The LAMBDA Group Los Angeles Multi-Band Data Analysis Department of Mathematics, UCLA "Dedicated to innovative research in hyperspectral and geospatial image processing for the betterment of mankind."

PEOPLE
Principal Investigators Prof. Andrea Bertozzi Prof. Stanley Osher Postdocs Jerome Darbon Guy Gilboa Shao-Ching Huang Arthur Szlam Todd Wittman	Graduate Students Alex Chen Julia Dobrosotskaya Undergraduate Students Meiching Fong Zhong Hu

PRESENTATIONS The presentations below were given on Dec 13-14, 2006. A password is required to view the presentation files. Contact the site administrator for access. Road Inpainting Overview: Processing Images with Nonlinear PDEs, Andrea Bertozzi Cahn-Hilliard and Wavelet Inpainting, Julia Dobrosotskaya Long-Time Behavior of Cahn-Hilliard Systems, Shao-Ching Huang Road Inpainting Demo, Todd Wittman Hyperspectral Image Processing Active Contours and their Higher-Order Feature-Preserving Regularization, Andrea Bertozzi Image Segmentation with Statistical Shape Priors, Stanley Osher Unsupervised Classification of Hyperspectral Data, Meiching Fong & Zhong Hu Hyperspectral Image Classification, Alex Chen Nonlocal Evolutions for Image Reuglarization and Supervised Segmentation, Guy Gilboa Fast and Exact Discrete Total Variation Minimization, Jerome Darbon Dimension Reduction = Smoothing, Arthur Szlam Hyperspectral Dimension Reduction & Super-Resolution, Todd Wittman

SOFTWARE & DATA Image Database Access requires different password than the other files. C.H.R.I.S. v2.0 -- Cahn-Hilliard Road Inpainting Software, zip file MANI -- Manifold Learning Demo, website Semi-supervised Classification by Diffusion Maps by Arthur Szlam Hypercube by the US Army Hyperactive -- Hyperspectral Image Analysis Toolkit

RELATED PUBLICATIONS Inpainting Andrea Bertozzi, Selim Esedoglu, and Alan Gillette. Inpainting of Binary Images Using the Cahn-Hilliard Equation IEEE Transactions on Image Processing, January 2007. Andrea Bertozzi, Selim Esedoglu, and Alan Gillette. Analysis of a Two-Scale Cahn-Hilliard Model for Image Inpainting. UCLA CAM Report, May 2006. Alan Gillette. Image Inpainting Using a Modified Cahn-Hilliard Equation. PhD Thesis, UCLA, December 2006. Marcelo Bertalmio, Andrea Bertozzi, and Guillermo Sapiro. Navier-Stokes, Fluid Dynamics and Image and Video Inpainting. CVPR 2000. Ivars Peterson. Filling in the blanks: Automating the restoration of a picture's missing pieces. Science News, May 2002. Denoising and Deblurring Guy Gilboa, Jerome Darbon, Stanley Osher, and Tony Chan. Nonlocal Convex Functionals for Image Regularization. UCLA CAM Report, October 2006. Jerome Darbon. A Note on the Discrete Binary Mumford-Shah Model. UCLA CAM Report, November 2006. Jerome Darbon and Marc Sigelle. Fast and Exact Total Variation Minimization. IBPRIA 2005. Antoni Buades, Bartomeu Coll, and Jean-Michel Morel. A Nonlocal Algorithm for Image Denoising. CVPR 2005. Segmentation and Classification Alex Chen, Meiching Fong, and Zhong Hu. Hyperspectral Image Classification. Summer Research Project Report, August 2006. Guy Gilboa and Stanley Osher. Nonlocal Image Regularization and Supervised Segmentation. UCLA CAM Report, September 2006. Daniel Cremers, Stanley Osher and Stefano Soatto. Kernel Density Estimation and Intrinsic Alignment for Knowledge-driven Segmentation: Teaching Level Sets to Walk. Pattern Recognition, 2004. Daniel Cremers. Statistical Shape Knowledge in Variational Image Segmentation. PhD thesis, July 2002. Dimension Reduction Resources: Manifold Learning Resource Site ISOMAP: J.B. Tenenbaum, V. de Silva and J. C. Langford. A global geometric framework for nonlinear dimensionality reduction. Science, vol. 290, pp. 2319--2323, 2000. LLE: L. K. Saul and S. T. Roweis. Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifolds. Journal of Machine Learning Research, v4, pp. 119-155, 2003. Hessian LLE: D. L. Donoho and C. Grimes. Hessian Eigenmaps: new locally linear embedding techniques for high-dimensional data. Technical Report TR-2003-08, Department of Statistics, Stanford University, 2003. Laplacian Eigenmaps: M. Belkin, P. Niyogi, Laplacian Eigenmaps for Dimensionality Reduction and Data Representation, Neural Computation, June 2003; 15 (6):1373-1396. Diffusion Maps: Nadler, Lafon, Coifman, and Kevrekidis. Diffusion maps, spectral clustering and reaction coordinates of dynamical systems LTSA: Zhenyue Zhang and Hongyuan Zha. Principal Manifolds and Nonlinear Dimension Reduction via Tangent Space Alignment. SIAM Journal of Scientific Computing, 2004, 26 (1): 313-338.