Submitted to Scale-Space 2003 Lowekamp and Yoo

Multiscale Shape Operators for Sampled Manifolds

Bradley C. Lowekamp - Terry S. Yoo

yoo@nlm.nih.gov

Abstract:

Computer vision attempts to create models from input images, while computer graphics attempts the inverse process of using models to generate output images. Our work applies scale-space concepts to neither the input nor output images, but to the geometric models that are the intermediate abstractions of both fields. We develop a multiscale shape operator for sampled manifolds based on Monte Carlo sampling and numeric differentiation. By varying the aperture of our differential geometric measuring tool, we analyze second-order properties of the surface, discriminating surface features from noise as well as ranking features according to shape saliency across scale. We present visual examples and discuss the differences of our methods from similar level set techniques. The resulting differential attributes allow scale-space of shape to be considered in computer graphics algorithms such and polygonal simplification, geometric smoothing and constraint selection of data dependent implicit surfaces.