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Host: Institute for Mathematics and its Applications
Homepage: http://www.ima.umn.edu/multimedia/fall/m2.html
Email: staff@ima.umn.edu
Organizers: Allen Tannenbaum, Peter Olver, D.E. McClure, P. Perona
Description:
Recent years have seen significant advances in the application of sophisticated mathematical theories to the problems arising in
image processing. As yet, even very low level visual processing by computers remains a challenging problem. Both planar and
three-dimensional images are of importance, and these arise in a wide variety of applications, including medical
imagery---ultrasound, nuclear magnetic resonance, X-ray computed topography, etc.--- military and industrial imaging, and film
restoration and animation. Basic issues include image smoothing and denoising, image enhancement, morphology, image
compression, segmentation (determining boundaries of objects--- including problems of camera distortion and partial
occlusion). Several mathematical approaches have emerged, including methods based on nonlinear partial differential equations,
stochastic and statistical methods, and signal processing techniques, including wavelets and other transform theories. Partial
differential equations are used to describe the evolution of shapes under curvature-controlled diffusions, providing a multi-scale
representation that is based upon curvature flows of fundamental importance in differential geometry. These methods have
proven successful in noise reduction while maintaining edge retention. Applications to segmentation are based on a variational
formulation of the method of "snakes" or moving contours, in which an initial contour converges to the object boundary via a
gradient descent flow based on a conformally Riemannian metric. Wavelets have applications to practical image compression
methods, and texture characterization. Statistical methods such as the EM algorithm have been successfully applied to a variety
of low level vision problems. A primary goal of this workshop is to educate and interest mathematicians in the mathematical and
scientific problems that arise in basic image processing.
Date received: February 02, 2000
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