A general framework of piecewise-polynomial Mumford–Shah model for image segmentation

ABSTRACT

A new general framework of piecewise-polynomial Mumford–Shah model is proposed. In terms of the fidelity term, we use piecewise polynomials to approximate the inner and outer regions of the contour of the objective image. For more accurate approximation of the image, the proposed model has no constraint on the regularization term for polynomials. Moreover, we apply the anisotropic control to drive the initial contour to the desirable position. The proposed model generalizes the well-known Chan–Vese model and improves Vese's model, which is almost the simplest framework to apply piecewise polynomials to approximate the original Mumford–Shah model. Instead of solving the Euler–Lagrange equation by evolution implementation, we utilize the split Bregman iteration, which is shown to be a fast algorithm. Experimental results demonstrate that the proposed model has more desirable performance in terms of segmentation accuracy, efficiency and robustness, compared with several other variational models in addressing some challenging segmentation scenarios.

KEYWORDS:

• Image segmentation
• piecewise-polynomial approximation
• anisotropic control
• intensity heterogeneity
• split Bregman iteration

2010 AMS Subject Classifications:

• 11Y11
• 11Y16
• 11G20
• 11G99
• 68W20

Acknowledgements

The authors would like to express their sincere gratitude to the anonymous reviewers for their constructive suggestions, which helped to improve greatly the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of C. Chen was supported in part by National Natural Science Foundation of China (NSFC) for youth under the grant [11301520]. The work of G. Xu was supported in part by NSFC under the grants [11101401, 81173663] and NSFC Fund for Creative Research Groups of China under the grant [11321061].