Abstract
The goal of image segmentation is to partition the image plane into a set of meaningful regions. While generic low-level segmentation algorithms often impose a prior which favors shorter boundaries, for segmenting familiar structures in images it may be advantageous to impose a more object-specific shape prior. Over the years, researchers have proposed different algorithms to impose prior shape knowledge based on either explicit or implicit representations of shape. In the following, I will provide a brief review of several approaches.
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References
Amini AA, Weymouth TE, Jain RC (1990) Using dynamic programming for solving variational problems in vision. IEEE Trans Pattern Anal Mach Intell 12(9):855–867
Awate SP, Tasdizen T, Whitaker RT (2006) Unsupervised texture segmentation with nonparametric neighborhood statistics. In: European conference on computer vision (ECCV), Graz, Austria, May 2006. Springer, Berlin, pp 494–507
Blake A, Isard M (1998) Active contours. Springer, London
Blake A, Zisserman A (1987) Visual reconstruction. MIT Press, Cambridge
Bookstein FL (1978) The measurement of biological shape and shape change. Lect notes in biomath, vol 24. Springer, New York
Boykov Y, Kolmogorov V (2003) Computing geodesics and minimal surfaces via graph cuts. In: IEEE int conf on computer vision, Nice, pp 26–33
Boykov Y, Kolmogorov V (2004) An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE Trans Pattern Anal Mach Intell 26(9):1124–1137
Brox T, Rousson M, Deriche R, Weickert J (2003) Unsupervised segmentation incorporating colour, texture, and motion. In: Petkov N, Westenberg MA (eds) Computer analysis of images and patterns, Groningen, The Netherlands, August 2003. LNCS, vol 2756. Springer, Berlin, pp 353–360
Brox T, Weickert J (2004) A TV flow based local scale measure for texture discrimination. In: Pajdla T, Hlavac V (eds) European conf. on computer vision, Prague. LNCS, vol 3022. Springer, Berlin, pp 578–590
Caselles V, Kimmel R, Sapiro G (1995) Geodesic active contours. In: Proc IEEE intl conf on comp vis, Boston, USA, pp 694–699
Chambolle A, Cremers D, Pock T (2012) A convex approach to minimal partitions. SIAM J Imaging Sci 5(4):1113–1158
Chan T, Esedoḡlu S, Nikolova M (2006) Algorithms for finding global minimizers of image segmentation and denoising models. SIAM J Appl Math 66(5):1632–1648
Chan TF, Vese LA (2001) Active contours without edges. IEEE Trans Image Process 10(2):266–277
Cipolla R, Blake A (1990) The dynamic analysis of apparent contours. In: IEEE int. conf on computer vision. Springer, Berlin, pp 616–625
Cootes TF, Taylor CJ, Cooper DM, Graham J (1995) Active shape models—their training and application. Comput Vis Image Underst 61(1):38–59
Coughlan J, Yuille A, English C, Snow D (2000) Efficient deformable template detection and localization without user initialization. Comput Vis Image Underst 78(3):303–319
Courant R, Hilbert D (1953) Methods of mathematical physics, vol 1. Interscience, New York
Cremers D (2006) Dynamical statistical shape priors for level set based tracking. IEEE Trans Pattern Anal Mach Intell 28(8):1262–1273
Cremers D (2008) Nonlinear dynamical shape priors for level set segmentation. J Sci Comput 35(2–3):132–143
Cremers D, Kohlberger T, Schnörr C (2003) Shape statistics in kernel space for variational image segmentation. Pattern Recognit 36(9):1929–1943
Cremers D, Osher SJ, Soatto S (2006) Kernel density estimation and intrinsic alignment for shape priors in level set segmentation. Int J Comput Vis 69(3):335–351
Cremers D, Rousson M, Deriche R (2007) A review of statistical approaches to level set segmentation: integrating color, texture, motion and shape. Int J Comput Vis 72(2):195–215
Cremers D, Schmidt FR, Barthel F (2008) Shape priors in variational image segmentation: convexity, Lipschitz continuity and globally optimal solutions. In: IEEE conference on computer vision and pattern recognition (CVPR), Anchorage, Alaska, June 2008
Cremers D, Soatto S (2005) Motion Competition: a variational framework for piecewise parametric motion segmentation. Int J Comput Vis 62(3):249–265
Cremers D, Sochen N, Schnörr C (2006) A multiphase dynamic labeling model for variational recognition-driven image segmentation. Int J Comput Vis 66(1):67–81
Cremers D, Tischhäuser F, Weickert J, Schnörr C (2002) Diffusion Snakes: introducing statistical shape knowledge into the Mumford–Shah functional. Int J Comput Vis 50(3):295–313
Dervieux A, Thomasset F (1979) A finite element method for the simulation of Raleigh-Taylor instability. Springer Lect Notes in Math, vol 771. pp 145–158
Dryden IL, Mardia KV (1998) Statistical shape analysis. Wiley, Chichester
Farin G (1997) Curves and surfaces for computer–aided geometric design. Academic Press, San Diego
Franchini E, Morigi S, Sgallari F (2009) Segmentation of 3d tubular structures by a pde-based anisotropic diffusion model. In: Intl. conf. on scale space and variational methods. LNCS, vol 5567. Springer, Berlin, pp 75–86
Fréchet M (1961) Les courbes aléatoires. Bull Inst Int Stat 38:499–504
Geiger D, Gupta A, Costa LA, Vlontzos J (1995) Dynamic programming for detecting, tracking and matching deformable contours. IEEE Trans Pattern Anal Mach Intell 17(3):294–302
Greig DM, Porteous BT, Seheult AH (1989) Exact maximum a posteriori estimation for binary images. J R Stat Soc B 51(2):271–279
Grenander U, Chow Y, Keenan DM (1991) Hands: a pattern theoretic study of biological shapes. Springer, New York
Heiler M, Schnörr C (2003) Natural image statistics for natural image segmentation. In: IEEE int. conf. on computer vision, pp 1259–1266
Kass M, Witkin A, Terzopoulos D (1988) Snakes: active contour models. Int J Comput Vis 1(4):321–331
Kendall DG (1977) The diffusion of shape. Adv Appl Probab 9:428–430
Kervrann C, Heitz F (1999) Statistical deformable model-based segmentation of image motion. IEEE Trans Image Process 8:583–588
Kichenassamy S, Kumar A, Olver PJ, Tannenbaum A, Yezzi AJ (1995) Gradient flows and geometric active contour models. In: IEEE int. conf. on computer vision, pp 810–815
Kim J, Fisher JW, Yezzi A, Cetin M, Willsky A (2002) Nonparametric methods for image segmentation using information theory and curve evolution. In: Int. conf. on image processing, vol 3, pp 797–800
Klodt M, Cremers D (2011) A convex framework for image segmentation with moment constraints. In: IEEE int. conf. on computer vision
Kohlberger T, Cremers D, Rousson M, Ramaraj R (2006) 4d shape priors for level set segmentation of the left myocardium in SPECT sequences. In: Medical image computing and computer assisted intervention, October 2006. LNCS, vol 4190, pp 92–100
Leventon M, Grimson W, Faugeras O (2000) Statistical shape influence in geodesic active contours. In: Int. conf. on computer vision and pattern recognition, Hilton Head Island, SC, vol 1. pp 316–323
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
Matheron G (1975) Random sets and integral geometry. Wiley, New York
Menet S, Saint-Marc P, Medioni G (1990) B–snakes: implementation and application to stereo. In: Proc. DARPA image underst workshop, April 6–8, pp 720–726
Mercer J (1909) Functions of positive and negative type and their connection with the theory of integral equations. Philos Trans R Soc Lond A 209:415–446
Mumford D, Shah J (1989) Optimal approximations by piecewise smooth functions and associated variational problems. Commun Pure Appl Math 42:577–685
Nain D, Yezzi A, Turk G (2003) Vessel segmentation using a shape driven flow. In: MICCAI, pp 51–59
Nieuwenhuis C, Cremers D (2013) Spatially varying color distributions for interactive multi-label segmentation. IEEE Trans Pattern Anal Mach Intell 35(5):1234–1247
Osher SJ, Sethian JA (1988) Fronts propagation with curvature dependent speed: algorithms based on Hamilton–Jacobi formulations. J Comp Physiol 79:12–49
Paragios N, Deriche R (2002) Geodesic active regions and level set methods for supervised texture segmentation. Int J Comput Vis 46(3):223–247
Parent P, Zucker SW (1989) Trace inference, curvature consistency, and curve detection. IEEE Trans Pattern Anal Mach Intell 11(8):823–839
Parzen E (1962) On the estimation of a probability density function and the mode. Ann Math Stat 33:1065–1076
Rochery M, Jermyn I, Zerubia J (2006) Higher order active contours. Int J Comput Vis 69(1):27–42
Rosenblatt F (1956) Remarks on some nonparametric estimates of a density function. Ann Math Stat 27:832–837
Rousson M, Brox T, Deriche R (2003) Active unsupervised texture segmentation on a diffusion based feature space. In: Proc. IEEE conf. on comp. vision patt. recog, Madison, WI, pp 699–704
Rousson M, Cremers D (2005) Efficient kernel density estimation of shape and intensity priors for level set segmentation. In: MICCAI, vol 1, pp 757–764
Rousson M, Paragios N, Deriche R (2004) Implicit active shape models for 3d segmentation in MRI imaging. In: MICCAI. LNCS, vol 2217. Springer, Berlin, pp 209–216
Rosenfeld A, Zucker SW, Hummel RA (1977) An application of relaxation labeling to line and curve enhancement. IEEE Trans Comput 26(4):394–403
Schmidt FR, Cremers D (2009) A closed-form solution for image sequence segmentation with dynamical shape priors. In: Pattern recognition (Proc. DAGM), September 2009
Schmidt FR, Farin D, Cremers D (2007) Fast matching of planar shapes in sub-cubic runtime. In: IEEE int. conf. on computer vision, Rio de Janeiro, October 2007
Schoenemann T, Cremers D (2007) Globally optimal image segmentation with an elastic shape prior. In: IEEE int. conf. on computer vision, Rio de Janeiro, Brasil, October 2007
Schoenemann T, Cremers D (2007) Introducing curvature into globally optimal image segmentation: minimum ratio cycles on product graphs. In: IEEE int conf on computer vision, Rio de Janeiro, October 2007
Schoenemann T, Cremers D (2008) Matching non-rigidly deformable shapes across images: a globally optimal solution. In: IEEE conference on computer vision and pattern recognition (CVPR), Anchorage, Alaska, June 2008
Schoenemann T, Cremers D (2009) A combinatorial solution for model-based image segmentation and real-time tracking. IEEE Trans Pattern Anal Mach Intell
Schoenemann T, Kahl F, Masnou S, Cremers D (2012) A linear framework for region-based image segmentation and inpainting involving curvature penalization. Int J Comput Vis 99:53–68
Schoenemann T, Schmidt FR, Cremers D (2008) Image segmentation with elastic shape priors via global geodesics in product spaces. In: British machine vision conference, Leeds, UK, September 2008
Sebastian T, Klein P, Kimia B (2003) On aligning curves. IEEE Trans Pattern Anal Mach Intell 25(1):116–125
Serra J (1982) Image analysis and mathematical morophology. Academic Press, London
Tsai A, Wells W, Warfield SK, Willsky A (2004) Level set methods in an EM framework for shape classification and estimation. In: MICCAI
Tsai A, Yezzi A, Wells W, Tempany C, Tucker D, Fan A, Grimson E, Willsky A (2001) Model–based curve evolution technique for image segmentation. In: Comp vision patt recog, Kauai, Hawaii, pp 463–468
Tsai A, Yezzi AJ, 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
Unal G, Krim H, Yezzi AY (2005) Information-theoretic active polygons for unsupervised texture segmentation. Int J Comput Vis, May
Unger M, Pock T, Cremers D, Bischof H (2008) TVSeg—interactive total variation based image segmentation. In: British machine vision conference (BMVC), Leeds, UK, September 2008
Zhu SC, Yuille A (1996) Region competition: unifying snakes, region growing, and Bayes/MDL for multiband image segmentation. IEEE Trans Pattern Anal Mach Intell 18(9):884–900
Acknowledgements
The work described here was done in collaboration with numerous researchers. The author would like to thank T. Schoenemann, F.R. Schmidt, C. Schnoerr, S. Soatto, N. Sochen, T. Kohlberger, M. Rousson and S.J. Osher for their support.
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Cremers, D. (2013). Shape Priors for Image Segmentation. In: Dickinson, S., Pizlo, Z. (eds) Shape Perception in Human and Computer Vision. Advances in Computer Vision and Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-4471-5195-1_7
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