Computational geometry and applications

我的研究计划集中在使用几何驱动技术来解决计算几何中的基本问题，以及在网络和图形/图像处理领域的应用中对这些几何计算解决方案的适应和扩展。这一研究方案为培养高素质人才提供了广泛的机会，并在从网络到计算机动画到医学成像等领域具有商业应用的潜力。在计算几何领域，我的研究涉及点集、多边形和多边形曲面的优化和表征问题。特别地，这些包括根据子多边形的面积和形状对多边形进行优化划分，以及表征可划分为例如全等块的多边形。这些工作的应用包括模式识别和计算机图形学。在网络应用领域，我正在研究基于位置的移动自组织网络（manet）中的路由问题。所提出的研究的总体目标是设计在manet中具有保证交付（或高交付率）的路由到目标节点的算法，同时限制路由算法发现的路径长度，相对于最短路径可能。特别是，我们正在探索在二维和三维manet路由研究中使用新的几何子图（网络模型的子图，如单位磁盘图）和随机化。在图形/图像处理的应用领域，我研究的问题与3D科学数据和医学图像的视觉数据处理有关。其中一个项目涉及提取和描述随时间变化的体积数据的动态成分，并将其应用于科学可视化和计算机动画。第二个项目涉及开发一个健康信息学工具，用于使用图像处理技术对癌细胞活组织检查的细胞学图像的恶性程度进行计算机辅助分级。

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.