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

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  • 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
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    References listed on IDEAS

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    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. 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.
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    4. 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.
    5. 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.
    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.
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    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.

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