# An Image Segmentation Method Using an Active Contour Model Based on Improved SPF and LIF
## 1 Introduction  
Image segmentation is an important task in the field of image analysis and object detection and aims to segment an image into distinctive subregions that are meaningful to analyze [1]. Segmentation is the intermediate step between image processing and image analysis as well as the bridge from low-to high-level research in computer vision. Inhomogeneity, noise, and low contrast in real images have increased the difficulty of image segmentation [2]. Over the past few decades, many segmentation methods have been proposed. The active contour model (ACM), which was proposed by [PERSON] et al. [3], has been proven to be an efficient framework for image segmentation. The fundamental idea of the ACM framework is to control a curve to move toward its interior normal and then stop on the true boundary of an object based on an energy minimization model [4]. The two main shortcomings of ACM algorithms are (1) sensitivity to the initial position and (2) difficulties related to topological changes [5]. Generally, existing ACM methods can be roughly divided into the following types, edge-based models [6; 7; 8; 9] and region-based models [10; 11; 12; 13; 14]. The geodesic active contour (GAC) model [15] is the most typical of edge-based methods. Owing to the edge-indicator function, the model can stop at high-contrast image gradients [16]. Edge-based models have distinct disadvantages. For example, these methods can effectively segmentan object with strong edges; however, they cannot detect the weak edges of an object. Moreover, the methods are sensitive to noise and do not easily obtain satisfactory segmentation results for blurred images [2]. In addition, the contour should initially be set near the object; otherwise, it is difficult to obtain correct segmentation results [17]. Region-based models make full use of image statistical information, whereas edge-based models do not. Thus, region-based models have multiple advantages over edge-based models. For example, because regional information is used, region-based models are less sensitive to contour initialization and noise. Furthermore, these region-based models can easily segment images with weak boundaries or even those without boundaries [18]. One of the most typical region-based methods was proposed by [PERSON] and [PERSON] (C-V) [11], which is based on the Mumford-Shah functional [19]. The C-V model is based on the assumption that image intensities are homogeneous in each region. However, this assumption does not suit the intensity of inhomogeneous images, which limits the method's further applications [20; 21]. Recently, hybrid methods have gained popularity among region-based methods. These methods combine region (local or global) and edge information in their energy formulations [22]. [PERSON] et al. [23] proposed the selective binary and Gaussian filtering regularized level set (SBGFRLS) model. This model combines the advantages of region-based and edge-based active contours and introduces a region-based SPF function, which utilizes the image global intensity means from the C-V method. This method adopts an approach similar to that of the GAC model. However, the edge-indicator function is replaced with a region-based SPF function in the model. Moreover, the traditional regularization function is usually replaced with a Gaussian smoothing function. This traditional method uses only global image intensity information. Therefore, the method is unable to analyze intensity-inhomogeneous images [21; 22]. [PERSON] et al. [24] investigated a local binary fitting (LBF) model, which is an efficient region-based level set method. The LBF model introduces a local binary fitting energy with a kernel function and uses the intensity of the current pixel to approximate the intensities of the neighboring pixels to obtain accurate segmentation performance; the model can be used to address intensity-inhomogeneous images and has attracted extensive attention due to its satisfactory segmentation performance [25]. However, this model involves high computational complexity.