Functoriality in Geometric Data

Overview

A recent trend, emerging independently in multiple theoretical and applied communities, is to understand collections, or networks, of geometric data sets through their relations and interconnections, a point of view that can be broadly described as exploiting the functoriality of data, which has a long tradition associated with it in mathematics. Functoriality, in its broadest form, is the notion that in dealing with any kind of mathematical object, it is at least as important to understand the maps, transformations or symmetries possessed by the object or the family of objects to which it belongs, as it is to study the object itself. This general idea has led to deep insights into the structure of various geometric spaces as well as to the state-of-the-art methods in various application domains.

This focused program is intended to bring together researchers who are interested in the fundamental questions of similarity and correspondence across geometric and visual data sets, including collections of GPS traces, images, videos, 3D shapes and many other types of data, to explore and exploit functoriality in geometric data from an algorithmic perspective.