共形几何代数与运动和形状的刻画  

Conformal Geometric Algebra for Motion and Shape Description

作　　者：李洪波[1] 

机构地区：[1]中国科学院数学机械化重点实验室,北京100080

出　　处：《计算机辅助设计与图形学学报》2006年第7期895-901,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(10471143);国家重点基础研究发展规划项目(2004CB318001)

摘　　要：共形几何代数在基于运动和形状刻画的视觉和图形学若干问题中的应用,反映了它能够提供统一和有效的表示和算法,这些应用主要集中在采纳几何体的Grassmann分级表示以及刚体运动的旋量和扭量表示.着重介绍了Grassmann分级表示如何被应用于单眼视觉问题并带来解决方法的简化;通过对刚体运动不同表示的分析,介绍旋量和扭量表示如何克服刚体运动蹬矩阵表示中参数空间具有过多非线性约束的缺点,从而为姿态估计、形状逼近和曲线拼接等问题的解决提供简化方案.Applications of conformal geometric algebra （CGA） in problems of computer vision and graphics related to motion and shape description show that, CGA can provide universal and effective representations and algorithms. By now, such applications have been focused on adopting the Grassmannian structure, the spinor and twist representations of rigid body motions. By analyzing different representations of rigid body motions, we show how the Grassmannian structure is applied to monocular vision problems and simplifies the solving procedure. We then show how the spinor and twist representations can reduce the number of nonlinear constraints in the space of parameters, in sharp contrast to the matrix representation of rigid body motions. This feature makes the spinor and twist representations often very effective in solving problems like pose estimation, shape approximation and curve blending, to name a few.

关 键 词：共形几何代数 刚体运动 单眼视觉 形状逼近 曲线拼接 

分 类 号：O151.24[理学—数学] TP301.6[理学—基础数学]