Geometric algorithms for image and surface analysis

Anastasia Dubrovina-Karni, Ph.D. Thesis Seminar
Tuesday, 3.2.2015, 11:30
Taub 337
Prof. Ron Kimmel

Various problems involving image and shape representation, analysis and processing share the following common denominator: the complexity and the accuracy of the solution depend on the specific problem formulation and data representation being used. We propose to utilize geometric problem formulations together with novel data representation domains for efficient object segmentation in images and three dimensional shape matching. For automatic image segmentation, we consider the active contours model, combined with the level set framework, and extend its classical solution to obtain an efficient and accurate algorithm for multi-region image and volume segmentation, while exploiting a single level-set function. For user-assisted image segmentation, based on propagating information between pixels via shortest paths between them, we revisit the problem formulation. We show that representing the image as a graph of its level sets, rather than using the standard Cartesian grid, leads to improved segmentation results. For the non-rigid shape matching problem, we show how the matching continuity and the smoothness of the pointwise and pairwise shape properties can be exploited in two different forms to facilitate and improve the matching. It is done by employing a multi-resolution matching algorithm, and by formulating the matching problem in the natural spectral domain.

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