# An Image Segmentation Method Based on Improved Regularized Level Set Model
## 1 Introduction
[PERSON] and [PERSON] [15] presented image segmentation by histogram thresholding using fuzzy sets according to the similarity between gray levels, which is easy to implement and has a low computational burden. However, it does not consider the spatial contextual information in the threshold selection process. [PERSON] and [PERSON] [16] designed a fast context-sensitive threshold selection technique to solve image segmentation problems. [PERSON] et al. [17] investigated \(L\)-interval-valued intuitionistic fuzzy sets and set the least entropy as the threshold to segment the image. However, the method may lead to increased computation time, especially when dealing with multithreshold image segmentation [18]. [PERSON] et al. [19] introduced an enhanced artificial bee colony optimizer into multilevel threshold image segmentation. For the traditional interactive image segmentation, the robots only work for region-based methods, excluding the important class of approaches that rely on the boundary tracking paradigm. Then, [PERSON] and [PERSON] [20] proposed robot users to simulate human user behavior when segmenting an image through the addition of anchor points close to the object's boundary. [PERSON] et al. [21] developed an optimum user-steered boundary tracking approach for image segmentation, which simulates the behavior of water flowing through a riverbed. However, the inefficiency of these approaches lies in the fact that they cannot deal with real-life complex problems that are tolerant of partial truths, imprecision, uncertainty, and approximations [2]. Note that none of these methods are good at segmenting a variety of images, and they usually perform well in one class of images while performing poorly in another class of images. In recent years, the active contour model (ACM) [22] has become one of the most promising frameworks and effective and accurate methods for image segmentation. Currently, most existing ACMs can be categorized into two basic classes: edge-based models and region-based models, according to image features for segmentation. The basic idea of the ACM framework is to attract the curve toward the true boundary of an object based on an energy minimization model. The two main shortcomings of ACM algorithms are as follows: (1) the sensitivity to the initial position and (2) the difficulties related to topological changes [23]. Until now, scholars [22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41] have investigated a large amount of ACM algorithms for the performance improvement of image segmentation. In 1988, [PERSON] and [PERSON] [24] first presented a level set model, which is the most successful and important part of the ACM family. The evolution of the level set function is controlled by partial differential equations that describe the image, which drives the zero level set to move toward the target edge of the image. This model is a numerical method for interface tracking and shape modeling that avoids tracking and parameterizing the curve as it evolves and can flexibly deal with topological changes. Hence, the calculation accuracy is high, and the related algorithm is stable. In addition, the numerical calculations required by the level set method can be performed on a Cartesian grid without the need to parameterize the points on the contour. Due to the abovementioned advantages, it has become a very useful tool for segmenting images [25; 26; 27; 28]. To solve all these issues, it is necessary to explore new ways or directions for image segmentation to achieve better overall performance. Thus, we focus on studying the ACM algorithm in this paper to identify a new image segmentation method. Thus far, there are many variations to the level set model, which can roughly be divided into three categories: edge-based methods [29; 30; 31], region-based methods [32; 33; 34; 35], and hybrid methods [36; 37; 38; 39; 40; 41; 42; 43; 44].