Computational geometry and applications

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My research programme is centred on using geometrically motivated techniques to solve basic problems in Computational Geometry as well as work on the adaptation and extension of such Geometric Computing solutions to applications primarily in the areas of Networks and Graphics/Image Processing. This research programme has extensive opportunities for the training of highly qualified personel as well as the potential for commercial applications in areas ranging from Networks to Computer Animation to Medical Imaging. In the area of Computational Geometry, my research deals with optimization and characterization problems for point sets, polygons and polygonal surfaces. In particular, these include the optimized partition of polygons in terms of area and shape of the sub-polygons, and characterizing polygons that may be partitioned into, for example, congruent pieces. Applications of such work include Pattern Recognition and Computer Graphics. In the application area of Networks, I am in the process of working on routing problems in position-based mobile ad-hoc networks (MANETs). The general goal of the proposed research is to devise algorithms for routing to destination nodes with guaranteed delivery (or high delivery rates) in MANETs, while limiting the length of the paths discovered by the routing algorithm with respect to the shortest path possible. In particular, we are exploring the use of new geometric sub-graphs (of the network model such as the unit disk graph) and randomization in our study of routing in two dimensional and three dimensional MANETs. In the application area of Graphics/Image Processing, the problems I work on are related to visual data processing of 3D Scientific Data and Medical Imagery. One project involves extracting and characterizing the dynamic component of time-dependent volume data, with application to Scientific Visualization and Computer Animation. A second project involves developing a Health Informatics tool for computer assisted grading of the malignancy of cytological images of cancer cell biopsies using Image Processing techniques.