Transportation Techniques for Geometric Data Processing

Justin Solomon - Stanford University
Sep 17 2014 - 3:00pm
Event type: 
110 Fine Hall

Many methods dealing with data on geometric domains suffer from noise, nonconvexity, and other challenges because they are forced to make choices among nearly-indistinguishable possibilities.  For instance, edge-preserving image filters must assign pixels near the boundary of an object to either its interior or its exterior, inheriting different colors, textures, and other properties depending on the particular outcome.  In geometry processing, algorithms for registering scans of three-dimensional objects must break discrete (e.g. left-right) and continuous (e.g. cylindrical or translational) symmetries to settle on a single correspondence.
In this talk, I will present techniques for explicitly acknowledging these and other ambiguities within graphics, imaging, and data processing pipelines.  Rather than making arbitrary tie-breaking decisions, these methods maintain distributions over potential outcomes.  This “soft” probabilistic framework is supported by the use of optimal transportation distances, which extend notions from classical geometry to the probabilistic domain. In addition to introducing the relevant theory, I will show how it can be used to derive practical algorithms for photo processing, network analysis, and surface mapping.
Selected relevant papers:
• Solomon, Justin, Raif Rustamov, Leonidas Guibas, and Adrian Butscher.  “Earth Mover’s Distances on Discrete Surfaces.”  SIGGRAPH 2014, Vancouver.
• Solomon, Justin, Raif Rustamov, Leonidas Guibas, and Adrian Butscher. “Wasserstein Propagation for Semi-Supervised Learning.” ICML 2014, Beijing.
• Solomon, Justin, Leonidas Guibas, and Adrian Butscher. “Dirichlet Energy for Analysis and Synthesis of Soft Maps.” SGP 2013, Genoa.
Bio:  Justin Solomon is a PhD candidate in the Geometric Computing Group at Stanford University (PI: Leonidas Guibas).  He studies problems in graphics, learning, and imaging combining techniques from mathematical theory and computer science.  His work has led to practical applications in geometry processing, computational photography, and medical imaging and is supported by the Hertz Foundation Fellowship, the NSF Graduate Research Fellowship, and the NDSEG Fellowship.
Justin holds bachelors degrees in mathematics and computer science and a masters degree in computer science from Stanford.  He is a dedicated instructor and has served as the lecturer for courses in graphics, differential geometry, and numerical methods.  His forthcoming textbook entitled Numerical Algorithms focuses on applications of numerical methods to graphics, learning, and vision.  Before beginning his graduate studies, Justin was a member of Pixar's Tools Research group.  Outside the lab, he is a pianist, cellist, and amateur musicologist with award-winning research on early recordings of the Elgar Cello Concerto.