Research

Fast localized active contour for inhomogeneous image segmentation

In this paper, we introduce a fast algorithm based on the localized active contour framework. A key concept of the proposed algorithm is its consideration of the curve evolution based on the speed function only at active points that change across time, rather than at all points in a narrow band. We additionally propose a modified speed function to address inhomogeneous image segmentation. The experimental results demonstrate significant advantages of the proposed method over existing methods, both in terms of computational efficiency and segmentation accuracy, for homogeneous and inhomogeneous images.

To reduce time consumption, the proposed method uses only active points to control the curve evolution. The main idea is that the temporal equilibrium of the curve enables detection of the active points. To design the active point detection, we consider two moving blocks, as shown in Fig. 1. Here, block 1 moves to the outward contour, and block 2 moves to the inward contour. Table 1 lists all the possible stages of change from list Lt-1 to Lt with time. The points are deemed active only if the current list of grid points Lt does not include zeros and the absolute values in Lt are equal to or greater than the absolute values in the previous list Lt-1.

Fig. 1. Diagram of the proposed method (D denotes the active point detection module)

Results

Fig. 2. The progression of the active contour in terms of iterations

Fig. 3. The initial contours in the first row; the second, third, fourth, fifth, sixth, and seventh rows show the methods of Shi [4], Bernard [8], Lankton [5], Zheng [6], the proposed method w/o inactive points, and the proposed method w/ inactive points, respectively

Fig. 4. Comparison of different methods for the ‘Degrade’ image in terms of

a number of active points

b accuracy of segmentation

Reference

[4] Shi, Y., Karl, W.: ‘A real-time algorithm for the approximation of level-set-based curve evolution’, IEEE Trans. Image Process., 2008, 17, (5), pp. 645–656

[5] Lankton, S., and Allen, T.: ‘Localizing region-based active contours’, IEEE Trans. Image Process., 2008, 17, (11), pp. 2029–2039

[6] Zheng, Q., Dong, E., Cao, Z., Sun, W., & Li, Z.: ‘Active contour model driven by linear speed function for local segmentation with robust initialization and applications in {MR} brain images’, Signal Processing, 2014, 97, pp. 117–133

[7] Bernard, O., Friboulet, D., Thevenaz, P. ,Unser, M.: ‘Variational B-Spline Level-Set: A Linear Filtering Approach for Fast Deformable Model Evolution’, IEEE Trans. Image Process., 2009, 18, (6), pp. 1179–1191

[11] Roberts, M., Packet, J., Sousa, M.C., Mitchell, J.R.: ‘A Work-Efficient GPU Algorithm for Level Set Segmentation’, High Performance Graphics, 2010, pp. 123–132