A Local Statistical Information Active Contour Model for Image Segmentation

Introduction

Image segmentation is fundamental problem in the field of computer vision, because recognition and reconstruction often rely on this information (Peng et al., 2013; Ning et al., 2013; Peng et al., 2012). This is the process of dividing images into meaningful subsets that correspond to surfaces or objects. And it is often defined as a partitioning of pixels or image blocks into homogeneous groups. The goal of image segmentation is to simplify and/or change the representation of an image into something that is more meaningful and easier to analyze. Over the last few decades, researchers have also done great efforts and a large variety of segmentation algorithms have been proposed to improve the performance of the image segmentation algorithms (Peng et al., 2011; Ning et al., 2010; Peng et al., 2014).

Active contour model or snake, which is proposed by Kass et al. (1987), is a curve defined within an image domain that can move toward the boundary of the object under the influence of internal forces coming from within the curve itself and external forces computed from the image data. And it has been proved to be an efficient approach for image segmentation. When compared with the edge detectors based on threshold, e.g. Canny or Sobel operator, which often results in discontinuous boundaries, one main advantage of the active contour model is that it can partition an image into sub-regions with continuous boundaries. In early works the explicit snake model with a standard parametric curve representation was used (Caselles et al., 1997; Xu & Prince, 1998; Zhang et al., 2010). But one main drawback of this model is the difficulty associated with topological changes like the merging and splitting of the evolving curve. Since the active contour model was proposed, many methods have been proposed to improve it, in which the most important and successful one is the PDE-based level set method introduced by Osher and Sethian (1988).

The level set method, originally used as numerical technique for tracking interfaces and shapes (Xu & Prince, 1998), has been successful applied to image segmentation in the past decade. It generalizes the Euler-Lagrange equation and evolves the contour that automatically accounts for cusps, corners and topological changes. The contour is represented implicitly as the zero level set of a smooth function, usually called the level set function, of higher dimension. Moving the curves can be done by evolving the level set functions instead of directly moving the curves in the classical active contour model. With the level set representation, the image segmentation problem can be formulated and solved by calculus of variations and partial differential equations (PDE). The main advantages of the level set method are that it can efficiently represent contours with complex topology and handle the topological changes. So, the level set methods can segment more than one object simultaneously. Moreover, the numerical computations involving curves can be performed on a fixed Cartesian grid without having to parameterize these objects.

According to the nature of constraints, most of the existing active contour models can be categorized into two types: edge-based (Caselles et al., 1997; Xu & Prince, 1998; Zhang et al., 2010) and region-based (Zhang & Zhang, 2013; Chan & Vese2001; Vese & Chan, 2002; Zhang et al., 2010). These two types of models both have their pros and cons, and the choice of them in applications depends on image characteristics.