Program

The field of image analysis is one of the newest and most active sources of inspiration for applied mathematics. While the scientific study of vision dates from the work of Helmholtz, the unfolding of its mathematical side started some 20 years ago: wavelets were invented at about this time in vision and other applications; ideas from statistical mechanics and variational calculus were related to the fundamental problem of segmenting images, i.e. finding objects, distinguishing foreground from background; and the formulation of image analysis as a problem in Bayesian statistical inference was introduced. Soon after, a series of quite novel non-linear PDE's were discovered which unified many image analysis problems. Present day mathematical challenges in image analysis span a wide range of mathematical territory, from harmonic analysis (the development of new mathematical tools for decomposing image data into elementary units), statistical learning theory (learning from empirical data about the underlying basic components of image data) and the search for new stochastic models, e.g. of 'shape' and of grammars. There are even important technical challenges; very recently, the problem of image 'inpainting' (filling-in missing information in images) has stimulated demand for existence and solution theory for certain high-order nonlinear PDE.s. We expect that the push and pull between image analysis and applied mathematics will remain a strong factor in the foreseeable future. From its inception, image analysis has always been one of the most interdisciplinary of fields, and so this program is open to all mathematicians, statisticians, engineers, computer scientists and life scientists interested in image analysis. As a symbol of the many challenges remaining to be faced in this area, consider the problem of segmenting an image into objects, parts and foreground/background in the same way that humans do it. Although this has been one of main goals in image analysis for 20 years, the best current algorithms, as illustrated in the figure above from Jitendra Malik's group, produce very plausible segmentations but still lack the ability to extract and label regions in a way compatible with human image understanding. An Exciting Challenge: Producing automatic segmentations of images which match human segmentations. In each pair the left-hand image is produced by a state-of-the-art algorithm and the right-hand image is produced by a human image analyst. The schedule for this program is Weekly Seminar Jan, Feb and March, 'The Integration of Generative, Descriptive and Discriminative Methods'. Organized by Song Chun Zhu Weekly Seminar Jan-May, 'Methods for Representing Knowledge about Images'. Organized by David Donoho. Jan 24-28: Introductory tutorial workshop. Organized by David Donoho, Olivier Faugeras and David Mumford Feb 7-11: Joint emphasis week with Redwood Neuroscience Institute. Organized by David Donoho and Bruno Olshausen Feb 21-25: Emphasis week on 'Learning and Inference in Low and Mid Level Vision' Organized by Andrew Blake and Yair Weiss March 21-25: Workshop on 'Pattern Classification and Learning'. Organized by Don Geman, Jitendra Malik and Pietro Perona April 18-22: Emphasis week on perceptual organization. Organized by Jean-Michel Morel, Jitendra Malik, Song Chun Zhu May 6-9: Related meeting at the American Institute of Mathematics on Statistical Inferences on Shape Manifolds. Organizers Mio, David Mumford and Srivastava.