Relaxation Methods in Vision: Convex or just plain vexing?

02/11/2009 - 10:00
02/11/2009 - 11:00
Seminar Topic: 
CSIRO ICT Centre Seminars
Simon Lucey
ARC Future Fellow
Convex quadratic objective functions are an attractive means of expressing some goal/task in vision like alignment or classification as: (i) local minima = global minimum, (ii) the sum of N convex quadratics is itself a convex quadratic, and (iii) they offer computationally efficient solutions. Famous algorithms in vision such as the Lucas-Kanade (LK) algorithm (alignment), and the Support Vector Machines (classification) can both be viewed as minimizing a convex quadratic objective function. ------ In the first part of this talk, I will be exploring problems/applications in vision where the original objective function can be suitably relaxed to take advantage of the convex quadratic form. We will introduce two examples of such successful relaxations: (i) Convex Quadratic Fitting (CQF) for non-rigid face alignment with local-experts, and (ii) Least-Squares Congealing (LSC) for the task of unsupervised image ensemble alignment. Both examples, at the time of writing, exhibit superior performance to current state of the art performance. ------ In the second part of this talk, I will explore the concept that if our learning goal can be expressed as a convex quadratic, and our feature extraction step linear, then the sequential feature extraction and optimization steps can be re-interpreted within a single learning goal. This alternate view of linear feature extraction with respect to a convex quadratic learning goal has a number of advantages. First, for the case of classification within the well known linear support vector machine (SVM) framework the memory and computational overheads, typically occurring due to the high dimensionality of the feature extraction process now disappear. ------ From a theoretical perspective the feature extraction step can now be viewed alternately as manipulating the margin of the SVM. This insight is synergetic with recent work in learning that has demonstrated that the choice of margin employed while learning a SVM is critical for high classification performance in many circumstances. Second, for the case of alignment we demonstrate that a similar approach can be applied when employing linear feature extraction in conjunction with the LK algorithm for alignment. By framing the LK algorithm within the Fourier-domain, an algorithm we refer to as Fourier-LK (FLK), we demonstrate superior alignment performance with nearly no additional computational overhead.
Speaker's biography: 
Simon Lucey is a Senior Research Scientist in the CSIRO ICT Centre and a current "Futures Fellow Award" recipient from the Australian Research Council. Previous to joining the CSIRO, Simon was an Assistant Research Professor in the Robotics Institute at Carnegie Mellon University, and was a faculty member there from 2005 to October 2009. Before that he was a Post Doctoral Fellow in the Electrical and Computer Engineering (ECE) department at Carnegie Mellon University. Dr.Lucey's research interests are in computer vision and machine learning with specific interests in their application to human behaviour (particularly with reference to faces and bodies).
Location Details: 
CSIRO Marsfield Lecture Theatre, Cnr Vimiera and Pembroke Rds, Epping, NSW