CAREER: Methods for Nonrigid Motion Analysis

这是一个为期四年的持续奖励的第一年资助。本提案概述了一个扩展的研究计划，以调查非刚性运动类的层次结构，以及它们的识别和分析。该计划的教育部分包括研究生和本科生课程的发展，努力在研究和教学活动之间建立协同作用，并在拟议的课程中制定积极的学习策略。微分几何中的不变测度主要用于我们的非刚体运动分析。我们提出了一般的非刚性运动分析算法，基于新的距离测量使用判别，单位？曲面的法向曲率和高斯曲率变化。所提出的系统由一系列非刚性运动模型组成，这些模型以一种简单的方式排列。复杂的时尚。我们的重点不仅在于设计不同类别的非刚性运动，并提出不同的技术来提取运动参数和点对应，而且还在于将这些算法应用于涉及人脸和云运动的大量真实数据集，特别是飓风运动。我们认为这是设计、测试、验证和评估我们系统的一个很好的测试平台，因为脸和云涉及各种各样的非刚性运动。本提案旨在解决三个主要的科学问题：(i)如何有效地估计一般非刚性运动中的点对应和运动参数？（ii）对于给定的未知非刚性运动，什么运动参数可用于精确的模型拟合？（iii）如何对非刚性运动进行分类？拟议研究的优势有三个方面。首先，使用不变的微分几何参数进行非刚体运动分析，允许独立于坐标系和参数化的能力，特别是因为我们的优化函数是基于前运动帧的主坐标系。我们方法的第二个优势在于它能够将层次结构中所有非刚性运动类的运动参数相互关联。第三个优势是通过单一优化程序估计点对应，非刚性运动参数和非刚性运动类型的能力。该教育计划包括将研究活动与教学相结合，并努力使本科生参与研究。建议开设的新课程包括研究生水平的计算机视觉课程、视频计算课程和可成形物体分析与可视化研讨会课程。

This is the first year funding of a four year continuing award. This proposal outlines an extended research program to investigate a hierarchy of nonrigid motion classes, along with their identification and analysis. The educational component of this plan involves graduate and undergraduate course development, efforts for a synergy between research and teaching activities and development of active learning strategies in the proposed courses.Invariant measures from differential geometry are mainly used for our purpose of nonrigid motion analysis. We propose algorithms for general nonrigid motion analysis, based on new distance measures using discriminant, unit?normal and Gaussian curvature variations of surfaces. The proposed system consists of a hierarchy of nonrigid motion models arranged in a simple?to?complex fashion. Our emphasis is not only in designing different classes of nonrigid motions and proposing different techniques to extract motion parameters and point correspondences, but also in applying these algorithms to extensive sets of real data involving face and cloud motion, in particular, hurricane motion. We feel that this is a good testbed for designing, testing, validating and evaluating our system, as face and clouds involve a wide variety of nonrigid motions.This proposal seeks to address three major scientific issues: (i) How to efficiently estimate point correspondences and motion parameters during a general nonrigid motion? (ii) What motion parameters are to be used for an accurate model fit of a given unknown nonrigid motion? (iii) How to classify nonrigid motion?The strengths of the proposed research are threefold. First, the use of invariant differential geometric parameters for nonrigid motion analysis allow the ability to be independent of coordinate system and parameterization, especially since our optimization functions are based on before motion frame's principal coordinate system. The second strength of our approach lies in its ability to interrelate the motion parameters of all the nonrigid motion classes in the hierarchy. The third strength is the ability to estimate point correspondences, nonrigid motion parameters and nonrigid motion type through a single optimization procedure.The educational plan involves integration of research activities in teaching and efforts for undergraduate research involvement. Proposed new courses include graduate level courses in computer vision, video computing and seminar course in analysis and visualization of formable bodies.