Hessian Eigenfunctions for Triangular Mesh Parameterization

Daniel Mejia, Oscar Ruiz-Salguero, Carlos A. Cadavid

2016

Abstract

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 meshes. 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 2 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%).

Paper Citation

in Harvard Style

Mejia D., Ruiz-Salguero O. and Cadavid C. (2016). Hessian Eigenfunctions for Triangular Mesh Parameterization . In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2016) ISBN 978-989-758-175-5, pages 75-82. DOI: 10.5220/0005668200730080

in Bibtex Style

@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 - Volume 1: GRAPP, (VISIGRAPP 2016)},
year={2016},
pages={75-82},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005668200730080},
isbn={978-989-758-175-5},
}

in EndNote Style

TY - CONF
JO - Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2016)
TI - Hessian Eigenfunctions for Triangular Mesh Parameterization
SN - 978-989-758-175-5
AU - Mejia D.
AU - Ruiz-Salguero O.
AU - Cadavid C.
PY - 2016
SP - 75
EP - 82
DO - 10.5220/0005668200730080