High level vision tasks (recognition, understanding, etc.) for video processing require tracking of the complete contour of the objects. In general, objects undergo non-rigid deformations, which limit the applicability of using motion models (e.g. affine, projective) that impose rigidity constraints on the objects. In this paper, we propose a contour tracking algorithm for video captured using ...

In this paper, a novel segmentation algorithm for color video sequences using the level set technique is proposed. This algorithm is applied to the problem of automatic face region segmentation in video sequences. Given a target color range training set, a model of that color distribution is formed. An objective function is then defined that seeks the boundaries of any regions in an image that ...

We provide a probabilistic interpretation of a class of natural capacities on Euclidean space in terms of the level sets of a suitably chosen multiparameter additive Lévy process X . We also present several probabilistic applications of the aforementioned potential-theoretic connections. They include areas such as intersections of Lévy processes and level sets, as well as Hausdorff dimension co...

Point based level sets are a recently developed implicit surface representation that combines the benefits of point-set surfaces and grid-based level sets. They provide convenient topology changes and adaptivity and are thus useful for tracking the evolution of heavily deforming surfaces. However, it is often useful to extract an explicit mesh from the implicit surface, for example for renderin...

A new data structure is presented for geometrically modeling multi-objects. The model can exhibit elastic and fluid-like behavior to enable interpretability between tasks that require both deformable registration and active contour segmentation. The data structure consists of a label mask, distance field, and springls (a constellation of disconnected triangles). The representation has sub-voxel...

This report looks at employing optimization techniques to generate cubic splines restricted to lie on the surfaces. We implement a recent algorithm designed for exactly this problem, and attempt to understand its motivation and examine its effectiveness. We also pose the problem in AMPL and apply a standard nonlinear solver to verify our results, and to compare the relative benefits of using th...

We prove that the set of all points of effective Hausdorff dimension 1 in Rn (n ≥ 2) is connected, and simultaneously that the complement of this set is not path-connected when n = 2.

A level set approach for computing solutions to incompressible two-phase ow. A viscosity solutions approach to shape-from-shading. SIAM. 19 Proof: Every simply connected shape has a simply connected skeleton 20]. Only circles have skeletons that are single points. Therefore, the skeletons of all other simply connected shapes have at least two end points. The proof follows immediately from Lemma...

ACKNOWLEDGEMENTS This thesis would not have been possible without the help and support of many extraordinary people. I am indebted to all of them. I wish to thank my advisor Allen Tannenbaum for his support, guidance, and his joyfulness, making it a pleasure to work with him and in his lab. I feel very indebted to Larry Jacobs, for his genuine support, interest and friendship, especially throug...

In bivariate density representation there is an extensive literature on level set estimation when the level is fixed, but this is not so much the case when choosing which level is (or which levels are) of most interest. This is an important practical question which depends on the kind of problem one has to deal with as well as the kind of feature one wishes to highlight in the density, the answ...