Networks of Shapes and Images

Multimedia content has become a ubiquitous presence on all our computing devices, spanning the gamut from live content captured by device sensors such as smartphone cameras to immense databases of images, audio, video, 3D scans and 3D models  stored in the cloud. As we try to maximize the utility and value of all these petabytes of content, we often do so by analyzing each piece of data individually and foregoing a deeper analysis of the relationships between the media. In this talk we focus on developing rigorous mathematical and computational tools for making such relationships or correspondences between signal and media data sets first-class citizens -- so that the relationships themselves become explicit, algebraic, storable and searchable objects. We discuss mathematical and algorithmic issues on how to represent and compute relationships or mappings at multiple levels of detail -- and go on to build entire networks based on these relationships in collections of inter-related data.

Information transport and aggregation in such networks naturally lead to abstractions of objects and other visual entities,  allowing data compression while capturing variability as well as shared structure. Furthermore, the network can act as a regularizer, allowing us to to benefit from the "wisdom of the collection" in performing operations on individual data sets or in map inference between them, ultimately enabling a certain joint understanding of data that provides the powers of abstraction, analogy, compression, error correction, and summarization. Examples include entity extraction from images or videos, 3D segmentation, the propagation of annotations and labels among images/videos/3D models, variability analysis in a collection of shapes, etc.

Finally we briefly describe the ShapeNet effort, an attempt to build a large-scale repository of 3D models richly annotated with geometric, physical, functional, and semantic information -- both individually and in relation to other models and media. More than a repository, ShapeNet is a true network that allows information transport not only between its nodes but also to/from new visual data coming from sensors. This effectively enables us to add missing information to signals, giving us for example the ability to infer what an occluded part of an object in an image may look like, or what other object arrangements may be possible, based on the world-knowledge encoded in ShapeNet.

This is joint work with several collaborators, as will be discussed during the talk.

Leonidas Guibas obtained his Ph.D. from Stanford under the supervision of Donald Knuth. His main subsequent employers were Xerox PARC, DEC/SRC, MIT, and Stanford. He is currently the Paul Pigott Professor of Computer Science (and by courtesy, Electrical Engineering) at Stanford University. He heads the Geometric Computation group and is part of the Graphics Laboratory, the AI Laboratory, the Bio-X Program, and the Institute for Computational and Mathematical Engineering. Professor Guibas’ interests span geometric data analysis, computational geometry, geometric modeling, computer graphics, computer vision, robotics, ad hoc communication and sensor networks, and discrete algorithms. Some well-known past accomplishments include the analysis of double hashing, red-black trees, the quad-edge data structure, Voronoi-Delaunay algorithms, the Earth Mover’s distance, Kinetic Data Structures (KDS), Metropolis light transport, heat-kernel signatures, and functional maps. Professor Guibas is an ACM Fellow, an IEEE Fellow and winner of the ACM Allen Newell award.