Motor Algebra for 3D Kinematics: The Case of the Hand-Eye Calibration

In this paper we apply the Clifford geometric algebra for solving problems of visually guided robotics. In particular, using the algebra of motors we model the 3D rigid motion transformation of points, lines and planes useful for computer vision and robotics. The effectiveness of the Clifford algebra representation is illustrated by the example of the hand-eye calibration. It is shown that the problem of the hand-eye calibration is equivalent to the estimation of motion of lines. The authors developed a new linear algorithm which estimates simultaneously translation and rotation as components of rigid motion.     

一类高维Mobius变换

利用高维Ｍｏｂｉｕｓ变换的Ｃｌｉｆｆｏｒｄ矩阵表示，证明了一个高维Ｍｏｂｉｕｓ变换是弦度量等距的四个等价条件．同时，利用这些等价条件，得到了三维广义椭圆群及椭圆群的特征．     

两类半群的整体决定性

证明两类半群G0和G’都是整体决定的．设G是群,P是G的单位元．记GO—GU{0}为由G添加一个零元0所得的半群,即G0是0一群．记G’=GU（1）为由G另外添加了一个幺元1所得的半群,注意1≠e,且1是半群G’的幺元．设Go为由所有G0所构成的半群类和G1为由所有G’所构成的半群类．     

A Geometric Approach for the Theory and Applications of 3D Projective Invariants

A central task of computer vision is to automatically recognize objects in real-world scenes. The parameters defining image and object spaces can vary due to lighting conditions, camera calibration and viewing position. It is therefore desirable to look for geometric properties of the object which remain invariant under such changes in the observation parameters. The study of such geometric invariance is a field of active research. This paper presents the theory and computation of projective invariants formed from points and lines using the geometric algebra framework. This work shows that geometric algebra is a very elegant language for expressing projective invariants using n views. The paper compares projective invariants involving two and three cameras using simulated and real images. Illustrations of the application of such projective invariants in visual guided grasping, camera self-localization and reconstruction of shape and motion complement the experimental part.     

Clifford L. Fawl (1930-2002): Obituary.

Obituary for Clifford L. Fawl (1930-2002). (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

电动力学的新表述体系

利用Hestenes的时空代数,可以使电动力学的表达达到空前紧凑的协变形式,同时也与电磁场的现代理解建立了最自然的联系,而这些都是在使用直接观测量E与B的情况下得到的。     

基于Adaboost与Clifford代数的人脸检测

Adaboost算法在光照不均、背景复杂的条件下进行人脸检测时误检率较高。为解决该问题,提出一种基于Adaboost算法与Clifford代数矢量积性质的人脸检测方法。利用Adaboost算法初步定位人脸可能存在的区域,对该区域进行基于知识的校验,如果校验失败,根据Clifford矢量积性质,寻找与待验证区域相似度较高的人脸,当相似度大于阈值时,判断其为人脸。实验结果表明,与Viola-Jones方法相比,该方法在保持较高检测率的同时,降低了误检率,且鲁棒性较好。     

复Clifford代数周期性定理的一个证明

在近代微分几何和数学物理的研究领域中，Clifford代数起着越来越重要的作用，并于Clifford代数，LawsonH B和Michelsohn M L在他们的专著中做了一定的研究，得出了Clifford代数中的周期性同构现象，本文作者在复Clifford代数中引进超结构的概念，给出了复Clifford代数周期性定理的一个新的证明。     

基于超混沌映射和加法模运算的图像保密通信方案

提出了一种基于Clifford超混沌映射的图像加密方案,发送方利用Clifford映射快速地产生混沌序列,对图像在时域作加密预处理;然后通过简单的加法模运算对像素的灰度值进行替换与扩散,并且在每次迭代中采用不同的密钥.经通信双方同步之后,接收方即可解密出原始图像.实验结果表明本方案是可行的,并对系统密钥空间、密钥敏感性等密码学特性进行了分析.