18 January 2006 POSS: efficient nonlinear optimization for parameterization methods
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We propose a new, generic method called POSS (Parameterization by Optimization in Spectral Space) to efficiently obtain parameterizations with low distortions for 3D surface meshes. Given a mesh, first we compute a valid initial parameterization using an available method and then express the optimal solution as a linear combination of the initial parameterization and an unknown displacement term. The displacement term is approximated by a linear combination of the eigenvectors with the smallest eigenvalues of a mesh Laplacian. This approximation considerably reduces the number of unknowns while minimizing the deviation from the optimality. Finally, we find a valid parameterization with low distortion using a standard constrained nonlinear optimization procedure. POSS is fast, flexible, generic, and hierarchical. Its advantage has been confirmed by its application to planar parameterizations of surface meshes that represent complex human cortical surfaces. This method has a promising potential to improve the efficiency of all parameterization techniques which involve constrained nonlinear optimization.
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Fijoy Vadakkumpadan, Fijoy Vadakkumpadan, Yunxia Tong, Yunxia Tong, Yinlong Sun, Yinlong Sun, } "POSS: efficient nonlinear optimization for parameterization methods", Proc. SPIE 6066, Vision Geometry XIV, 60660O (18 January 2006); doi: 10.1117/12.643270; https://doi.org/10.1117/12.643270

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