Computational geometry and applications

我的研究计划集中在使用几何驱动的技术来解决计算几何中的基本问题，以及致力于将这种几何计算解决方案适应和扩展到主要在网络和图形/图像处理领域的应用。这一研究方案为培训高素质的人才提供了广泛的机会，并具有在从网络到计算机动画到医学成像等领域的商业应用的潜力。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。具体地，这些包括关于子多边形的面积和形状的多边形的优化划分，以及表征可以被划分成例如全等分片的多边形。这些工作的应用包括模式识别和计算机图形学。在网络的应用领域，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用于在MANET中路由到具有保证递送(或高递送速率)的目的节点的算法，同时相对于可能的最短路径限制由路由算法发现的路径的长度。特别是，我们正在探索使用新的几何子图(如单位圆盘图等网络模型)和随机化来研究二维和三维MANET中的路由。在图形/图像处理的应用领域，我研究的问题与三维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表征依赖时间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种健康信息学工具，用于使用图像处理技术对癌细胞活检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.