The Robotics Institute

RI | Seminar | February 13

Robotics Institute Seminar, February 13
Time and Place | Seminar Abstract | Speaker Biography | Speaker Appointments

Generalized Principal Component Analysis GPCA: Geometric Clustering for Vision and Control Networks

Rene Vidal

Assistant Professor of Biomedical Engineering

Johns Hopkins University


Time and Place

Mauldin Auditorium (NSH 1305)
Refreshments 3:15 pm
Talk 3:30 pm



Data segmentation is usually though of as a "chiken-and-egg" problem. In order to estimate a mixture of models one needs to first segment the data and in order to segment the data one needs to know the model parameters. Therefore, data segmentation is usually solved in two stages (1) data clustering and (2) model fitting, or else iteratively using, e.g. the Expectation Maximization (EM) algorithm.


This talk will show that for a wide class of segmentation problems (eigenvector segmentation, mixtures of subspaces, mixtures of fundamental matrices/trifocal tensors, mixtures of linear dynamical models), the "chicken-and-egg" dilemma can be tackled using algebraic geometric techniques. In fact, it is possible to eliminate the data segmentation step algebraically and then use all the data to recover all the models without previously segmenting the data. The solution can be obtained using linear algebraic techniques and is closed form if and only if the number of groups is less than or equal to 4. Examples of the applications of GPCA to segmentation of static and dynamic scenes and identification of hybrid dynamical models systems will also be presented.




Speaker Biography

Professor Ren Vidal received his B.S. degree in Electrical Engineering (highest honors) from the Pontificia Universidad Catlica de Chile in 1997 and his M.S. and Ph.D. degrees in Electrical Engineering and Computer Sciences from the University of California at Berkeley in 2000 and 2003, respectively. He was a research fellow at the National ICT Australia since September 2003 and joined The Johns Hopkins University in January 2004 as an Assistant Professor in the Department of Biomedical Engineering and the Center for Imaging Science. His areas of research are generalized principal component analysis (GPCA), segmentation of static and dynamic scenes, multiple view geometry, omnidirectional vision, vision-based coordination and control of unmanned vehicles and hybrid systems identification and control. Professor Vidal is recipient of the 2003 Eli Jury award from UC Berkeley for outstanding achievement in the area of Systems, Communications, Control, or Signal Processing. He is also recipient of the 2002 Student Continuation Award from NASA Ames, the 1998 Marcos Orrego Puelma Award from the Institute of Engineers of Chile, and the 1997 Award of the School of Engineering of the Pontificia Universidad Catlica de Chile to best graduating student of the school.



Speaker Appointments

For appointments, please contact Martial Hebert

The Robotics Institute is part of the School of Computer Science, Carnegie Mellon University.