A 3D multi-grid algorithm for the Chan–Vese model of variational image segmentation

Abstract

Variational segmentation models provide effective tools for image processing applications. Although existing models are continually refined to increase their capabilities, solution of such models is often a slow process, since fast methods are not immediately applicable to nonlinear problems. This paper presents an efficient multi-grid algorithm for solving the Chan–Vese model in three dimensions, generalizing our previous work on the topic in two dimensions, but this direct generalized method is low performance or unfeasible. So here, we first present two general smoothers for a nonlinear multi-grid method and then give our three new adaptive smoothers which can choose optimal a parameter of the smoothers automatically, also we analyse them using a local Fourier analysis and our theorem to inform how to obtain an optimal parameter and the best smoother selection. Finally, various advantages of our recommended algorithm are illustrated, using both synthetic and real images.

Keywords:

• variational problems
• optimization
• Euler–Lagrange equation
• 3D image segmentation
• multi-grid algorithm
• adaptive smoothers
• local Fourier analysis

2000 AMS Subject Classification :

• 62H35
• 65N55
• 74G65
• 74G75

Acknowledgements

This work is partially supported by the National Natural Science Foundation of China grant numbered 11171051 and the Fundamental Research Funds for the Central Universities (China).