Shape Priors for Image Segmentation

Part of the Advances in Computer Vision and Pattern Recognition book series (ACVPR)

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.

Keywords

Manifold Covariance Coherence 

Notes

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.

References

  1. 1.
    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 CrossRefGoogle Scholar
  2. 2.
    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 Google Scholar
  3. 3.
    Blake A, Isard M (1998) Active contours. Springer, London CrossRefGoogle Scholar
  4. 4.
    Blake A, Zisserman A (1987) Visual reconstruction. MIT Press, Cambridge Google Scholar
  5. 5.
    Bookstein FL (1978) The measurement of biological shape and shape change. Lect notes in biomath, vol 24. Springer, New York MATHCrossRefGoogle Scholar
  6. 6.
    Boykov Y, Kolmogorov V (2003) Computing geodesics and minimal surfaces via graph cuts. In: IEEE int conf on computer vision, Nice, pp 26–33 CrossRefGoogle Scholar
  7. 7.
    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 CrossRefGoogle Scholar
  8. 8.
    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 CrossRefGoogle Scholar
  9. 9.
    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 Google Scholar
  10. 10.
    Caselles V, Kimmel R, Sapiro G (1995) Geodesic active contours. In: Proc IEEE intl conf on comp vis, Boston, USA, pp 694–699 CrossRefGoogle Scholar
  11. 11.
    Chambolle A, Cremers D, Pock T (2012) A convex approach to minimal partitions. SIAM J Imaging Sci 5(4):1113–1158 MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    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 MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Chan TF, Vese LA (2001) Active contours without edges. IEEE Trans Image Process 10(2):266–277 MATHCrossRefGoogle Scholar
  14. 14.
    Cipolla R, Blake A (1990) The dynamic analysis of apparent contours. In: IEEE int. conf on computer vision. Springer, Berlin, pp 616–625 Google Scholar
  15. 15.
    Cootes TF, Taylor CJ, Cooper DM, Graham J (1995) Active shape models—their training and application. Comput Vis Image Underst 61(1):38–59 CrossRefGoogle Scholar
  16. 16.
    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 CrossRefGoogle Scholar
  17. 17.
    Courant R, Hilbert D (1953) Methods of mathematical physics, vol 1. Interscience, New York Google Scholar
  18. 18.
    Cremers D (2006) Dynamical statistical shape priors for level set based tracking. IEEE Trans Pattern Anal Mach Intell 28(8):1262–1273 CrossRefGoogle Scholar
  19. 19.
    Cremers D (2008) Nonlinear dynamical shape priors for level set segmentation. J Sci Comput 35(2–3):132–143 MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Cremers D, Kohlberger T, Schnörr C (2003) Shape statistics in kernel space for variational image segmentation. Pattern Recognit 36(9):1929–1943 MATHCrossRefGoogle Scholar
  21. 21.
    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 CrossRefGoogle Scholar
  22. 22.
    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 CrossRefGoogle Scholar
  23. 23.
    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 Google Scholar
  24. 24.
    Cremers D, Soatto S (2005) Motion Competition: a variational framework for piecewise parametric motion segmentation. Int J Comput Vis 62(3):249–265 CrossRefGoogle Scholar
  25. 25.
    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 CrossRefGoogle Scholar
  26. 26.
    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 MATHCrossRefGoogle Scholar
  27. 27.
    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 Google Scholar
  28. 28.
    Dryden IL, Mardia KV (1998) Statistical shape analysis. Wiley, Chichester MATHGoogle Scholar
  29. 29.
    Farin G (1997) Curves and surfaces for computer–aided geometric design. Academic Press, San Diego MATHGoogle Scholar
  30. 30.
    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 CrossRefGoogle Scholar
  31. 31.
    Fréchet M (1961) Les courbes aléatoires. Bull Inst Int Stat 38:499–504 MATHGoogle Scholar
  32. 32.
    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 CrossRefGoogle Scholar
  33. 33.
    Greig DM, Porteous BT, Seheult AH (1989) Exact maximum a posteriori estimation for binary images. J R Stat Soc B 51(2):271–279 Google Scholar
  34. 34.
    Grenander U, Chow Y, Keenan DM (1991) Hands: a pattern theoretic study of biological shapes. Springer, New York Google Scholar
  35. 35.
    Heiler M, Schnörr C (2003) Natural image statistics for natural image segmentation. In: IEEE int. conf. on computer vision, pp 1259–1266 CrossRefGoogle Scholar
  36. 36.
    Kass M, Witkin A, Terzopoulos D (1988) Snakes: active contour models. Int J Comput Vis 1(4):321–331 CrossRefGoogle Scholar
  37. 37.
    Kendall DG (1977) The diffusion of shape. Adv Appl Probab 9:428–430 CrossRefGoogle Scholar
  38. 38.
    Kervrann C, Heitz F (1999) Statistical deformable model-based segmentation of image motion. IEEE Trans Image Process 8:583–588 CrossRefGoogle Scholar
  39. 39.
    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 CrossRefGoogle Scholar
  40. 40.
    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 Google Scholar
  41. 41.
    Klodt M, Cremers D (2011) A convex framework for image segmentation with moment constraints. In: IEEE int. conf. on computer vision Google Scholar
  42. 42.
    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 Google Scholar
  43. 43.
    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 Google Scholar
  44. 44.
    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 CrossRefGoogle Scholar
  45. 45.
    Matheron G (1975) Random sets and integral geometry. Wiley, New York MATHGoogle Scholar
  46. 46.
    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 Google Scholar
  47. 47.
    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 MATHCrossRefGoogle Scholar
  48. 48.
    Mumford D, Shah J (1989) Optimal approximations by piecewise smooth functions and associated variational problems. Commun Pure Appl Math 42:577–685 MathSciNetMATHCrossRefGoogle Scholar
  49. 49.
    Nain D, Yezzi A, Turk G (2003) Vessel segmentation using a shape driven flow. In: MICCAI, pp 51–59 Google Scholar
  50. 50.
    Nieuwenhuis C, Cremers D (2013) Spatially varying color distributions for interactive multi-label segmentation. IEEE Trans Pattern Anal Mach Intell 35(5):1234–1247 CrossRefGoogle Scholar
  51. 51.
    Osher SJ, Sethian JA (1988) Fronts propagation with curvature dependent speed: algorithms based on Hamilton–Jacobi formulations. J Comp Physiol 79:12–49 MathSciNetMATHGoogle Scholar
  52. 52.
    Paragios N, Deriche R (2002) Geodesic active regions and level set methods for supervised texture segmentation. Int J Comput Vis 46(3):223–247 MATHCrossRefGoogle Scholar
  53. 53.
    Parent P, Zucker SW (1989) Trace inference, curvature consistency, and curve detection. IEEE Trans Pattern Anal Mach Intell 11(8):823–839 CrossRefGoogle Scholar
  54. 54.
    Parzen E (1962) On the estimation of a probability density function and the mode. Ann Math Stat 33:1065–1076 MathSciNetMATHCrossRefGoogle Scholar
  55. 55.
    Rochery M, Jermyn I, Zerubia J (2006) Higher order active contours. Int J Comput Vis 69(1):27–42 CrossRefGoogle Scholar
  56. 56.
    Rosenblatt F (1956) Remarks on some nonparametric estimates of a density function. Ann Math Stat 27:832–837 MathSciNetMATHCrossRefGoogle Scholar
  57. 57.
    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 Google Scholar
  58. 58.
    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 Google Scholar
  59. 59.
    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 Google Scholar
  60. 60.
    Rosenfeld A, Zucker SW, Hummel RA (1977) An application of relaxation labeling to line and curve enhancement. IEEE Trans Comput 26(4):394–403 Google Scholar
  61. 61.
    Schmidt FR, Cremers D (2009) A closed-form solution for image sequence segmentation with dynamical shape priors. In: Pattern recognition (Proc. DAGM), September 2009 Google Scholar
  62. 62.
    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 Google Scholar
  63. 63.
    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 Google Scholar
  64. 64.
    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 Google Scholar
  65. 65.
    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 Google Scholar
  66. 66.
    Schoenemann T, Cremers D (2009) A combinatorial solution for model-based image segmentation and real-time tracking. IEEE Trans Pattern Anal Mach Intell Google Scholar
  67. 67.
    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 MathSciNetMATHCrossRefGoogle Scholar
  68. 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 Google Scholar
  69. 69.
    Sebastian T, Klein P, Kimia B (2003) On aligning curves. IEEE Trans Pattern Anal Mach Intell 25(1):116–125 CrossRefGoogle Scholar
  70. 70.
    Serra J (1982) Image analysis and mathematical morophology. Academic Press, London Google Scholar
  71. 71.
    Tsai A, Wells W, Warfield SK, Willsky A (2004) Level set methods in an EM framework for shape classification and estimation. In: MICCAI Google Scholar
  72. 72.
    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 Google Scholar
  73. 73.
    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 MATHCrossRefGoogle Scholar
  74. 74.
    Unal G, Krim H, Yezzi AY (2005) Information-theoretic active polygons for unsupervised texture segmentation. Int J Comput Vis, May Google Scholar
  75. 75.
    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 Google Scholar
  76. 76.
    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 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Departments of Computer Science & MathematicsTU MunichGarchingGermany

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