Justin Solomon: 2014 Networks of Shapes, Images, and Programs: The Power of Joint Data Analysis Workshop

 

Wednesday, April 16, 2014
Location: Fisher Conference Center, Arrillaga Alumni Center

"Dual Spaces and Functional Maps"
9:15am - 9:45am

Abstract:

The problem of finding a map between two or more domains finds application in machine learning, computer graphics, vision, and many other fields. In its most basic form, the mapping problem seeks pairs of matching points from one domain to another. For example, computer graphics applications might need to register multiple 3D scans of a human, while machine learning packages might need to identify similar actors in different social networks.


The mapping problem is well-known to be a combinatorial challenge. In this talk, however, I will describe how to view a map as a means for transferring attributes or labels. This /dual/ perspective will allow us to use simple tools from linear algebra to compute, manipulate, and compose maps while avoiding computational issues -- while at the same time broadening the notion of map itself in a useful manner. In particular, map computation becomes a regularized linear solve.


Bio:

Justin Solomon is a fourth-year PhD candidate in Computer Science at Stanford. His research focuses on finding maps and relationships between domains with geometric structure, with application-- as mentioned above -- to computer graphics, optimization, learning, and other fields. He also is an active instructor and has taught Stanford courses on computer graphics, differential geometry, and numerical methods; his forthcoming textbook entitled Numerical Algorithms will be distributed by AK Peters/CRC Press in the coming year.


Justin holds an MS in computer science and undergraduate degrees in computer science and mathematics, all from Stanford. His work is supported by the NSF GRFP, NDSEG, and Hertz fellowships. Previous to becoming a full-time PhD student, he also was a member of the research group at Pixar Animation Studios.