A variational level set model based on local-global function approximation for image segmentation

The variational level set model is widely used in image segmentation tasks due to its sound theoretical basis and reliable performance. However, it often faces limitations when dealing with images that contain intensity inhomogeneity and noise. To address this challenge, a novel variational level set model based on local -global function approximation (LSM-LGA) is proposed in this paper. In this approach, an approximation function space is first introduced for the input image. This space defines the function as a linear combination of a local approximation image and a global one, weighted by two coefficients and two complementary characteristic functions defined by a level set function. To achieve the optimal representation of the input image within this approximation function space, a hybrid -metric strategy that combines Euclidean distance and Jeffreys divergence is introduced. An alternating direction method of multiplier (ADMM) based on Euclidean distance is developed to solve for the optimal weight coefficients of the local and global approximation images. Additionally, gradient descent based on Jeffreys divergence is utilized to solve for the optimal level set function. Furthermore, the existence and uniqueness of the optimal approximation function are proven using the theory of projection onto convex sets. Extensive numerical experiments on natural and synthetic images with intensity inhomogeneity, textures, and noise validate that the LSM-LGA exhibits superior performance compared with several state-of-theart models in terms of segmentation quality and computational efficiency.