The Taub Faculty of Computer Science Events and Talks

A fundamental problem in geometry processing is to characterize the possible transformations a shape can undergo, and still remain "the same". Such transformations are called isometries, since they preserve some notion of distance between all points on the shape. In many cases, however, especially when dealing with discrete shapes, approximate isometries better characterize the wealth of shapes which represent the same object, such as different poses of a character. Such maps are harder to represent and parameterize, in particular when considering geodesic distances - along paths on the shape.

We tackle this challenge by using Killing vector fields - a special type of vector fields which are the generators of isometries. We show how approximate continuous isometries can be parameterized by approximate Killing vector fields (AKVFs), and how to find those efficiently on a discrete shape. Our approach gives rise to a new operator, whose spectral data conveys much information about a shape. We show how these insights on representing shape isometries can be applied to various problems in geometry processing, such as texture generation, segmentation and deformation.