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Variational sparse diffusion and its application in mesh processing

Yongjiang Xue (School of Computer Science and Technology, Tiangong University, Tianjin, China)
Wei Wang (School of Electronic and Information Engineering, Tiangong University, Tianjin, China)
Qingzeng Song (School of Computer Science and Technology, Tiangong University, Tianjin, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 4 March 2024

Issue publication date: 16 April 2024




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.


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.


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.


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.



We would thank the authors of Tong et al. (2020) for providing their results and Huayan Zhang for providing suggestions for the algorithms. This work was funded by the NSF of China (Nos. 61802279 and 61602341) and NSF of Tianjin (Nos. 18JCQNJC00100 and 17JCQNJC00600).


Xue, Y., Wang, W. and Song, Q. (2024), "Variational sparse diffusion and its application in mesh processing", Engineering Computations, Vol. 41 No. 2, pp. 289-306.



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