the skeleton of a shape and the distance at each point on the skeleton to the boundary curve.
This project tackles two problems related to the Blum axis:
 In particular applications of shape modeling, does the Blum axis perform well? Some applications we will consider are fruit stem locating, fire boundary tracking, dance recognition and schizophrenia diagnosis.
 Is there another axis structure that does a better job of modeling particular shapes than the Blum axis? This project builds on KL's previous work with the Blum axis, and the recent development of the mathematical theory of a generalized medial axis by Damon and Pizer.
