Areas of Interest:
My main research interest is in finding the most pertinent mathematical principles for analyzing and understanding high-dimensional sensorial data such as images, so that machines and human can make more intelligent decisions. The research endeavor has led me into the following specific areas.
|Computer Vision||Mathematics & Statistics||Decision & Control|
|- Multiple-View Geometry - Image & Video Segmentation - Object Recognition & Detection||- Algebraic Sets and Manifolds - Data Clustering & Classification - Sparse Representation||- Vision-Based Decision & Control - Identification of Hybrid Systems - Autonomous Robot Navigation|
A recent essay by me reflecting on the methodology for research: Warning Signs of Bogus Research Progresses.
Powerpoint slides from a recent talk by me on How to do Research.
- Low-Rank Matrix Recovery and Completion via Convex Optimization (with Wright, Ganesh, Lin, and Candes et. al.).
- Face Recognition via Sparse Representation (with Wright, Ganesh, Yang, Zhou, and Wagner et. al.).
- Clustering and Classification via Lossy Compression (with Wright, Yang, Mobahi, and Rao, et. al.).
- Generalized Principal Component Analysis (with Huang and Vidal).
- Multiple-View Geometry and 3D Reconstruction (with Kosecka, Soatto, and Sastry).
- Advances in the Theory and Practice of Low-Rank Matrix Recovery and Modeling (with Emmanuel Candes, sponsored by NSF).
- Harnessing Sparse and Low-Dimensional Structures for Robust Clustering of Visual Data (sponsored by ONR).
- SGER: Explorations of Robust Image Classification (sponsored by NSF-IIS).
- PHYSNET: Physical Interaction Using the Internet (with Ruzena Bajcsy et. al., sponsored by NSF-HCC).
- Control and Sensing under Limited Information (with Daniel Liberzon, sponsored by NSF-ECS).
- Estimation of Hybrid Models as Algebraic Sets (with Robert Fossum, sponsored by NSF-CCF).
- Estimation of Hybrid Models in Computer Vision (sponsored by ONR).
- Identification of Hybrid Dynamical Systems (with Rene Vidal, sponsored by NSF-EHS).
- Identifying Spatial and Dynamical Patterns from Images (sponsored by NSF-IIS).
- DARPA Urban Challenge (sponsored by the University of Illinois and others).
- Geometry and Algebra in Computer Vision, RAP Program (sponsored by Math Department, the University of Illinois).
- Vision-Based Control (sponsored by the University of Illinois Research Board).
- Microsoft Research Fellowship (sponsored by the Microsoft Live Lab.).