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A fast, efficient, and explicit phase-field model for 3D mesh denoising

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  • Wang, Jian
  • Han, Ziwei
  • Jiang, Wenjing
  • Kim, Junseok

Abstract

In this paper, we propose a fast and efficient explicit three-dimensional (3D) mesh denoising algorithm that utilizes the Allen–Cahn (AC) equation with a fidelity term. The phase-field model is used to describe the characteristics of both the surface and interior of an object, allowing us to represent the 3D mesh model with noise using a phase-field function. By using the phase separation property of the AC equation and the fidelity term, the model can effectively preserve the original structures and features during the smoothing process, even in the presence of noise in various regions. The modified AC equation is numerically discretized using the explicit finite difference method, where the values at neighboring grid points are used as Dirichlet boundary conditions. Because the algorithm is local and explicit, it guarantees both effective denoising of 3D mesh models and rapid implementation speed. To validate the efficacy of the proposed algorithm, we conduct various computational experiments. Furthermore, we propose an implicit-explicit numerical scheme using the Crank–Nicolson method to address the denoising problem of 3D mesh models and perform related experiments.

Suggested Citation

  • Wang, Jian & Han, Ziwei & Jiang, Wenjing & Kim, Junseok, 2023. "A fast, efficient, and explicit phase-field model for 3D mesh denoising," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    • Handle: RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323004083
    DOI: 10.1016/j.amc.2023.128239
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    References listed on IDEAS

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    1. Buyun Sheng & Feiyu Zhao & Xiyan Yin & Chenglei Zhang & Hui Wang & Peide Huang, 2018. "A Lightweight Surface Reconstruction Method for Online 3D Scanning Point Cloud Data Oriented toward 3D Printing," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-16, May.
    2. Upadhyay, Prateep & Upadhyay, S.K. & Shukla, K.K., 2021. "Magnetic resonance images denoising using a wavelet solution to laplace equation associated with a new variational model," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    3. Cascarano, Pasquale & Piccolomini, Elena Loli & Morotti, Elena & Sebastiani, Andrea, 2022. "Plug-and-Play gradient-based denoisers applied to CT image enhancement," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    4. Tan, Zhijun & Yang, Junxiang & Chen, Jianjun & Kim, Junseok, 2023. "An efficient time-dependent auxiliary variable approach for the three-phase conservative Allen–Cahn fluids," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    5. Liu, Jingjing & Ma, Ruijie & Zeng, Xiaoyang & Liu, Wanquan & Wang, Mingyu & Chen, Hui, 2021. "An efficient non-convex total variation approach for image deblurring and denoising," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    6. Li, Xiao & Meng, Xiaoying & Xiong, Bo, 2022. "A fractional variational image denoising model with two-component regularization terms," Applied Mathematics and Computation, Elsevier, vol. 427(C).
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