Authors:
Daniel Mejia
;
Oscar Ruiz-Salguero
and
Carlos A. Cadavid
Affiliation:
Universidad EAFIT, Colombia
Keyword(s):
Applied Differential Geometry, Dimensionality Reduction, Hessian Locally Linear Embedding, Manifold Learning, Mesh Parameterization.
Related
Ontology
Subjects/Areas/Topics:
CAGD/CAD/CAM Systems
;
Computer Vision, Visualization and Computer Graphics
;
Geometric Computing
;
Geometry and Modeling
;
Texture Models, Analysis, and Synthesis
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%).