# An Image Segmentation Method Based on Improved Regularized Level Set Model
## 1 Introduction
The geodesic active contour [45] is the most typical of the edge-based methods, but these methods have one very marked disadvantage: they are very sensitive to the initial position of the level set and can easily divulge the weak edges [46]. To address the above defects, the Chan Vese (CV) model [33], as the most typical of region-based level set methods, was studied. The CV method is insensitive to the initial position and independent of the image gradients so that it can handle images with weak edges [46]. The hybrid level set methods associate the edge-based models with region-based models for image segmentation [41; 42; 43; 44]. Note that this CV method, as a global segmentation model, has all the merits of the region-based level set model, but this model cannot segment heterogeneous images well when the intensity is not homogenous [23]. Many real-world images, especially medical images, exhibit intensity inhomogeneity. Researchers [47; 48; 49; 50; 51; 52; 53; 54; 55] have proposed different solutions to address this issue. For example, [PERSON] et al. [47] integrated fuzzy decisions and the local energy functional and presented a robust ACM to segment preprocessed vessel images. [PERSON] and [PERSON] [48] introduced the Mumford and Shah method to develop an image segmentation algorithm with a multiphase level set model. However, this algorithm is still time-consuming to compute, which limits its application. [PERSON] et al. [49] studied a region-based ACM and designed a local binary fitting (LBF) method, which enables the extraction of accurate local image information. However, the model is sensitive to the initial position and noisy images. [PERSON] et al. [50] introduced a local image fitting (LIF) energy functional to extract the local image information, and proposed a Gaussian filtering method for variational level set to regularize the level set function, which can be interpreted as a constraint on the differences between the original image and the fitting image. [PERSON] et al. [51] exploited a local image region statistics-based improved ACM (LSACM) and provided a level set method in the presence of intensity inhomogeneity that is robust to noise while suppressing the intensity overlapping to some extent. [PERSON] et al. [52] investigated an improved scheme for a region-scalable fitting method. However, a defect of this method is its sensitivity to the initialization position. [PERSON] and [PERSON] [53] investigated a local and global binary fitting model that can segment an inhomogeneous image with less iteration and avoid the reinitialization of the curve evolution. [PERSON] et al. [27] designed a type of level set evolution called distance regularized level set evolution (DRLSE), which eliminates the costly process of reinitialization, uses the simple difference method to decrease the computational complexity, and improves the evolution efficiency [54]. According to this analysis, most of the existing approaches are sensitive to the initialization. Furthermore, some methods are unable to handle images with noise and intensity inhomogeneity. All of these drawbacks limit their practical applications. Thus, we focus on solving the abovementioned issues in this paper. In this study, an image segmentation method based on an improved regularized level set model is investigated. A type of energy functional in our model consists of three parts: an external energy term, an internal energy term and a distance regularization term. Since the external energy is introduced, the inhomogeneous images can be efficiently segmented. Moreover, the reinitialization step can be avoided by employing a distance regularization term with a new potential function. As a result,the time costs and iterations are greatly reduced. Notably, a curve of the level set evolution can automatically stop on the true boundaries of objects. The results of our study indicate that the proposed IRLS-IS method not only segments inhomogeneous images and noisy images but also effectively analyzes complex medical images.