In this talk, I will introduce two algorithms for image segmentation and graph clustering. One of the most influential image segmentation models is the Mumford-Shah's model. Several algorithms such as the level set method have been introduced to compute a minimizing solution to the MS's problem, but none of them can compute a global solution. We...
Creator:
Bresson, Xavier (University of California, Los Angeles)
Created:
2009-10-05
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The Gromov-Hausdorff distance provides a powerful tool for formalizingthe problem of shape matching. Two problems with it are that (1) inpractice it leads to combinatorial optimization problems which are NPhard and (2) despite its theoretical attractiveness and naturality,it has been difficult to use for studying and establishing links tothe man...
Creator:
Mémoli, Facundo (Stanford University)
Created:
2009-10-05
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The problem of representing a large dataset consisiting of complex patterns with a smaller more compact form has been tackled through synthesis of new data points to represent clusters of the original data points (feature transformation). In contrast, the focus of this research is on the development of a generic methods for selecting canonical s...
Creator:
Shokoufandeh, Ali (Drexel University)
Created:
2009-10-05
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Gromov-Hausdorff distance (dGH) is a definition for the discrepancybetween metric spaces. Until recently, it has been applied mainly in theoreticalexploration of metric spaces in metric geometry, as well as in theoreticalcomputer science, specifically, in the context of metric embedding ofgraphs. A couple of years ago it was introduced into the ...
Creator:
Kimmel, Ron (Technion-Israel Institute of Technology)
Created:
2009-10-05
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In this talk, we study the problem of extracting localscales of oscillatory patterns in images and on plane curves. In thefirst case, Given a multi-scale representation {u(t)} of an image f,we are interested in automatically picking out a few choices of t_i(x), which we call local scales, that better represent the multi-scale structure of f at x...
Creator:
Le, Triet Minh (Yale University)
Created:
2009-10-05
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Image processing and recognition has traditionally relied on hard-wiredfeatures and trainable classifiers. The next challenge of computervision, machine learning, and image processing, is to devise methodsthat can automatically learn feature extractors and high-level imagerepresentations from labeled and unlabeled data. The set of methodscollect...
Creator:
LeCun, Yann (New York University)
Created:
2009-10-05
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We present a geometric flow approach to the segmentation of two- three- dimensional shapesby minimizing a cost function similar to the ones used with geometric active contours or to the Chan-Vese approach. Our goal, well-adapted to many shape segmentation problems, including those arising from medical images, is to ensure that the evolving conto...
Creator:
Younes, Laurent (Johns Hopkins University)
Created:
2009-10-05
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Conformal mappings are angle-preserving mappings. All closed surfaces can be conformally mapped to one of three canonical spaces: the sphere, the plane or the hyperbolic disk. All surfaces with boundaries can be mapped to the canonical spaces with circular holes. The computational algorithms for finding such mappings will be explained.Two surfac...
Creator:
Gu, Xianfeng David (The State University of New York)
Created:
2009-10-05
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
