A Partition Based Method for Spectrum-Preserving Mesh Simplification

Download

A Partition Based Method for Spectrum-Preserving Mesh Simplification.pdf

Date

2022-8-29

Author

Yazgan, Misranur

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

199
views

349
downloads

When the complexity of a mesh starts introducing high computational costs, mesh simplification methods come into the picture, to reduce the number of elements utilized to represent the mesh. Majority of the simplification methods focus on preserving the appearance of the mesh, ignoring the spectral properties of the differential operators derived from the mesh. The spectrum of the Laplace-Beltrami operator is essential for a large subset of applications in geometry processing. Coarsening a mesh without considering its spectral properties might result with incorrect calculations on the simplified mesh. Given a 3D triangular mesh, this thesis aims to decrease its resolution by applying mesh simplification, while focusing on preserving the spectral properties of the associated cotangent Laplace-Beltrami operator. Unlike the existing spectrum-preserving coarsening methods, this work utilizes solely the eigenvalues of the operator, in order to preserve the spectrum. The presented method is partition based, in a way that the input mesh is divided into smaller patches and each patch is simplified individually. The method is evaluated on a variety of meshes, by using functional maps and quantitative norms. These metrics are used to measure how well the eigenvalues and eigenvectors of the Laplace-Beltrami operator computed on the input mesh are maintained by the output mesh. At the end of this thesis, it is demonstrated that the achieved spectrum preservation is at least as effective as the existing spectral coarsening methods.

Subject Keywords

Laplace-Beltrami operator, Mesh simplification, Spectral mesh simplification, Spectral coarsening, Geometry processing

URI

https://hdl.handle.net/11511/99624

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

IMPROVED PREDICTION FOR LAYERED PREDICTIVE ANIMATED MESH COMPRESSION Bici, M. Oguz; Akar, Gözde (2010-09-29) In this paper, we deal with layered predictive compression of animated meshes represented by series of 3D static meshes with same connectivity. We propose two schemes to improve the prediction. First improvement is using weighted spatial prediction rather than averaging neighbor vertices. The second improvement is a novel predictor based on rotation angle of incident triangles in current and previous frames. The experimental results show that around 6- 10 % bitrate reduction can be achieved by replacing the...
A METHOD FOR COMPARATIVE-EVALUATION OF EIT ALGORITHMS USING A STANDARD DATA SET IDER, YZ; EYUBOGLU, BM; KUZUOGLU, M; Leblebicioğlu, Mehmet Kemal; BAYSAL, U; CAGLAR, BK; BIRGUL, O (IOP Publishing, 1995-08-01) The point spread function (PSF) is the most widely used tool for quantifying the spatial resolution of imaging systems. However, prerequisites for the proper use of this tool are linearity and space invariance. Because EIT is non-linear it is only possible to compare different reconstruction algorithms using a standard data set. In this study, the FEM is used to generate simulation data, which are used to investigate the non-linear behaviour of EIT, the space dependence of its PSF and its capability of reso...
A FAST IMAGE-RECONSTRUCTION ALGORITHM FOR ELECTRICAL-IMPEDANCE TOMOGRAPHY Kuzuoğlu, Mustafa; Leblebicioğlu, Mehmet Kemal (IOP Publishing, 1994-05-01) In this paper, we propose a fast algorithm for the reconstruction of the conductivity perturbation DELTAsigma about a known conductivity variation sigma0. The method is based on the minimization of a quadratic functional subject to linear constraints, where the existence of a unique solution is guaranteed. The algorithm developed for this purpose is iterative and each iteration is composed of a simple matrix multiplication. The validity of this method is illustrated with several examples.
An algorithm for line matching in an image by mapping into an n-dimensional vector space Sultanov, Raiymbek; Atakan, Ahmet; Ismailova, Rita (2019-01-01) This paper proposes a minimal length difference algorithm for construction of a line in an image by solving the problem of optimal contour approximation. In this algorithm, a method for finding interest points is proposed, and the object matching (classification) is done by mapping interest points onto a vector space. In cases where the lines in the representation of the images are not smooth, the algorithm converges rapidly. The results of the experiments showed that for convergence of the contour simplifi...
Improved prediction methods for scalable predictive animated mesh compression Bici, M. Oguz; Akar, Gözde (2011-10-01) Animated meshes represented as sequences of static meshes sharing the same connectivity require efficient compression. Among the compression techniques, layered predictive coding methods efficiently encode the animated meshes in a structured way such that the successive reconstruction with an adaptable quality can be performed. The decoding quality heavily depends on how well the prediction is performed in the encoder. Due to this fact, in this paper, three novel prediction structures are proposed and integ...

Citation Formats

M. Yazgan, “A Partition Based Method for Spectrum-Preserving Mesh Simplification,” M.S. - Master of Science, Middle East Technical University, 2022.