Dimensionality Reduction of Laplacian Embedding for 3D Mesh Reconstruction

Abstract

Laplacian eigenbases are the important thing that we have to process from 3D mesh information. The information of geometric 3D mesh are include vertices locations and the connectivity of graph. Due to spectral analysis, geometric 3D mesh for large and sparse graphs with thousands of vertices is not practical to compute all the eigenvalues and eigenvector. Because of that, in this paper we discuss how to build 3D mesh reconstruction by reducing dimensionality on null eigenvalue but retain the corresponding eigenvector of Laplacian Embedding to simplify mesh processing. The result of reducing information should have to retained the connectivity of graph. The advantages of dimensionality reduction is for computational eficiency and problem simplification. Laplacian eigenbases is the point of dimensionality reduction for 3D mesh reconstruction. In this paper, we show how to reconstruct geometric 3D mesh after approximation step of 3D mesh by dimensionality reduction. Dimensionality reduction shown by Laplacian Embedding matrix. Furthermore, the effectiveness of 3D mesh reconstruction method will evaluated by geometric error, differential error, and final error. Numerical approximation error of our result are small and low complexity of computational.