Abstract
We introduce a novel evolution-based segmentation algorithm which uses the heat flow analogy to gain practical advantage. The proposed algorithm consists of two parts. In the first part, we represent a particular heat conduction problem in the image domain to roughly segment the region of interest. Then we use geometric heat flow to complete the segmentation, by smoothing extracted boundaries and removing noise inside the prior segmented region. The proposed algorithm is compared with active contour models and is tested on synthetic and medical images. Experimental results indicate that our approach works well in noisy conditions without pre-processing. It can detect multiple objects simultaneously. It is also computationally more efficient and easier to control and implement in comparison with active contour models.
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References
Kass M, Witkin A, Terzopoulos D (1987) Snakes: active contour models. Int J Comput Vision 321–331
Xu C, Prince JL (1998) Snakes, shapes and gradient vector flow. IEEE Trans Image Process 7(3):359–369
Li B, Acton ST (2007) Active contour external force using vector field convolution for image segmentation. IEEE Trans Image Process 16(8):2096–2106
Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J Comput Phys 79(1):12–49
Caselles V, Catte F, Coll T, Dibos F (1993) A geometric model for active contours. Numerische Mathematic 66:1–31
Malladi R, Sethian JA, Vemuri BC (1995) Shape modeling with front propagation: a level set approach. IEEE Trans Pattern Anal Mach Intell 17(2):158–175
Caselles V, Kimmel R, Sapiro G (1997) Geodesic active contours. Int J Comput Vision 22(1):61–79
Siddiqi K, Lauziere Y, Tannenbaum A, Zucker S (1998) Area and length minimizing flows for shape segmentation. IEEE Trans Image Process 7(3):433–443
Xie X, Mirmehdi M (2004) RAGS: region-aided geometric snake. IEEE Trans Image Process 13(5):640–652
Adalsteinsson D, Sethian J (1995) A fast level set method for propagating interfaces. J Comput Phys 118(2):269–277
Sethian J (1999) Level set methods and fast marching methods. Cambridge Univ Press, New York
Weickert J, Romeny BMTH, Viergever MA (1998) Efficient and reliable schemes for nonlinear diffusion filtering. IEEE Trans Image Process 7(3):398–410
Chan T, Vese L (2001) Active Contours without Edges. IEEE Trans Image Process 10(2):266–277
Mumford D, Shah J (1989) Optimal approximation by piecewise smooth functions and associated variational problems. Commun Pure Appl Math 42(4):577–685
Vese L, Chan T (2002) A multiphase level set framework for image segmentation using the Mumford and Shah Model. Int J Comput Vision 50:271–293
Tsai A, Yezzi A, Willsky AS (2001) Curve evolution implementation of the mumford-shah functional for image segmentation, denoising, interpolation, and magnification. IEEE Trans Image Process 10(8):1169–1186
Li C, Kao C, Gore J, Ding Z (2007) Implicit active contours driven by local binary fitting energy. IEEE IntConf Comput Vision Pattern Recognit 1–7
Li C, Kao C, Gore J, Ding Z (2008) Minimization of region-scalable fitting energy for image segmentation. IEEE Trans Image Process 17(10):1940–1949
Zhang K, Song H, Zhang L (2010) Active contours driven by local image fitting energy. Pattern Recognit 43:1199–1206
Zimmer C, Olivo-Marin JC (2005) Coupled parametric active contours. IEEE Trans Pattern Anal Mach Intell 27(11):1838–1842
Paragios N, Deriche R (2000) Coupled geodesic active regions for image segmentation: a level set approach. Eur Conf Comput Vision 224–240
Xie X, Mirmehdi M (2008) MAC: magnetostatic active contour model. IEEE Trans Pattern Anal Mach Intell 30(4):632–646
Huang X, Metaxas D (2008) Metamorphs: deformable shape and appearance models. IEEE Trans Patt Anal Mach Intell 30(8):1444–1459
Adams R, Bischof L (1994) Seeded region growing. IEEE Trans Pattern Anal Mach Intell 16(6):641–647
Fung PW, Grebbin G, Attikiouzel Y (1990) Model-based region growing segmentation of textured images. IEEE Int Conf Acoust Speech Signal Process 4:2313–2316
Xiaohan Y, Yla-Jailski J, Huttunen O, Vehkomiiki T, Sipila O, Katila T (1992) Image segmentation combining region growing and edge detection. Int Conf Pattern Recognit 3:481–484
Yu Q, Clausi DA (2008) IRGS: image segmentation using edge penalties and region growing. IEEE Trans Pattern Anal Mach Intell 30(12):2126–2139
Qin AK, Clausi DA (2010) Multivariate image segmentation using semantic region growing with adaptive edge penalty. IEEE Trans Image Process 19(8):2157–2170
Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 22(8):629–639
Manay S, Yezzi A (2003) Anti-geometric diffusion for adaptive thresholding and fast segmentation. IEEE Trans Image Process 12(11):1310–1323
Ji X, Feng J (2004) A new approach to thinning based on time-reversed heat conduction model. IEEE Int Conf Image Process 1:653–656
Kimia BB, Siddiqi K (1994) Geometric heat equation and nonlinear diffusion of shapes and images. IEEE Int Conf Comput Vision Pattern Recognit 113–120
Makrogiannis SK, Bourbakis NG (2004) Motion analysis with application to assistive vision technology. IEEE Int Conf Tools Artif Intell 344–352
Direkoğlu C, Nixon MS (2006) Low level moving-feature extraction via heat flow analogy. Int Symp Visual Comput LNCS 4291:243–252
Direkoğlu C, Nixon MS (2010) Moving-edge detection via heat flow analogy. Pattern Recognit Lett (in press)
Direkoğlu C, Nixon MS (2007) Shape extraction via heat flow analogy. Int Conf Adv Concepts Intell Vision LNCS 4678:553–564
Nixon MS, Liu XU, Direkoğlu C, Hurley DJ (2011) On using physical analogies for feature and shape extraction in computer vision. Comput J 54(1):11–25
Holman JP (2002) Heat transfer, McGraw-Hill, 9th edn
Wasilewski M (2002) Active contours without edges matlab codes. http://www.postulate.org/segmentation.php
Li C, Kao C, Gore J, Ding Z (2008) Region-scalable fitting energy based active contour matlab codes. http://www.engr.uconn.edu/~cmli/
Xu C, Prince JL (1999) Gradient vector flow snake matlab codes. http://iacl.ece.jhu.edu/projects/gvf/
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Direkoğlu, C., Nixon, M.S. On using an analogy to heat flow for shape extraction. Pattern Anal Applic 16, 125–139 (2013). https://doi.org/10.1007/s10044-011-0223-0
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DOI: https://doi.org/10.1007/s10044-011-0223-0