An improved hybrid gradient variation level set method for image segmentation and bias correction

Abstract

Minimizing an energy functional defined on the level set function with gradient descent method is called variational level set methods. The variational methods are characterized by deriving an energy functional from some priori mathematical models and minimizing this energy functional by calculating the $L^2$ gradient over all possible partitions. The Sobolev gradient is more effective for minimizing the curve length functional than the $L^2$ gradient by the gradient descent method. In this paper, we propose a novel hybrid gradient active contour model in partial differential equation formulation based on method of Li et al. to correct the bias for image segmentation. By using the Sobolev gradient for the internal energy (curve length), and using $L^2$ gradient for the external energy during the evolution of curve. The proposed model can effectively and efficiently segment images with intensity inhomogeneity. Experimental results obtained on synthetic and real images show the advantages of our method in terms of computational efficiency.

Keywords:

• image segmentation
• Sobolev gradient
• $L^2$ gradient
• level set method
• bias fieldcorrection

2010 AMS Subject Classification:

• 62H35
• 35A15
• 74G65
• 65N06

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by 111 Project of Chinese Ministry of Education [Grant No. B12018], the National Natural Science Foundation of China [Grant No. 61373055] and the Industrial Support Program of Jiangsu Province [Grant No. BE2012031].