变量稀疏扩散及其在网格处理中的应用

IF 1.5 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Yongjiang Xue, Wei Wang, Qingzeng Song
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引用次数: 0

摘要

目的本研究的主要目的是解决在计算机图形中处理几何数据时如何保持特征完整性这一长期难题。我们开发了一种变异稀疏扩散模型,该模型将高阶 L1 正则化框架与 Dirichlet 边界约束整合在一起,专门用于保留边缘定义。该模型采用创新的顶点更新策略,优化了网格修复的质量。我们利用增强拉格朗日方法来解决这种方法固有的计算难题,从而有效地管理扩散强度和特征保留之间的权衡。我们的方法涉及对分割和修复过程的详细分析,重点是保持三角形曲面上特征的清晰度。研究结果我们的研究结果表明,在网格处理过程中,所提出的变异稀疏扩散模型在保留尖锐特征方面明显优于传统的平滑扩散方法。该模型可确保在网格分割中划定清晰的边界,并在修复任务中实现对劣化网格的高保真还原。模型中创新的顶点更新策略有助于提高修复后的网格质量。经验评估表明,我们的方法能更有效地保持原始、清晰特征的完整性,尤其是在具有复杂细节的复杂几何图形中。 原创性/价值这项研究的原创性在于将高阶 L1 正则化框架新颖地应用于网格处理领域,而这种方法在此领域并未得到常规应用。我们工作的价值在于为网格处理过程中的特征退化问题提供了稳健的解决方案。我们模型独特的顶点更新策略和增强拉格朗日法的优化使用是我们的独特贡献,提升了几何处理的先进水平。我们的模型在网格分割和修复过程中成功地保留了特征,是计算机图形学的一大进步,为学术研究和工业应用带来了实际好处。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Variational sparse diffusion and its application in mesh processing

Purpose

The primary objective of this study is to tackle the enduring challenge of preserving feature integrity during the manipulation of geometric data in computer graphics. Our work aims to introduce and validate a variational sparse diffusion model that enhances the capability to maintain the definition of sharp features within meshes throughout complex processing tasks such as segmentation and repair.

Design/methodology/approach

We developed a variational sparse diffusion model that integrates a high-order L1 regularization framework with Dirichlet boundary constraints, specifically designed to preserve edge definition. This model employs an innovative vertex updating strategy that optimizes the quality of mesh repairs. We leverage the augmented Lagrangian method to address the computational challenges inherent in this approach, enabling effective management of the trade-off between diffusion strength and feature preservation. Our methodology involves a detailed analysis of segmentation and repair processes, focusing on maintaining the acuity of features on triangulated surfaces.

Findings

Our findings indicate that the proposed variational sparse diffusion model significantly outperforms traditional smooth diffusion methods in preserving sharp features during mesh processing. The model ensures the delineation of clear boundaries in mesh segmentation and achieves high-fidelity restoration of deteriorated meshes in repair tasks. The innovative vertex updating strategy within the model contributes to enhanced mesh quality post-repair. Empirical evaluations demonstrate that our approach maintains the integrity of original, sharp features more effectively, especially in complex geometries with intricate detail.

Originality/value

The originality of this research lies in the novel application of a high-order L1 regularization framework to the field of mesh processing, a method not conventionally applied in this context. The value of our work is in providing a robust solution to the problem of feature degradation during the mesh manipulation process. Our model’s unique vertex updating strategy and the use of the augmented Lagrangian method for optimization are distinctive contributions that enhance the state-of-the-art in geometry processing. The empirical success of our model in preserving features during mesh segmentation and repair presents an advancement in computer graphics, offering practical benefits to both academic research and industry applications.

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来源期刊
Engineering Computations
Engineering Computations 工程技术-工程:综合
CiteScore
3.40
自引率
6.20%
发文量
61
审稿时长
5 months
期刊介绍: The journal presents its readers with broad coverage across all branches of engineering and science of the latest development and application of new solution algorithms, innovative numerical methods and/or solution techniques directed at the utilization of computational methods in engineering analysis, engineering design and practice. For more information visit: http://www.emeraldgrouppublishing.com/ec.htm
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