CAREER - Intelligent PDE's: Introducing Knowledge into Geometry Driven Image Deformations

sapiro该项目致力于发展应用于图像处理和计算机视觉领域的数学技术的综合研究和教育计划。特别是使用几何偏微分方程（GPDE）。使用GPDE是一种相对较新的图像分析方法，它带来了许多好处，并且已经产生了一些最先进的结果。本研究的重点是理论和实践研究如何将先进的先验和学习的知识和信息引入GPDE的框架，超越了通常使用的简单边缘信息。可以纳入知识的关键示例包括MRI和SAR，其中图像中存在的不同物体的数量是先验已知的；视频中的对象跟踪，例如人机交互，可以使用前一帧的信息；医学图像分析和可视化，其中重要的生物信息是可用的。这些知识结合了贝叶斯规则、学习技术、耦合GPDE系统和驱动GPDE的特殊几何力。这些新方程的理论研究是该计划的一个组成部分。该项目的教育部分侧重于改进多学科培训和创建一个基于个人计算机的新图像处理实验室。关于GPDE和几何视觉跟踪的新课程正在引入。这些和基本的图像处理课程面向不同的受众，来自大学许多部门的学生都参加了这些课程。与工业界和其他部门的合作也涉及确定联合项目。整个研究和教育计划的目标是为经常在个人电脑上与视觉信息交互的用户提供更方便的图像分析高级工具。

SapiroThis project addresses the development of a comprehensive research and educational program in mathematical techniques applied to the areas of image processing and computer vision. In particular, Geometric Partial Differential Equations (GPDE's) are used. Using GPDE's is a relatively new approach to image analysis that brings numerous benefits and has already lead to several state-of-the-art results. This research focuses on the theoretical and practical study of ways to introduce advanced a-priori and learned knowledge and information into the GPDE's framework, moving beyond the simple edge information commonly used. Key examples where knowledge can be incorporated include MRI and SAR, where the number of different objects present in the image is known a-priori; object tracking in video, for human-computer interaction for example, where information from previous frames can be used; and medical image analysis and visualization, where important biological information is available. This knowledge is incorporated combining Bayes rule, learning techniques, systems of coupled GPDE's, and special geometric forces driving the GPDE's. The theoretical study of these new equations is an integral part of the program. The educational component of this project focuses on improving multi-disciplinary training and creating a new image processing laboratory based on personal computers. New courses on GPDE's and on Geometric Visual Tracking are being introduced. These and the basic image processing courses are oriented to a diverse audience and are attended by students from many departments across the University. The collaboration with industry and other departments is also addressed defining joint projects. The whole research and educational program is oriented toward making advanced tools in image analysis more accessible to users that frequently interact with visual information in their personal computers.