An Integrated Bayesian Approach to Shape Representation and Perceptual Organization

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


We present a unified Bayesian approach to shape representation and related problems in perceptual organization, including part decomposition, shape similarity, figure/ground estimation, and 3D shape. The approach is based on the idea of estimating the skeletal structure most likely to have generated the observed shape via a process of stochastic “growth.” We survey the approach briefly and show how it can be extended in a principled way to solve a wide array of related problems.


Medial Axis Perceptual Organization Part Decomposition Shape Representation Contour Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Barenholtz E, Tarr MJ (2008) Visual judgment of similarity across shape transformations: evidence for a compositional model of articulated objects. Acta Psychol 128(2):331–338 CrossRefGoogle Scholar
  2. 2.
    Baylis G, Driver J (1995) Obligatory edge assignment in vision: the role of figure and part segmentation in symmetry detection. J Exp Psychol Hum Percept Perform 21(6):1323–1342 CrossRefGoogle Scholar
  3. 3.
    Biederman I (1987) Recognition by components: a theory of human image understanding. Psychol Rev 94:115–147 CrossRefGoogle Scholar
  4. 4.
    Blum H (1973) Biological shape and visual science (part I). J Theor Biol 38:205–287 CrossRefGoogle Scholar
  5. 5.
    Blum H, Nagel RN (1978) Shape description using weighted symmetric axis features. Pattern Recognit 10:167–180 zbMATHCrossRefGoogle Scholar
  6. 6.
    Briscoe E (2008) Shape skeletons and shape similarity. PhD thesis, Rutgers University Google Scholar
  7. 7.
    Cole F, Sanik K, DeCarlo AFD, Funkhouser T, Rusinkiewicz S, Singh M (2009) How well do line drawings depict shape? In: ACM transactions on graphics (Proc. SIGGRAPH), vol 28 Google Scholar
  8. 8.
    Cortese JM, Dyre BP (1996) Perceptual similarity of shapes generated from Fourier descriptors. J Exp Psychol Hum Percept Perform 22(1):133–143 CrossRefGoogle Scholar
  9. 9.
    de Winter J, Wagemans J (2006) Segmentation of object outlines into parts: a large-scale integrative study. Cognition 99(3):275–325 CrossRefGoogle Scholar
  10. 10.
    Demirci F, Shokoufandeh A, Keselman Y, Bretzner L, Dickinson S (2006) Object recognition as many-to-many feature matching. Int J Comput Vis 69(2):203–222 CrossRefGoogle Scholar
  11. 11.
    Driver J, Baylis GC (1996) Edge-assignment and figure-ground segmentation in short-term visual matching. Cogn Psychol 31:248–306 CrossRefGoogle Scholar
  12. 12.
    Feldman J (1997) Curvilinearity, covariance, and regularity in perceptual groups. Vis Res 37(20):2835–2848 CrossRefGoogle Scholar
  13. 13.
    Feldman J (2001) Bayesian contour integration. Percept Psychophys 63(7):1171–1182 CrossRefGoogle Scholar
  14. 14.
    Feldman J, Singh M (2005) Information along contours and object boundaries. Psychol Rev 112(1):243–252 CrossRefGoogle Scholar
  15. 15.
    Feldman J, Singh M (2006) Bayesian estimation of the shape skeleton. Proc Natl Acad Sci 103(47):18014–18019 MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Froyen V, Feldman J, Singh M (2010) A Bayesian framework for figure-ground interpretation. In: Lafferty J, Williams CKI, Shawe-Taylor J, Zemel R, Culotta A (eds) Advances in neural information processing systems, vol 23, pp 631–639 Google Scholar
  17. 17.
    Hochberg J, Brooks V (1962) Pictoral recognition as an unlearned ability: a study of one child’s performance. Am J Psychol 75(4):624–628 CrossRefGoogle Scholar
  18. 18.
    Hoffman DD, Richards WA (1984) Parts of recognition. Cognition 18:65–96 CrossRefGoogle Scholar
  19. 19.
    Hung CC, Carlson ET, Connor CE (2012) Medial axis shape coding in macaque inferotemporal cortex. Neuron 74(6):1099–1113 CrossRefGoogle Scholar
  20. 20.
    Kanizsa G, Gerbino W (1976) Convexity and symmetry in figure-ground organization. In: Henle M (ed) Vision and artifact. Springer, New York Google Scholar
  21. 21.
    Katz RA, Pizer SM (2003) Untangling the Blum medial axis transform. Int J Comput Vis 55(2/3):139–153 CrossRefGoogle Scholar
  22. 22.
    Kim S (2011) The influence of axiality on figure/ground assignment. Master’s thesis, Rutgers University Google Scholar
  23. 23.
    Kimia BB (2003) One the role of medial geometry in human vision. J Physiol (Paris) 97:155–190 CrossRefGoogle Scholar
  24. 24.
    Koffka K (1935) Principles of gestalt psychology. Harcourt, New York Google Scholar
  25. 25.
    Kovács I, Fehér A, Julesz B (1970) Medial-point description of shape: a representation for action coding and its psychophysical correlates. Vis Res 38:2323–2333 CrossRefGoogle Scholar
  26. 26.
    Lescroart MD, Biederman I (2012) Cortical representation of medial axis structure. In: Cerebral cortex Google Scholar
  27. 27.
    Leymarie FF, Kimia BB (2007) The medial scaffold of 3d unorganised point clouds. IEEE Trans Pattern Anal Mach Intell 29(2):313–330 CrossRefGoogle Scholar
  28. 28.
    Leyton M (1989) Inferring causal history from shape. Cogn Sci 13:357–387 Google Scholar
  29. 29.
    Ling H, Jacobs DW (2007) Shape classification using the inner-distance. IEEE Trans Pattern Anal Mach Intell 29(2):286–299 CrossRefGoogle Scholar
  30. 30.
    Lowe DG (2004) Distinctive image features from scale-invariant keypoints. Int J Comput Vis 60(2):91–110 CrossRefGoogle Scholar
  31. 31.
    Mackworth A (1973) Interpreting pictures of polyhedral scenes. Artif Intell 4:121–137 CrossRefGoogle Scholar
  32. 32.
    Malik J (1987) Interpreting line drawings of curved objects. Int J Comput Vis 1:73–103 CrossRefGoogle Scholar
  33. 33.
    Mardia KV (1972) Statistics of directional data. Academic Press, London zbMATHGoogle Scholar
  34. 34.
    Marr D (1982) Vision: a computational investigation into the human representation and processing of visual information. Freeman, San Francisco Google Scholar
  35. 35.
    Marr D, Nishihara HK (1978) Representation and recognition of the spatial organization of three-dimensional shapes. Proc R Soc Lond B 200:269–294 CrossRefGoogle Scholar
  36. 36.
    Palmer S, Davis J, Nelson R, Rock I (2008) Figure-ground effects on shape memory for objects versus holes. Perception 37(10):1569–1586 CrossRefGoogle Scholar
  37. 37.
    Richards W, Dawson B, Whittington D (1988) Encoding contour shape by curvature extrema. In: Natural computation. MIT Press, Cambridge Google Scholar
  38. 38.
    Rosin PL (2000) Shape partitioning by convexity. IEEE Trans Syst Man Cybern, Part A, Syst Hum 30:202–210 CrossRefGoogle Scholar
  39. 39.
    Sebastian TB, Kimia BB (2005) Curves vs. skeletons in object recognition. Signal Process 85:247–263 zbMATHCrossRefGoogle Scholar
  40. 40.
    Siddiqi K, Shokoufandeh A, Dickinson S, Zucker S (1999) Shock graphs and shape matching. Int J Comput Vis 30:1–24 Google Scholar
  41. 41.
    Siddiqi K, Tresness KJ, Kimia BB (1996) Parts of visual form: psychophysical aspects. Perception 25:399–424 CrossRefGoogle Scholar
  42. 42.
    Singh M, Froyen V, Feldman J (2013, forthcoming) Unifying parts and skeletons: a Bayesian approach to part decomposition Google Scholar
  43. 43.
    Singh M, Fulvio JM (2005) Visual extrapolation of contour geometry. Proc Natl Acad Sci USA 102(3):939–944 CrossRefGoogle Scholar
  44. 44.
    Singh M, Fulvio JM (2007) Bayesian contour extrapolation: geometric determinates of good continuation. Vis Res 47:783–798 CrossRefGoogle Scholar
  45. 45.
    Singh M, Hoffman DD (2001) Part-based representations of visual shape and implications for visual cognition. In: Shipley T, Kellman P (eds) From fragments to objects: segmentation and grouping in vision, advances in psychology, vol 130. Elsevier, New York, pp 401–459 CrossRefGoogle Scholar
  46. 46.
    Singh M, Seyranian GD, Hoffman DD (1999) Parsing silhouettes: the short-cut rule. Percept Psychophys 61(4):636–660 CrossRefGoogle Scholar
  47. 47.
    Telea A, Sminchisescu C, Dickinson S (2004) Optimal inference for hierarchical skeleton abstraction. In: Proceedings IEEE international conference on pattern recognition, Cambridge Google Scholar
  48. 48.
    Twarog NR, Tappen MF, Adelson EH (2012) Playing with puffball: simple scale-invariant inflation for use in vision and graphics. In: Proceedings of the ACM symposium on applied perception, pp 47–54 CrossRefGoogle Scholar
  49. 49.
    Waltz D (1975) Understanding line drawings of scenes with shadows. In: Winston PH (ed) The psychology of computer vision, pp 19–91 Google Scholar
  50. 50.
    Wang X, Burbeck CA (1998) Scaled medial axis representation: evidence from position discrimination task. Vis Res 38(13):1947–1959 CrossRefGoogle Scholar
  51. 51.
    Weiss Y (1997) Interpreting images by propagating Bayesian beliefs. In: Adv. in neural information processing systems, pp 908–915 Google Scholar
  52. 52.
    Wilder J, Feldman J, Singh M (2011) Superordinate shape classification using natural shape statistics. Cognition 119:325–340 CrossRefGoogle Scholar
  53. 53.
    Zhu S-C (1999) Stochastic jump-diffusion process for computing medial axes. IEEE Trans Pattern Anal Mach Intell 21(11):1158–1169 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Department of Psychology, Center for Cognitive ScienceRutgers UniversityNew BrunswickUSA
  2. 2.Department of PsychologyRutgers UniversityNew BrunswickUSA
  3. 3.Aerospace, Transportation and Advanced Systems LaboratoryGeorgia Tech Research InstituteAtlantaUSA

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