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A Nonparametric Statistical Snake Model Using the Gradient Flow of Minimum Probability Density Integration

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Abstract

Nonparametric statistical snakes, constructed under the independent and identically distributed assumption, are an important class of methods for cluttered image segmentation. However, in application, when object or background contains more than one subregions with different intensity distributions, some state-of-the-art nonparametric statistical snakes often converge to boundaries of some subregions and give a false segmentation. In this paper, we formulate the integration of the minimum of the probability densities inside and outside the active contour as an energy functional and seek to minimize it with our active contour model. The independent and identically distributed assumption is also needed here. However, our presented theoretical analysis and various experimental results demonstrate that the proposed model overcomes the problem of existing ones associated with converging to subregion boundary. In addition, the proposed model requires an explicit and uniform initial condition, and so is more convenient for application. Finally, it does not have the so-called numerical conditioning problem which arises with some existing active contour models.

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Acknowledgements

The authors would like to thank Yunmei Chen for her helpful comments on this paper. This work was supported by the National Natural Science Foundation of China (Grant No. 11471001) and the Fundamental Research Funds for the Central Universities. We are grateful to the anonymous reviewers for their comments and suggestions.

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  1. Harbin Engineering University, Harbin, China

    Qiang Li & Tingquan Deng

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  1. Qiang Li
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Correspondence to Qiang Li.

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Li, Q., Deng, T. A Nonparametric Statistical Snake Model Using the Gradient Flow of Minimum Probability Density Integration. J Math Imaging Vis 60, 1150–1166 (2018). https://doi.org/10.1007/s10851-018-0801-5

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