IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v458y2023ics0096300323004083.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323004083
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2023.128239?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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).
    3. 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).
    4. 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).
    5. 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).
    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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yang, Junxiang & Lee, Dongsun & Kwak, Soobin & Ham, Seokjun & Kim, Junseok, 2024. "The Allen–Cahn model with a time-dependent parameter for motion by mean curvature up to the singularity," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sining Huang & Yupeng Chen & Tiantian Qiao, 2021. "An Extended Reweighted ℓ 1 Minimization Algorithm for Image Restoration," Mathematics, MDPI, vol. 9(24), pages 1-15, December.
    2. Xuyuan Zhang & Yu Han & Sien Lin & Chen Xu, 2023. "A Fuzzy Plug-and-Play Neural Network-Based Convex Shape Image Segmentation Method," Mathematics, MDPI, vol. 11(5), pages 1-16, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323004083. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.