过测地线的调和Bézier曲面设计

极小曲面和测地线是建筑几何领域中2类重要的几何元素,而调和曲面常作为极小曲面的一种线性近似.文中将测地线和调和曲面结合起来,提出一种过给定测地线的调和Bézier曲面设计方法.首先给出了一种构造调和Bézier曲面的新方法,证明了调和Bézier曲面的形状由第一层和第二层的控制顶点完全决定;然后根据测地线的性质,证明了过给定测地线的调和Bézier曲面的形状由该测地线和第二层的首末2个控制顶点完全决定.最后通过若干实例验证了该方法的有效性.文中方法充分利用了测地线和调和曲面的特殊几何性质,对张拉膜建筑结构的几何设计具有一定的实用价值.     

Gender discriminating models from facial surface normals

In this paper, we show how to use facial shape information to construct discriminating models for gender classification. We represent facial shapes using 2.5D fields of facial surface normals, and investigate three different methods to improve the gender discriminating capacity of the model constructed using the standard eigenspace method. The three methods are novel variants of principal geodesic analysis (PGA) namely (a) weighted PGA, (b) supervised weighted PGA, and (c) supervised PGA. Our starting point is to define a weight map over the facial surface that indicates the importance of different locations in discriminating gender. We show how to compute the relevant weights and how to incorporate the weights into the 2.5D model construction. We evaluate the performance of the alternative methods using facial surface normals extracted from 3D range images or recovered from brightness images. Experimental results demonstrate the effectiveness of our methods. Moreover, the classification accuracy, which is as high as 97%, demonstrates the effectiveness of using facial shape information for gender classification.     

Geodesic Matching with Free Extremities

In this paper, we describe how to use geodesic energies defined on various sets of objects to solve several distance related problems. We first present the theory of metamorphoses and the geodesic distances it induces on a Riemannian manifold, followed by classical applications in landmark and image matching. We then explain how to use the geodesic distance for new issues, which can be embedded in a general framework of matching with free extremities. This is illustrated by results on image and shape averaging and unlabeled landmark matching. Laurent Garcin is a former student of the Ecole Polytechnique. He obtained his Ph.D. in 2004 at the Ecole Normale de Cachan, working on matching methods for landmarks and images. He is an engineer at the French National Geographic Institute. Laurent Younes is a former student of the Ecole Normale Superieure in Paris. He was awarded the Ph.D. from the University Paris Sud in 1989, and the thesis advisor certification from the same university in 1995. He works on the statistical analysis of images and shapes, and on modeling shape deformations and shape spaces. Laurent Younes entered CNRS, the French National Research Center in October 1991, in which he has been a “Directeur de Recherche" until 2003. He is now a professor at the Department of Applied Mathematics and Statistics Department and the Center for Imaging Science at Johns Hopkins University in July 2003.     

Smooth cutting pattern generation technique for membrane structures using geodesic line on subplane and spline interpolation

Practical techniques for smooth geodesic patterning of membrane structures were investigated, For the geodesic search, adjustment of the subplane of the extracted elements series was proposed, and various spline approximation methods were used to flatten the strip for the generation of a smooth pattern. This search approach is very simple, and the geodesic line could be easily attained by the proposed method without the need for a difficult computation method. Smooth cutting patterning can also be generated by spline approximation without the noise in discrete nodal information. Additionally, the geodesic cutting pattern saved about 21% of the required area for the catenary model due to the reduction of the curvature of the planar pattern seam line.     

采用测地线活动轮廓模型检测与跟踪运动目标

水平集几何活动轮廓模型能较好地适应曲线的拓扑变化.为了跟踪和获取刚体和非刚体运动目标的轮廓信息,提出了一种基于改进测地线活动轮廓(GAC)模型和Kalman滤波相结合的算法以检测和跟踪运动目标.该算法首先采用高斯混合模型和背景差分获取目标的运动区域,在运动区域内采用引入距离规则化项的GAC模型进行曲线演化,使改进GAC模型在运动目标的真实轮廓处收敛;然后通过结合Kalman滤波预测目标下一帧的位置,实现对目标轮廓跟踪.实验结果表明,该方法适用于刚体和非刚体目标,在部分遮挡的情况下也能保持良好的检测和跟踪效果.     

定常约束力学系统的相空间上的联络

提出动力学流关于切丛上联络的一种协变性，求出定常约束力学系统的联络，其测地线方程为系统的运动方程，该联络由系统的动力学函数和约束确定且当动力学流为二阶齐次时约化为通常的动力学联络。     

Research on Combination Winding of Revolving Bodies

A methematical model based upon the theory of differential geometry isestablished for the combination winding of revolving bodies and programs are developedfor the filament winding operations as well.Trial winding on a filament winding machineproved this model is right and useful.     

自动铺带轨迹规划中测地线算法研究

本文针对复合材料自动铺放轨迹规划中自然路径求解中的测地线问题给出了求解两点之间的测地线的数值计算方法。该方法将微分方程的边值问题转化为初值问题,在初始方向的选取上较以往方法几何意义更为直观,算例证明算法的正确性。     

A Mathematical Model for the Geodesic Winding of Surfaces of Rotation

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Classification of Supertransitive 2-Webs on Surfaces

We obtain a complete classification of supertransitive 2-webs on a closed oriented surface of genus p 1 in terms of asymptotic directions of leaves on the universal covering surface and represent all topological classes of 2-webs by means of compatible pairs of transversal perfect geodesic laminations.