## 2 Methodology  
In this section, we describe the details of the ACM methods used in our experiments, including traditional and the state-of-the-art methods. We also explain the database to which the methods are applied. The main idea of ACM is to segment an image based on an initial contour by minimizing the energy associated with the sum of internal and external energy. Depending on the contour representation (parametric or level set) and object boundary description (edge-based or region-based), ACMs can be classified into four categories: parametric representation with edge-based description [15; 35], parametric representation with region-based description [36; 37], level set representation with edge  
Figure 1: Overview of the proposed steps. -based description [38; 39] and level set representation with region-based description [40; 41]. In parametric ACM, the contour is explicitly represented as polynomials or splines [42; 43]. Given an initial contour, the external energies drive the evolution of a parametric ACM, while the internal energies maintain the shape of the contour. The parametric ACM is capable of extracting a single object given a single initial contour. Its strength is that the parametric snakes have a limited capture range, i.e., the range where the external forces are is strong enough to drive the contour evolution. Therefore, they must be initialized near the object contour. Another problem is that the parametric snakes are not able to accurately capture concave shapes. In the ACMs with level set, the contour is implicitly represented in the zero level set. In this method, the deformation of the level set function leads to contour evolution. Compared to the parametric ACMs, the level set model can capture multiple objects by a single initial contour and complex geometry. However, since the level set models require the deformation of a higher dimensional function, these methods are generally slower than parametric methods [39]. Moreover, for many applications, such as medical image processing, it is necessary to extract only a single object [44] and therefore, in such situations, the parametric representation is preferred over the level set representation. To solve the contour evolution equation, each representation scheme must select appropriate numerical methods. The finite element method [45] is used for parametric snake models, while the finite difference method [46] is used for level set models. Boundary-based segmentation methods for describing object boundaries based on the external force include region-based and edge-based models. Region-based models use more global information to define object boundaries. To control the evolution, region-based models use the statistical information inside and outside the contour [40; 41]. In the region-based approach, the deformation of ACM is based on an energy minimization algorithm. In the region-based method, many functions were considered as an edge stop function (ESF) [41], such as a signed pressure function (SPF). Edge-based models use image gradients to construct an ESF [39; 42], which is used to stop contour evolution at object boundaries. Using the ESF, the boundary points can be characterized by a differential property with respect to the image gradient. It should be noted that hybrid description approaches have been used recently to take advantage of edge-based and region-based methods and avoid their drawbacks [47]. Two important challenges in using ACMs are initialization and convergence. For example, some parametric ACMs are affected by saddle point and stationary point problems that lead to convergence failure [39]. ACM models respond quickly to initial conditions, so a poor initial contour can lead to a poor result, as shown in Figure 2, which shows the initialization of the contour outside, overlapping (cross), or inside the image. Figure 2: Three examples of initial contours considered outside (**a**), overlapping (**b**), and inside (**c**) the image.