Workshop

The introductory workshop will be a week long and concentrate on problems in what is typically described as ``early vision'' or ``low-level vision''. By this, people mean whatever you can understand about an image as a function or a signal without introducing explicitly the origin of the image on the basis of the physics and the specific objects present in the world. We have in mind the following themes, each of which will be introduced in a series of tutorial lectures, intended at a level that could be understood by mathematicians, physical scientists or engineers with no previous background in vision and image analysis. 1. Harmonic analysis applied to images. The last few years have seen a great deal interest in the computational harmonic analysis community on developing approximations and expansions specifically oriented to problems in dealing with images, for example edges and textures in images. The resulting multiscale processing tools start with wavelets and go considerably beyond (bandelets, curvelets, ridgelets, brushlets, etc.). There are numerous applications to compression, denoising etc. (Candes, Mallat, Meyer, Saito, Donoho) 2. Statistics of natural images at the signal as well as morphological levels. Because of its data intensive nature, a deep study of the statistics of images lagged some 20 years behind the statistical study of speech. However, many groups are now working out many types of statistics and constructing stochastic models for various aspects of natural images. (Malik, Grenander, Ruderman, Simoncelli, Olshausen, Gousseau, Lee, van Hateren, Freeman, Mumford) 3. Contours, textures, and perceptual organization. The gestalt school of psychophysics, from the 20.s through the 60.s, systematized in a qualitative way the rules by which the elements of images are grouped into larger structures. Vision scientists are now beginning to formalize these rules quantitatively. (Malik, Zhu, Morel, Moisan, Desolneux, Geman, Williams). 4. Variational approaches, partial differential equations for image analysis. These techniques date from the 80.s (Mumford-Shah/Blake-Zisserman functional, the .snakes. of Terzopoulos, Perona-Malik non-linear diffusion) and have been one of the main mathematical approaches to image processing, esp. in the schools of Osher and Morel. (Osher, Chan, Shah, Tannenbaum, Morel, Guichard, Faugeras, Mumford, Sethian). Lectures Tutorial/Introductory/Survey David Donoho (Stanford) 1. Natural Image Statistics and Bayesian Statistics, Information Theory vs. Computer Vision Perspectives 2. Image Manifolds and Image Complexes 3. Harmonic Analysis Analogies to Early Vision. Olivier Faugeras (INRIA) 1. Fundamental PDE's of Computer Vision 2. Approaches to Image Warping and Matching 3. Shape Topologies and Applications to Segmentation David Mumford (Brown) 1. Pattern theory: Grenander's ideas and examples. 2. Modeling shape: comparing metrics, L^1, L^2 and L^\infty techniques, the solid, liquid and conformal approaches. Research/Advanced 1. Image representation: Eero Simoncelli (NYU) 2. Biological vision: Bruno Olshausen (Davis/RNI) 3. Seeing as Statistical Inference: Song Chun Zhu (UCLA) 4. Statistics of Grouping and Figure/Ground in Natural images: J.Malik 5. Modern Classifier design: Trevor Hastie (Stanford) 6. Towards Unsupervised Learning of Categories: Pietro Perona (Caltech) 7. Strategies for visual recognition: Donald Geman (JHU/ENS Cachan) 8. Ecological optics: Jan Koenderink 9. Energy minimization and "u+v" models: Luminita Vese (UCLA) Schedule of Talks