A Modified Image Segmentation Method Using Active Contour Model

Active contours, or snakes, have extensive applications in image segmentation. Conventional snakes have several drawbacks, such as the initialization contour sensitivity and border leakage phenomenon. Many new methods have been proposed to address these problems. In this paper, we present an improved image segmentation method based on snakes. Firstly, we adopt the multi-step direction method to enlarge the scope of initial contour and obtain more precise edge map. Then, we decompose the Laplace operator to tangential direction and normal direction, weakening the border smoothing effect. Finally, two correlational self-adaptive weight functions are added to the two directions. Thus, the snakes can adaptively adjust the weights of smoothing item and diffusion item through the local image characteristics. Based on the subjective and objective evaluations, the proposed method outperforms the state-of-the-art methods and improves the segmentation accuracy. Introduction Active contour model, or snake model, was proposed by Kass et al [1], in 1987. Snake model has been widely applied in the fields of computer vision and image processing [2-6], such as image segmentation, target tracking, and edge detection. Although the conventional active contour model has been widely used, it still has its shortcomings [7]. First, the initial contour must be very close to the interesting image features. Second, border leakage phenomenon is occurred, losing a lot of important image information. Third, the snake curve is difficult to reach indentation boundaries. In order to solve these problems, Xu proposed gradient vector flow (GVF) snake model [7], which is able to expand the capture scope of initial contour and has a certain indentation convergence capability. The generalized gradient vector flow (GGVF) model proposed by Xu and Prince [8] adds two weight coefficients changing in the image field based on the original GVF external force field. Thus, the curve converges rapidly in the flat field and has certain boundary protection effect. However, the indentation convergence capability has not been greatly improved. NGVF proposed by Ning [9] decomposes the Laplace operator in the GVF external force field, and only retains normal component. Thereby NGVF further improves the curve’s indentation capability. Although the tangential component after decomposition has been added to GVF external force field by later NBGVF [10], the convergence capability of long and thin indentation has not been significantly improved. Based on the studies about GGVF and GVF, Qin [11] discovered that no matter GGVF or GVF can only converge to the indentation with odd pixel width and is of no convergence capability to the indentation with even pixel width. Therefore, CN-GGVF algorithm was proposed by Qin, with applying component normalization method in GGVF. CN-GGVF solved the problem that deformation curve cannot converge to even pixel width, and retained the fast convergence character in GGVF. However, CN-GGVF has no ideal effect on the protection of weak boundary features of interesting field and has boundary leakage phenomenon. 2nd International Conference on Electrical, Computer Engineering and Electronics (ICECEE 2015) © 2015. The authors Published by Atlantis Press 1162 Related Work Traditional Snake Model. In the active contours model first proposed in [1], an energy minimizing curve (snake) is guided by external and internal energies to create a contour around an object. It can be expressed by ( ) ( ) ( ) ( ) [ ] , , 0,1 x s x s y s s = ∈ . The energy function is as follows: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 2 2 0 0 x x = x x x snake int ext ext E E s E s ds s s E s ds s s a β     ′ ′′ = + + +     ∫ ∫ . (1) where ( ) ( ) x int E s , the snake’s internal energy or prior, is the weighted sum of first and second derivatives of ( ) x s . ( ) ( ) x ext E s represents external energy. ( ) s a is the elastic coefficient and ( ) s β denotes intensity coefficient. Based on the variational principle [12], the Eq. 1 satisfies Euler-Lagrange equation at the maximization of contour curve energy: ( ) ( ) ( ) ( ) ( ) ( ) 0 x x x ext s s s s E s a β ′′ ′′′′ − −∇ = . (2) where ( ) x s ′′′′ represents the fourth derivative of ( ) x s . Eq. 2 can be regarded as force balance equation: ( ) ( ) ( ) ( ) 0 x x int ext F s F s + = . (3) where ( ) ( ) ( ) ( ) ( ) ( ) x x x int F s s s s s a β ′′ ′′′′ = − represents internal forces constraining curve smoothing and stretching; ( ) ( ) ( ) ( ) x x ext ext F s E s = −∇ denotes external force, driving curve to move to expected feature boundaries. GVF Snake Model. GVF snake proposed by Xu et al. will not consider snake model from the perspective of energy minimization, but consider it as a force balance process. Eq. 3 is the basic equation for the construction of GVF snake model. External force ( ) ( ) x ext F s is substituted by a GVF field ( ) ( ) ( ) , , , , x y u x y v x y u =     . The following energy function is obtained through minimize its components: ( ) 2 2 2 2 2 x y x y E u u v v f f dxdy μ u = + + + + ∇ −∇ ∫∫ . (4) where f represents the edge map of processed image I ; f ∇ denotes gradient field of f ; μ represents a parameter controlling the smoothness of GVF field. The gradient vector flow field satisfies the Euler equation: