Abstract: Visual tracking is the problem of estimating the motion or positions of an object given a sequence of images. It has extensive applications in autonomous robots, surveillance, and medical image analysis. In this talk, we propose a novel tracking method based on density matching flows. The method aims at tracking a non-rigid object moving in clutter using photometric information. In this method, the object being tracked is represented as curves; the prior knowledge about the object is represented as a model density of photometric variables. In the tracking process, the curves move in directions minimizing the distance between a sample density and the model density. Three variants of the method can be derived. These methods are formulated by PDEs and are solved numerically by level sets. Experiments show the method has strong ability in tracking.

Eunyoung Seol - Flexible Distributed Meshbase for Parallel Automated Adaptive Simulations

Abstract: A mesh is piece-wise decomposition of the space/time domain used by numerical simulation procedures. A general topology-based mesh representation consists of 0 to 3D topological entities and adjacencies between them. From a fact that the most flexibility of a mesh data structure comes from the levels of mesh entities and adjacencies present in the representation and by the needs of the distributed mesh data structures that operate in a scalable manner on parallel applications, the aim of the thesis is to develop a Flexible distributed Mesh DataBase (FMDB), that is capable of shaping its representation based on the specific needs of the applications and efficiently supports parallel adaptive analysis in a parallel computing environment.

In order to properly maintain the needed representation even for mesh modification, the mesh entity creation/deletion operators are designed as functors, initially undetermined. Once the needed representation is provided, they are dynamically set to the proper operators. The needed representation can be provided to the mesh database either by the user explicitly or by running the Dynamic Mesh Usage Monitor, which monitors mesh usage of the application and provides an appropriate representation. For the purpose of supporting distributed meshes on parallel computers, a partition model has been developed. The partition model is located between the partitioned mesh and the geometric model to represent mesh partitioning and support the mesh-based inter-partition operations. Based on the design of the flexible mesh data structure and distributed meshes in accordance with the partition model, the efficient mesh migration procedure that works regardless of mesh representation options has been developed. Performance results of the FMDB demonstrates a good compromise between memory and computational costs. Compared to the one-level fixed representation, a decrease in storage requirement with reduced representations through flexibility is 10% - 77%. The migration procedure with reduced representations outperforms that with full representations as the mesh size and the number of partitions increase. The FMDB is embedded in SCOREC simulation packages effectively supporting parallel automated adaptive analyses such as parallel adaptive loop for SLAC and parallel discontinuous Galerkin methods.

Cigdem Gunduz Demir - The cell-graphs of brain cancer

Abstract: In traditional cancer diagnosis, pathologists examine biopsy samples under a microscope and make judgments based on their personal experience. While examining the biopsies, a pathologist typically assesses the deviations in the cell structures and/or the change in the distribution of the cells across the tissue. However, this judgment is subjective, and often leads to considerable variability. To circumvent this problem, it is important to develop computational tools for automated cancer diagnosis that operate on quantitative measures; this facilitates objective mathematical judgment complementary to that of a pathologist, reducing the inter-observer variability. For such automated cancer diagnosis, we introduce the cell-graph approach that relies on the distinctive properties of "cluster" formation in cancerous cells. The main advantages of our approach are its ability to work with low-magnification photomicrographs of biopsy samples and its likely immunity to the noise inherit in these photomicrographs.

Peng Hu - Solving Fluid-Rigid Object Interaction Problems by Discontinuous Galerkin Methods

Abstract: Multi-material interaction is wide spread in fluid mechanics, biomechanics, meteorology and many other fields. Therefore, the ability to numerically simulate the effects of two or more different, yet inter-related physical materials is important. Solving multi-materials interaction problems is still difficult and several open problems remain. Key problems are tracing the interfaces properly and applying correct interface conditions. Here, we are particularly interested in applications involving the motion of a high-speed rigid object in a compressible inviscid fluid. The basic characteristics of these problems include both the continuous change of the computational domain with respect to time and the strong discontinuities in the fluid because of the movement of the object.

Two different approaches -- a moving mesh approach and a fixed mesh approach, are considered. In our moving mesh approach, a mesh is defined over a domain excluding the rigid body, and then modified by using a spring analogy model during calculation to follow the object. In our fixed mesh approach, a novel idea is provided by using a level set function to implicitly track the fluid-solid interface; therefore, no mesh motion or modification is required. The interface boundary conditions are also captured implicitly by combining a Ghost Fluid technique with the level set approach.

The discontinuous Galerkin method (DGM) is used to numerically solve the Euler equations associated with a compressible inviscid fluid. The numerical tests give satisfactory results for both approaches, and serve to verify the correctness of our theoretic approximation and numerical implementation. The fixed mesh approach is a much more efficient approach because of not having to move the mesh. It also has a wide-spread applicability to handle problems with complex movement and/or complex geometry. This approach is also dimension free and easy to implement. The moving mesh approach provides a more natural way to consider the fluid-rigid object interaction problem and it provides an accurate way to simulate the interface interaction.