A general framework of piecewise-polynomial Mumford-Shah model for image segmentation. (English) Zbl 1416.94014
Summary: 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.
MSC:
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 68U10 | Computing methodologies for image processing |
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
| 65K05 | Numerical mathematical programming methods |
| 65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
Keywords:
image segmentation; piecewise-polynomial approximation; anisotropic control; intensity heterogeneity; split Bregman iterationReferences:
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