We are interested in modeling the variability of different images of the same scene, or class of objects, obtained by changing the imaging conditions, for instance the viewpoint or the illumination. Understanding of such a variability is key to reconstruction of objects despite changes in their appearance (e.g. due to non-Lambertian reflection), or to recognizing classes of objects (e.g. cars), or individual objects seen from different vantage points. We propose a model that can account for changes in shape or viewpoint, appearance, and also occlusions of line of sight. We learn a prior model of each factor (shape, motion and appearance) from a collection of samples using principal component analysis, akin a generalization of "active appearance models" to dense domains affected by occlusions. The ultimate goal of this work is stereo reconstruction in 3D, but first we have developed the first stage in this approach by addressing the simpler case of 2D shape/radiance detection in single images. We illustrate our model on a collection of images of different cars and show how the learned prior can be used to improve segmentation and 3D stereo reconstruction.

Recently proposed Sobolev active contours introduced a new paradigm for minimizing energies defined on curves by changing the traditional cost of perturbing a curve and thereby redefining their gradients. Sobolev active contours evolve more globally and are less attracted to certain intermediate local minima than traditional active contours. In this paper we analyze Sobolev active contours in the Fourier domain in order to understand their evolution across different scales. This analysis shows an important and useful behavior of Sobolev contours, namely, that they move successively from coarse to increasingly finer scale motions in a continuous manner. Along with other properties, the previous observation reveals that Sobolev active contours are ideally suited for tracking problems that use active contours. Our purpose in this work is to show how a variety of active contour based tracking methods can be significantly improved merely by evolving the active contours according to the Sobolev method.