IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v286y2016icp29-40.html
   My bibliography  Save this article

Radial basis functions and level set method for image segmentation using partial differential equation

Author

Listed:
  • Li, Shuling
  • Li, Xiaolin

Abstract

Combining nonlinear evolution equations, which arise from image segmentation using partial differential equation-based level set method, using radial basis functions, a meshless numerical algorithm is presented for image segmentation in this paper. Both globally supported and compactly supported radial basis functions are used to interpolate the level set function of the evolution equation with a high level of accuracy and smoothness. The nonlinear evolution equation is finally cast into ordinary differential equations and Euler’s scheme is employed. Compared with traditional level set approaches, the presented algorithm is robust to initialization or even free of manual initialization, and avoids the complex and costly re-initialization of the level set function. The capability of the presented algorithm is demonstrated through some numerical experiments.

Suggested Citation

  • Li, Shuling & Li, Xiaolin, 2016. "Radial basis functions and level set method for image segmentation using partial differential equation," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 29-40.
  • Handle: RePEc:eee:apmaco:v:286:y:2016:i:c:p:29-40
    DOI: 10.1016/j.amc.2016.04.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316302442
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2016.04.002?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. Kadalbajoo, Mohan K. & Kumar, Alpesh & Tripathi, Lok Pati, 2015. "A radial basis functions based finite differences method for wave equation with an integral condition," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 8-16.
    2. Boyd, John P., 2015. "A Fourier error analysis for radial basis functions and the Discrete Singular Convolution on an infinite uniform grid, Part 1: Error theorem and diffusion in Fourier space," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 132-140.
    3. Rad, Jamal Amani & Parand, Kourosh & Ballestra, Luca Vincenzo, 2015. "Pricing European and American options by radial basis point interpolation," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 363-377.
    4. Golbabai, Ahmad & Nikpour, Ahmad, 2015. "Stability and convergence of radial basis function finite difference method for the numerical solution of the reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 567-580.
    5. Guarin, Alexander & Liu, Xiaoquan & Ng, Wing Lon, 2011. "Enhancing credit default swap valuation with meshfree methods," European Journal of Operational Research, Elsevier, vol. 214(3), pages 805-813, November.
    6. Duan, Xianbao & Li, Feifei, 2015. "Material distribution resembled level set method for optimal shape design of Stokes flow," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 21-30.
    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. Reza Mollapourasl & Ali Fereshtian & Michèle Vanmaele, 2019. "Radial Basis Functions with Partition of Unity Method for American Options with Stochastic Volatility," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 259-287, January.

    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. Stolbunov, Valentin & Nair, Prasanth B., 2018. "Sparse radial basis function approximation with spatially variable shape parameters," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 170-184.
    2. Gong, Pu & Zou, Dong & Wang, Jiayue, 2018. "Pricing and simulation for real estate index options: Radial basis point interpolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 177-188.
    3. Luca Vincenzo Ballestra, 2018. "Fast and accurate calculation of American option prices," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 399-426, November.
    4. Mercadier, Mathieu & Lardy, Jean-Pierre, 2019. "Credit spread approximation and improvement using random forest regression," European Journal of Operational Research, Elsevier, vol. 277(1), pages 351-365.
    5. Somayeh Abdi-Mazraeh & Ali Khani & Safar Irandoust-Pakchin, 2020. "Multiple Shooting Method for Solving Black–Scholes Equation," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 723-746, December.
    6. Xubiao He & Pu Gong, 2020. "A Radial Basis Function-Generated Finite Difference Method to Evaluate Real Estate Index Options," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 999-1019, March.
    7. Mitra, Sovan & Date, Paresh & Mamon, Rogemar & Wang, I-Chieh, 2013. "Pricing and risk management of interest rate swaps," European Journal of Operational Research, Elsevier, vol. 228(1), pages 102-111.
    8. Guarin, Alexander & Liu, Xiaoquan & Ng, Wing Lon, 2014. "Recovering default risk from CDS spreads with a nonlinear filter," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 87-104.
    9. Seda Gulen & Catalin Popescu & Murat Sari, 2019. "A New Approach for the Black–Scholes Model with Linear and Nonlinear Volatilities," Mathematics, MDPI, vol. 7(8), pages 1-14, August.
    10. Hajimohammadi, Zeinab & Parand, Kourosh, 2021. "Numerical learning approximation of time-fractional sub diffusion model on a semi-infinite domain," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    11. Alessandro Andreoli & Luca Vincenzo Ballestra & Graziella Pacelli, 2018. "Pricing Credit Default Swaps Under Multifactor Reduced-Form Models: A Differential Quadrature Approach," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 379-406, March.
    12. Zaheer-ud-Din & Muhammad Ahsan & Masood Ahmad & Wajid Khan & Emad E. Mahmoud & Abdel-Haleem Abdel-Aty, 2020. "Meshless Analysis of Nonlocal Boundary Value Problems in Anisotropic and Inhomogeneous Media," Mathematics, MDPI, vol. 8(11), pages 1-19, November.
    13. Shirzadi, Mohammad & Rostami, Mohammadreza & Dehghan, Mehdi & Li, Xiaolin, 2023. "American options pricing under regime-switching jump-diffusion models with meshfree finite point method," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    14. Weiwei Liu & Zhile Yang & Kexin Bi, 2017. "Forecasting the Acquisition of University Spin-Outs: An RBF Neural Network Approach," Complexity, Hindawi, vol. 2017, pages 1-8, October.
    15. Li, Yang & Liu, Dejun & Yin, Zhexu & Chen, Yun & Meng, Jin, 2023. "Adaptive selection strategy of shape parameters for LRBF for solving partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    16. Antonio André Novotny & Jan Sokołowski & Antoni Żochowski, 2019. "Topological Derivatives of Shape Functionals. Part II: First-Order Method and Applications," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 683-710, March.
    17. Asif, Muhammad & Ali Khan, Zar & Haider, Nadeem & Al-Mdallal, Qasem, 2020. "Numerical simulation for solution of SEIR models by meshless and finite difference methods," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    18. Kirkby, J. Lars & Nguyen, Dang H. & Nguyen, Duy, 2020. "A general continuous time Markov chain approximation for multi-asset option pricing with systems of correlated diffusions," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    19. A. Golbabai & E. Mohebianfar, 2017. "A New Stable Local Radial Basis Function Approach for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 49(2), pages 271-288, February.
    20. Gong, Pu & Dai, Jun, 2017. "Pricing real estate index options under stochastic interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 309-323.

    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:286:y:2016:i:c:p:29-40. 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.