Geometric data in the form of 3D scans, images, videos, or GPS traces is becoming abundantly available on the Web and increasingly important to our economy and life. The usual pipeline in transforming such data to useful models involves data analysis operations such as feature extraction, interpolation, smoothing, fitting, segmentation, etc. In this talk we argue for a different perspective on understanding geometric data that is a based on the study of informative mappings between different data sets, within a single data set, or from a data set to a simpler space that captures its essential structure. The computation of such good mappings leads to interesting but challenging optimization problems. When our data acquisition samples the world in a dense fashion, correlations between multiple data sets create networks of maps that provide additional information both about the structure of the data as well as about the acquisition process itself. We present examples of this approach for understanding isometries between 3D scans, or for connecting large image corpora into useful webs through map networks.
Copyright. All Rights Reserved.