Variational Methods for Image Segmentation, Smoothing, Interpolation, Magnification, Stereo Matching, and Shape from Shading

Tuesday, October 17, 2000 - 3:30pm - 4:30pm
Keller 3-180
Anthony Yezzi (Georgia Institute of Technology)
Partial Differential Equations have been used extensively to derive geometric active contour models for the purpose of image segmentation and to derive anisotropic diffusion models for image smoothing. They have also been employed in low level vision problems of inferring 3D structure from one or more 2D images (e.g. stereo-matching and shape-from-shading).

In the first part of this talk we present a class of statistically driven active contour models based upon deterministic energy functionals designed to maximally separate the values of selected statistics inside and outside each evolving contour. We follow this with a less restrictive model, based upon the Mumford-Shah functional, which simultaneously diffuses the image while evolving a set of active contours towards the boundaries of objects. A straightforward generalization of this model allows us to treat images with regions of missing data and to create a unified framework for simultaneous image segmentation, smoothing, and magnification. In the second part of this talk, we will present a novel approach to multiframe shape-from-shading which is stronly motivated by the multiframe stereo-matching work of Faugeras and Keriven.