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Topology-Preserving Image Segmentation by Beltrami Representation of Shapes

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Abstract

A new approach using the Beltrami representation of a shape for topology-preserving image segmentation is proposed in this paper. Using the proposed model, the target object can be segmented from the input image by a region of user-prescribed topology. Given a target image I, a template image J is constructed and then deformed with respect to the Beltrami representation. The deformation on J is designed such that the topology of the segmented region is preserved as which the object is interior in J. The topology-preserving property of the deformation is guaranteed by imposing only one constraint on the Beltrami representation, which is easy to be handled. Introducing the Beltrami representation also allows large deformations on the topological prior J, so that it can be a very simple image, such as an image of disks, torus, disjoint disks. Hence, prior shape information of I is unnecessary for the proposed model. Additionally, the proposed model can be easily incorporated with selective segmentation, in which landmark constraints can be imposed interactively to meet any practical need (e.g., medical imaging). High accuracy and stability of the proposed model to deal with different segmentation tasks are validated by numerical experiments on both artificial and real images.

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Acknowledgements

L. M. Lui is supported by RGC GRF (Project ID: 402413, 14304715). X. C. Tai is supported by Norwegian Research Council project through ISP-Matematikk (Project no. 239033/F20). The authors would like to thank Martin et al. [36] and P. Arbelaez et al. [37] for providing some of the images used as experimental subjects in this paper.

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Authors and Affiliations

  1. The Chinese University of Hong Kong, 222B, Lady Shaw Building, Shatin, Hong Kong

    Hei-Long Chan

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China

    Shi Yan

  3. The Chinese University of Hong Kong, 207, Lady Shaw Building, Shatin, Hong Kong

    Lok-Ming Lui

  4. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Xue-Cheng Tai

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  1. Hei-Long Chan
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  2. Shi Yan
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  4. Xue-Cheng Tai
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Correspondence to Lok-Ming Lui.

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Chan, HL., Yan, S., Lui, LM. et al. Topology-Preserving Image Segmentation by Beltrami Representation of Shapes. J Math Imaging Vis 60, 401–421 (2018). https://doi.org/10.1007/s10851-017-0767-8

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  • DOI: https://doi.org/10.1007/s10851-017-0767-8

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