The Taub Faculty of Computer Science Events and Talks

In this talk we explore two contributions for shape analysis. In a first case, we consider surfaces and how local analysis of the angular oscillations and polynomial radial behavior around surface points leads to accurate normal estimation and new integral invariants. A direct application of these integral invariants is geometric detail exaggeration.

This however assumes that the shape can be represented as a height function over some parameterization plane in a neighborhood of fixed radius that is the same for all the surface.

In many cases, however, shapes, as they are acquired by laser scanners, might not fulfill this hypothesis: they can have isotropically sampled areas or curve parts. For example, street cables can be considered as curves, depending on the acquisition accuracy. We call this case the mixed dimension case. Armed with a well-defined probing operator associating a point of the ambient space to a point on the shape, we define Local Probing Fields, and analyze them in a non-local manner.

Hence, we are able to extract and describe data self-similarities. Exploiting these through learning algorithms allows us to revisit various shape processing tasks such as denoising, compression and shape resampling.