Intensity inhomogeneity image segmentation based on the gradient-based spaces and the prior constraint

Abstract

Image segmentation is a fundamental task in computer vision and image processing. How to efficiently decrease the effect such as high noise, low resolution and intensity inhomogeneity is the key to improve the accuracy of segmentation. To this end, we propose a novel segmentation model by assuming the image to be the product of a piecewise-constant function and a smooth function and then the model can be proposed based on the suitable gradient spaces. To improve the robustness of the proposed model, we add a prior constraint for the smooth function and then analyse the existence of the solution based on the functional theory. Since the proposed model includes two nonsmooth terms, we use a heat kernel convolution to approximately replace the length regularization term and then the alternating direction method of multipliers can be employed to solve it. Numerical experiments on several testing images demonstrate that the effectiveness and the robustness of the proposed model compared to some state-of-the-art segmentation models.