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http://dx.doi.org/10.9717/kmms.2013.16.2.160

Proposing a Connection Method for Measuring Differentiation of Tangent Vectors at Shape Manifold  

Hahn, Hee-Il (한국외국어대학교 정보통신공학과)
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Abstract
In this paper an algorithm that represents shape sequences with moving frames parallel along the sequences are developed. According to Levi-Civita connection, it is not easy to measure the variation of the vector fields on non-Euclidean spaces without tools to parallel transport them. Thus, parallel transport of the vector fields along the shape sequences is implemented using the theories of principal frame bundle and analyzed via extensive simulation.
Keywords
Shape Sequence; Manifold; Parallel Transport; Connection; Principal Frame Bundle;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 D.G. Kendall, "Shape manifolds, Procrustean Metrics, and Complex Projective Spaces," Bull London Math. Soc., Vol. 16, pp. 81-121, 1984.   DOI
2 T.F. Cootes, C.J. Taylor, and J. Graham, "Active Shape Model-Their Training and Application," Computer Vision and Image Understanding Vol. 61, No. 1, pp. 38-59, 1995.   DOI   ScienceOn
3 한희일, "ASM의 성능향상을 위한 형태 정렬 방식 제안," 멀티미디어학회 논문지, 제15권, 제1 호, Vol. 16, pp. 63-70, 2012.   과학기술학회마을   DOI   ScienceOn
4 E. Klassen, A. Srivastava, W. Mio, and S.H. Joshi, "Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces," IEEE Trans. PAMI , Vol. 26, No. 3, pp. 372-383, 2004.   DOI   ScienceOn
5 M.F. Abdelkader, W. Abd-Almageed, A. Srivastava, and R. Chellapa, "Silhoutte-Based Gesture and Action Recognition Via Modeling Trajectories on Riemannian Shape Manifolds," Computer Vision and Image Understanding, Vol. 115, Issue 3. pp. 439-455, 2011.   DOI   ScienceOn
6 S. Yi, H. Krim, and L.K. Norris, "Human Activity as a Manifold-Valued Random Process," IEEE Trans. Image Processing, Vol. 21, No. 8, pp. 3416-3428, 2012.   DOI   ScienceOn
7 S. Yi, H. Krim, and L.K. Norris, "A Invertible Dimension Reduction of Curves on a Manifold," ICCV Workshops, pp. 1378-1385, 2011.
8 김홍종, "리만 다양체의 홀로노미군," Comm. Korean Math. Soc., 제15권, 제4호, pp. 555-585, 2000.   과학기술학회마을
9 Spivak, A Comprehensive Introduction to Differential Geometry, Vol. 2, Publish or Perish Inc., USA, 2005.