Computational geometry and applications

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My research program is centered on the area of Computational Geometry where I am exploring how geometrically motivated techniques and data structures may be used to solve basic and applied computing problems. In the primary area of Computational Geometry, these problems include characterizing and developing algorithms for optimized partitioning problems for polygons, such as optimal partitioning. This work has applications in solid modeling and mesh generation. Many of the application area problems that I am interested in are in the areas of Networks and Visual Computing where I apply Geometric Computing ideas and techniques to find solutions. In the area of Networks, I continue to work on routing problems in position-based mobile ad hoc networks (MANETs). For 3-D position-based MANETS, it is known that guaranteed delivery is not possible with local routing algorithms so I am exploring new local routing algorithms for three dimensional MANETs with high delivery rates and relatively short path lengths, while modeling the networks as realistically as possible, with irregular transmission ranges, transmission delay, etc. In related work, I am building on my recent work to develop new geometric spanning subgraphs and explore their properties, including their effect on routing algorithms. In the application area of Visual Computing, I am studying problems related to visual data processing in 3-D Graphics and Medical Imaging. In 3-D Graphics, I am applying the Machine Learning techniques such as locally linear dimension reduction to the problem of modeling dynamic deformable geometric objects, based on single or multiple views. This work has applications in Computer Animation and Scientific Visualization. In the specific area of Medical Imaging, I am extending my recent research on Computer Aided Medical Diagnosis to Histopathological images, particularly high resolution microscopic slides of urine (to detect sediments and/or crystals) and blood smears (to detect diseases and cancers). Using the tools of Image Processing (to determine geometric features, etc.) and Machine Learning, I am developing Diagnosis tools to assist Clinicians who examine many such slides.