Abstract
In this paper, we propose a novel subspace learning of shape dynamics. In comparison with the previous works, our method is invertible and better characterises the nonlinear geometry of a shape manifold while being computationally more efficient. In this work, with a parallel moving frame on a shape manifold, each path of shape dynamics is uniquely represented in a subspace spanned by the moving frame, given an initial condition (the starting point and the starting frame). Given the parallelism of the frame and ensured by a Levi-Civita connection, and a path on a shape manifold, the parallel moving frame along the path is uniquely determined up to the choice of the starting frame.
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Yi, S., Krim, H. (2013). A Subspace Learning of Dynamics on a Shape Manifold: A Generative Modeling Approach. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_8
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DOI: https://doi.org/10.1007/978-3-642-40020-9_8
Publisher Name: Springer, Berlin, Heidelberg
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