Computational geometry and applications

我的研究项目集中在计算几何领域，我正在探索几何驱动的技术和数据结构如何用于解决基本和应用计算问题。在计算几何的主要领域，这些问题包括表征和开发优化多边形分割问题的算法，如最优分割。这项工作在实体造型和网格生成中有应用。我感兴趣的许多应用领域的问题是在网络和视觉计算领域，我应用几何计算的思想和技术来寻找解决方案。在网络领域，我继续致力于基于位置的移动的ad hoc网络（MANDO）中的路由问题。对于3-D基于位置的移动自组网，众所周知，保证交付是不可能的本地路由算法，所以我正在探索新的本地路由算法的三维移动自组网与高交付率和相对较短的路径长度，同时建模的网络尽可能现实，与不规则的传输范围，传输延迟等在相关的工作，我正在我最近的工作的基础上开发新的几何生成子图，并探索它们的属性，包括它们对路由算法的影响。 在视觉计算的应用领域，我正在研究与三维图形和医学成像中的视觉数据处理相关的问题。在3-D图形学中，我将机器学习技术，如局部线性降维，应用于基于单视图或多视图的动态可变形几何对象建模问题。这项工作在计算机动画和科学可视化中有应用。在医学成像的特定领域，我正在将我最近对计算机辅助医学诊断的研究扩展到组织学图像，特别是尿液的高分辨率显微镜载玻片（用于检测沉淀物和/或晶体）和血液涂片（用于检测疾病和癌症）。使用图像处理工具（确定几何特征等）和机器学习，我正在开发诊断工具，以帮助临床医生检查许多这样的幻灯片。

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.