Abstract
In this paper, a class of deformable contour methods using a constrained optimization approach of minimizing a contour energy function satisfying an interior homogeneity constraint is proposed. The class is defined by any positive potential function describing the contour interior characterization. An evolutionary strategy is used to derive the algorithm. A similarity threshold T v can be used to determine the interior size and shape of the contour. Sensitivity and significance of T v and σ (a spreadness measure) are also discussed and shown. Experiments on noisy images and the convergence to a minimum energy gap contour are included. The developed method has been applied to a variety of medical images from CT abdominal section, MRI image slices of brain, brain tumor, a pig heart ultrasound image sequence to visual blood cell images. As the results show, the algorithm can be adapted to a broad range of medical images containing objects with vague, complex and/or irregular shape boundary, inhomogeneous and noisy interior, and contour with small gaps.
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References
Atkins, M. and Mackiewich, B. 1998. Fully automatic segmentation of the brain in MRI. IEEE Trans. on Medical Imaging, 17(1):98–107.
Buck, T., Hammel, U., and Schwefel, H. 1997. Evolutionary computation: Comments on the history and current state. IEEE Transaction on Evolutionary Computation, 1(1):3–17.
Casellas, V., Kimmel, R., and Sapiro, G. 1997. Geodesic active contours. International Journal of Computer Vision, 22(1):61–79.
Chalana, V., Linker, D., Haynor, D., and Kim, Y. 1996. A multiple active contour model for cardiac boundary detection on echocardiographic sequences. IEEE Trans. on Medical Imaging, 15(3):290–298.
Cham, T. and Cipolla, R. 1999. Automated B-spline curve representation incorporating MDL and error minimizing control point insertion strategies. IEEE Trans. on PAMI, 21(1):49–53.
Chan, T. and Vese, L. 2001. Active contours without edges. IEEE Trans on Image Processing, 10(2):266–277.
Chakraborty, A. and Duncan, J.S. 1999. Game-theoretic integration for image segmentation. IEEE Trans. on PAMI, 21(1):12–30.
Chiou, G. and Huang, J. 1995. A neural network-based stochastic active contour model (NNS-SNAKE) for contour finding of distinct features. IEEE Trans. Image Processing, 4(10):1407–1416.
Cohen, L. 1991. On active contour models and balloons CVGIP: image understanding. 52(2):211–218.
Cohen, L. and Cohen, I. 1993. Finite element methods for active contour models and balloons for 2-D and 3-D images. IEEE Trans. on PAMI, 15:1131–1147.
Cohen, L. and Kimmel, R. 1997. Global minimum for active contour models: A minimal path approach. International Journal of Computing Vision, 24(1):57–78.
Fenster, S. and Kender, J. 1998. Sectored snakes: Evaluating learnedenergy segmentation. In ICCV, pp. 420–426.
Fok, Y., Chan, Y., and Chin, R. 1996. Automated analysis of nerve cell images using active contour models. IEEE Trans. on Medical Imaging, 15(3):353–358.
Friedland, N. and Rosenfeld, A. 1992. Compact object recognition using energy-function-based optimization. IEEE Trans. on PAMI, 14:770–777.
Grzeszczuk, R. and Levin, D. 1997. Brownian string, segmenting images with stochastically deformable contours. IEEE Trans. on PAMI, 19(10):1100–1114.
Jermyn, I. and Ishikawa, H. 2001. Globally optimal regions and boundaries as minimum ratio weight cycles. IEEE Transaction on Pattern Analysis and Machine Intellegence, 23(18):1075–1088.
Kass, M., Witkin, A., and Terzopoulos, D. 1988. Snakes: Active contour models. International Journal of Computer Vision, 1(4):321–331.
Lundervold, A. and Storvik, G. 1995. Segmentation of brain parenchyma and cerabrospinal fluid in multispectral magnetic resonance images. IEEE Trans. on Medical Imaging, 14(2):339–349.
Malladi, R., Sethian, J., and Vemuri, B. 1995. Shape modeling with front propagation. IEEE Trans on PAMI, 17(2):158–171.
McInerney, T. and Terzopoulos, D. 1999. Topology adaptive deformable surfaces for medical image volume segmentation. IEEE Trans on Medical Imaging, 18(10):840–850.
Pien, H., Desai, M., and Shah, J. 1997. Segmentation of MR images using curve evolution and prior information. International Journal of Pattern Recognition and Artificial Intelligence, 11(8):1233–1244.
Ranganath, S. 1995. Contour extraction from cardiac MRI studies using snakes. IEEE Trans. Medical Imaging, 14(2):328–338.
Samson, C., Blanc-Feraud, L., Aubert, G., and Zerubia, J. 2000. A level set model for image classification. International Journal of Computer Vision, 40(3):187–197.
Sethian, J. 1996. A fast marching level set method for monotonically advancing fronts. Proc. Nat. Acad. Sci., 93(4):1591–1595.
Siddiqi, K., Lauziere, Y.B., Tannenbaum, A., and Zucker, S.W. 1998. Area and length minimizing flows for shape segmentation. IEEE Trans on Image Processing, 7:433–443.
Stovik, G. 1994. A Bayesian approach to dynamic contours through stochastic sampling and simulated annealing. IEEE Trans. on PAMI, 16(10):976–986.
Toennies, K. and Rueckert, D. 1994. Image segmentation by stochastically relaxing contour fitting. In Medical Imaging 1994: Image Processing, Bellingham, WA: Int'l Soc. Optical Eng, vol. 2167, pp. 18–27.
Xu, C. and Prince, J. 1998. Snakes, shape, and gradient vector flow. IEEE Trans. on Image Processing, 7:359–369.
Yezzi, A., Kichenssamy, S., Kumar, A., Olver, P., and Tannebaum, A. 1997. A geometric snake model for segmentation of medical imagery. IEEE Trans. Medical Imaging, 16(2):199–209.
Zhong, M. 1997. The motion-constrained active contour model and its medical imaging application. MS. Thesis, University of Cincinnati.
Zhu, S. and Yuille, A. 1996. Region competition: Unifying snakes, region growing, and bayes/MDL for multiband image segmentation. IEEE Trans. on PAMI, 18(9):884–900.
Zhu, Y. and Yan, H. 1997. Computerized tumor boundary detection using a Hopfield neural network. IEEE Trans. on Medical Imaging, 16:55–67.
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Wang, X., He, L. & Wee, W. Deformable Contour Method: A Constrained Optimization Approach. International Journal of Computer Vision 59, 87–108 (2004). https://doi.org/10.1023/B:VISI.0000020672.14006.ad
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DOI: https://doi.org/10.1023/B:VISI.0000020672.14006.ad