Hessian Eigenfunctions for Triangular Mesh Parameterization



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Hessian Locally Linear Embedding (HLLE) is an algorithm that computes the nullspace of a Hessian functional H for Dimensionality Reduction (DR) of a sampled manifold M -- This article presents a variation of classic HLLE for parameterization of 3D triangular meses -- Contrary to classic HLLE which estimates local Hessian nullspaces, the proposed approach follows intuitive ideas from Differential Geometry where the local Hessian is estimated by quadratic interpolation and a partition of unity is used to join all neighborhoods -- In addition, local average triangle normals are used to estimate the tangent plane TxM at x ∈ M instead of PCA, resulting in local parameterizations which reflect better the geometry of the surface and perform better when the mesh presents sharp features -- A high frequency dataset (Brain) is used to test our algorithm resulting in a higher rate of success (96.63%) compared to classic HLLE (76.4%)


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@conference{grapp16, author={Daniel Mejia and Oscar Ruiz-Salguero and Carlos A. Cadavid}, title={Hessian Eigenfunctions for Triangular Mesh Parameterization}, booktitle={Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications}, year={2016}, pages={75-82}, doi={10.5220/0005668200730080}, isbn={978-989-758-175-5}, }