ECCV 2012 Short Course


Sparse Representation and Low-Rank Representation in Computer Vision

-- Theory, Algorithms, and Applications

                                John Wright Columbia University, New York

                                Allen Y. Yang University of California, Berkeley




The recent vibrant study of sparse representation and compressive sensing has led to numerous groundbreaking results in signal processing and machine learning. In this tutorial, we will present a series of three talks to provide a high-level overview about its theory, algorithms and broad applications to computer vision and pattern recognition. We will also point out ready-to-use MATLAB toolboxes available for participants to further acquire hands-on experience on these related topics.

Online Source Code and References:

Session 1: Introduction to Sparse Representation and Low-Rank Representation. 

This session introduces the basic concepts of sparse representation and low-rank representation. The emphasis will be on how to model and recover low-dimensional structures in high-dimensional signals, and how to verify that the models are appropriate. We will illustrate this process through examples drawn from a number of vision applications. We will gently introduce the foundational theoretical results in this area, and show how theory informs the modeling process.


Session 2: Variations of Sparse Optimization and Their Numerical Implementation.

This session discusses several extensions of the basic sparse representation concept, from the original l-1 minimization formulation to group sparsity, Sparse PCA, Robust PCA, and compressive phase retrieval. These variations extend the applications of compressive sensing to multiple-view objection recognition, informative feature selection, and medical imaging. Efficient numerical algorithms are a focus of our discussion, which are responsible for recovering stable estimates of the sparse signals in high-dimensional space. Finally, we briefly discuss how to properly implement the sparsity minimization algorithms on modern many-core CPU/GPU environments.


Session 3: Finding and Harnessing Low-Dimensional Structure of High-Dimensional Data.

This session extends the techniques to enable the analysis of large batches of visual data. We will show how tools and ideas from convex optimization give simple, robust algorithms for recovering low-rank matrices from incomplete, corrupted and noisy observations. Participants will learn how to identify problems for which these tools may be appropriate, and how to apply them effectively to solve practical problems such as robust batch image alignment and the detection of symmetric structures in images. We will illustrate the power and potential of these revolutionary tools in a wide range of applications in computer visions including but not limited to: Face and Text Recognition, Texture Repairing, Video Panorama, Camera Calibration, Holistic Reconstruction of Urban Scenes, etc. Finally, we will show generalizations to the problem of learning sparse codes for large sets of visual data, give example applications.

Speaker Bios: 

Yi Ma is the principal researcher and manager of the Visual Computing Group at Microsoft Research Asia, Beijing. His research interests include multiple-view geometry, vision-based control, clustering and classification of high-dimensional data, estimation of hybrid models and systems. He is the author of the vision textbook "An Invitation to 3D Vision: From Images to Geometric Models". He is the recipient of the David Marr Prize, NSF Career Award, and the ONR Young Investigator Award. He was an associate editor of the IEEE Transactions on Pattern Analysis and Machine Intelligence from 2007 to 2011 and current the associate editors of the International Journal of Computer Vision and the new IMA Journal on Information and Inference. He has also served as the chief guest editors for special issues for the Proceedings of IEEE and the IEEE Signal Processing Magazine. He will serve as Program Chair for ICCV 2013 and General Chair for ICCV 2015.

John Wright is an Assistant Professor in the Electrical Engineering Department at Columbia University. He received his PhD in Electrical Engineering from the University of Illinois at Urbana-Champaign in October 2009, and was with Microsoft Research from 2009-2011. His research is in the area of high-dimensional data analysis. In particular, his recent research has focused on developing algorithms for robustly recovering structured signal representations from incomplete and corrupted observations, and applying them to practical problems in imaging and vision. His work has received an number of awards and honors, including the 2009 Lemelson-Illinois Prize for Innovation for his work on face recognition, the 2009 UIUC Martin Award for Excellence in Graduate Research, and a 2008-2010 Microsoft Research Fellowship.

Allen Y. Yang is a Research Scientist in the Department of EECS at UC Berkeley. He has also served as a consultant to several major companies and startups in IT industry. His primary research areas include pattern analysis of geometric and statistical models in very high-dimensional data spaces and applications in motion segmentation, image segmentation, face recognition, and signal processing in heterogeneous sensor networks. He has published three books/chapters, ten journal papers and more than 20 conference papers. He is also the inventor of three US patents. He received his BEng degree in Computer Science from the University of Science and Technology of China (USTC) in 2001. From the University of Illinois at Urbana-Champaign (UIUC), he received two MS degrees in Electrical Engineering and Mathematics in 2003 and 2005, respectively, and a PhD in Electrical and Computer Engineering in 2006. Among the awards he received are a Best Bachelor's Thesis Award from USTC in 2001, a Henry Ford II Scholar Award from UIUC in 2003, a Best Paper Award from the International Society of Information Fusion and a Best Student Paper Award from Asian Conference on Computer Vision in 2009.