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Poincaré and Poincaré-Cartan integral invariants of a generalized Hamiltonian system

Communications in Nonlinear Science and Numerical Simulation 2001年第1期6卷 45-49页

作者： Yongxin GUO, Liyan JIANG and Ying YU (Department of Physics, Liaoning University, Shenyang 110026, China Department of Electronics and Information Engineering, Dandong Advanced Academy, Dandong 118000, China School of Science, Shenyang University of Te Department of Physics Liaoning University Shenyang 110036 China Dept. of Electronics and Info. Eng. Dandong Advanced Academy Dandong 118000 China School of Science Shenyang University of Technology Shenyang 110023 China

Without Darboux’s transformation, the traditional Hamiltonian formulation of dynamical systems is only suitable to conservative systems or self-adjoint systems. Based on an extension of dynamic space of Birkhoffian systems to a generalized phase space by intro- ducing dummy variables, a generalized Hamiltonian canonical formulation of general systems is constructed, which admits symplectic structure. There exist integral invariants of Poincare and Poincare-Cartan’s type for such systems.

关键词： Birkhoffian systems symplectic structure integral invariants

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Curvature-direction measures for 3D feature detection

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Science China(Information Sciences) 2013年第9期56卷 56-64页

作者： LI JinJiang FAN Hui Department of Computer Science and Technology Tsinghua University School of Computer Science and Technology Shandong Institute of Business and Technology

In this paper, we propose a new robust feature extraction algorithm for 3D models based on principal curvature direction. Generally, the feature regions tend to be more noisy, so it demands a robust technique to handle features effectively. Because the integral invariants are robust against noise, the principal curvature information is estimated based on principal component analysis. After fuzzy filtering of the principal curvature direction, it becomes a good description of the geometric discontinuity. Compared with the curvature values, the impact of noise on the principal curvature direction is small. Therefore, feature extraction based on principal curvature direction is more robust and accurate. The experimental results show that the proposed algorithm can efficiently extract feature and distinguish noise.

关键词： feature extraction integral invariants principal curvature direction

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