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A variational level set model combining with local Gaussian fitting and Markov random field regularization

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Abstract

To effectively and accurately segment images in the presence of intensity inhomogeneity and noise, a variational level set model based on maximum a posteriori (MAP) criterion is proposed in this paper. In the Bayesian framework, the posterior probability of the corrected smooth image under the observation condition is described by a likelihood function of the observation multiplied by a prior probability of the corrected smooth image. In the model, the likelihood function of the observation is computed under the assumption that the observed image obeys the local Gaussian distribution with both varying means and variances; and based on Markov random field (MRF) model, the prior probability of the corrected smooth image is defined as a Gibbs energy function that is related to the total variation. Maximizing the likelihood function can effectively capture the local change of image intensity, and maximizing the prior probability can restrain the influence of noise. An alternating direction iterative algorithm combining with fixed point iteration and gradient descent is introduced to solve the proposed model. The experiments for both synthetic and real images validate the proposed model. In addition, compared with several state-of-the-art variational level set models, the proposed model show the best segmentation performance.

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Acknowledgments

This work was supported in part by the Natural Science Foundation of China under Grant No. 62061016, 61561019.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei, 445000, People’s Republic of China

    Yanjun Ren, Liming Tang & Jie Zheng

  2. Enshi Polytechnic, Enshi, Hubei, 445000, People’s Republic of China

    Honglu Zhang

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  1. Yanjun Ren
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  2. Liming Tang
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  3. Honglu Zhang
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  4. Jie Zheng
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Correspondence to Liming Tang.

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Ren, Y., Tang, L., Zhang, H. et al. A variational level set model combining with local Gaussian fitting and Markov random field regularization. Multimed Tools Appl 81, 4511–4534 (2022). https://doi.org/10.1007/s11042-021-11783-2

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  • DOI: https://doi.org/10.1007/s11042-021-11783-2

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