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An Integrated Bayesian Approach to Shape Representation and Perceptual Organization

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

Abstract

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.

Keywords

  • 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.

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References

  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

    CrossRef  Google Scholar 

  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

    CrossRef  Google Scholar 

  3. Biederman I (1987) Recognition by components: a theory of human image understanding. Psychol Rev 94:115–147

    CrossRef  Google Scholar 

  4. Blum H (1973) Biological shape and visual science (part I). J Theor Biol 38:205–287

    CrossRef  Google Scholar 

  5. Blum H, Nagel RN (1978) Shape description using weighted symmetric axis features. Pattern Recognit 10:167–180

    MATH  CrossRef  Google Scholar 

  6. Briscoe E (2008) Shape skeletons and shape similarity. PhD thesis, Rutgers University

    Google Scholar 

  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. Cortese JM, Dyre BP (1996) Perceptual similarity of shapes generated from Fourier descriptors. J Exp Psychol Hum Percept Perform 22(1):133–143

    CrossRef  Google Scholar 

  9. de Winter J, Wagemans J (2006) Segmentation of object outlines into parts: a large-scale integrative study. Cognition 99(3):275–325

    CrossRef  Google Scholar 

  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

    CrossRef  Google Scholar 

  11. Driver J, Baylis GC (1996) Edge-assignment and figure-ground segmentation in short-term visual matching. Cogn Psychol 31:248–306

    CrossRef  Google Scholar 

  12. Feldman J (1997) Curvilinearity, covariance, and regularity in perceptual groups. Vis Res 37(20):2835–2848

    CrossRef  Google Scholar 

  13. Feldman J (2001) Bayesian contour integration. Percept Psychophys 63(7):1171–1182

    CrossRef  Google Scholar 

  14. Feldman J, Singh M (2005) Information along contours and object boundaries. Psychol Rev 112(1):243–252

    CrossRef  Google Scholar 

  15. Feldman J, Singh M (2006) Bayesian estimation of the shape skeleton. Proc Natl Acad Sci 103(47):18014–18019

    MathSciNet  MATH  CrossRef  Google Scholar 

  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. 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

    CrossRef  Google Scholar 

  18. Hoffman DD, Richards WA (1984) Parts of recognition. Cognition 18:65–96

    CrossRef  Google Scholar 

  19. Hung CC, Carlson ET, Connor CE (2012) Medial axis shape coding in macaque inferotemporal cortex. Neuron 74(6):1099–1113

    CrossRef  Google Scholar 

  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. Katz RA, Pizer SM (2003) Untangling the Blum medial axis transform. Int J Comput Vis 55(2/3):139–153

    CrossRef  Google Scholar 

  22. Kim S (2011) The influence of axiality on figure/ground assignment. Master’s thesis, Rutgers University

    Google Scholar 

  23. Kimia BB (2003) One the role of medial geometry in human vision. J Physiol (Paris) 97:155–190

    CrossRef  Google Scholar 

  24. Koffka K (1935) Principles of gestalt psychology. Harcourt, New York

    Google Scholar 

  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

    CrossRef  Google Scholar 

  26. Lescroart MD, Biederman I (2012) Cortical representation of medial axis structure. In: Cerebral cortex

    Google Scholar 

  27. Leymarie FF, Kimia BB (2007) The medial scaffold of 3d unorganised point clouds. IEEE Trans Pattern Anal Mach Intell 29(2):313–330

    CrossRef  Google Scholar 

  28. Leyton M (1989) Inferring causal history from shape. Cogn Sci 13:357–387

    Google Scholar 

  29. Ling H, Jacobs DW (2007) Shape classification using the inner-distance. IEEE Trans Pattern Anal Mach Intell 29(2):286–299

    CrossRef  Google Scholar 

  30. Lowe DG (2004) Distinctive image features from scale-invariant keypoints. Int J Comput Vis 60(2):91–110

    CrossRef  Google Scholar 

  31. Mackworth A (1973) Interpreting pictures of polyhedral scenes. Artif Intell 4:121–137

    CrossRef  Google Scholar 

  32. Malik J (1987) Interpreting line drawings of curved objects. Int J Comput Vis 1:73–103

    CrossRef  Google Scholar 

  33. Mardia KV (1972) Statistics of directional data. Academic Press, London

    MATH  Google Scholar 

  34. Marr D (1982) Vision: a computational investigation into the human representation and processing of visual information. Freeman, San Francisco

    Google Scholar 

  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

    CrossRef  Google Scholar 

  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

    CrossRef  Google Scholar 

  37. Richards W, Dawson B, Whittington D (1988) Encoding contour shape by curvature extrema. In: Natural computation. MIT Press, Cambridge

    Google Scholar 

  38. Rosin PL (2000) Shape partitioning by convexity. IEEE Trans Syst Man Cybern, Part A, Syst Hum 30:202–210

    CrossRef  Google Scholar 

  39. Sebastian TB, Kimia BB (2005) Curves vs. skeletons in object recognition. Signal Process 85:247–263

    MATH  CrossRef  Google Scholar 

  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. Siddiqi K, Tresness KJ, Kimia BB (1996) Parts of visual form: psychophysical aspects. Perception 25:399–424

    CrossRef  Google Scholar 

  42. Singh M, Froyen V, Feldman J (2013, forthcoming) Unifying parts and skeletons: a Bayesian approach to part decomposition

    Google Scholar 

  43. Singh M, Fulvio JM (2005) Visual extrapolation of contour geometry. Proc Natl Acad Sci USA 102(3):939–944

    CrossRef  Google Scholar 

  44. Singh M, Fulvio JM (2007) Bayesian contour extrapolation: geometric determinates of good continuation. Vis Res 47:783–798

    CrossRef  Google Scholar 

  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

    CrossRef  Google Scholar 

  46. Singh M, Seyranian GD, Hoffman DD (1999) Parsing silhouettes: the short-cut rule. Percept Psychophys 61(4):636–660

    CrossRef  Google Scholar 

  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. 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

    CrossRef  Google Scholar 

  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. Wang X, Burbeck CA (1998) Scaled medial axis representation: evidence from position discrimination task. Vis Res 38(13):1947–1959

    CrossRef  Google Scholar 

  51. Weiss Y (1997) Interpreting images by propagating Bayesian beliefs. In: Adv. in neural information processing systems, pp 908–915

    Google Scholar 

  52. Wilder J, Feldman J, Singh M (2011) Superordinate shape classification using natural shape statistics. Cognition 119:325–340

    CrossRef  Google Scholar 

  53. Zhu S-C (1999) Stochastic jump-diffusion process for computing medial axes. IEEE Trans Pattern Anal Mach Intell 21(11):1158–1169

    CrossRef  Google Scholar 

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Correspondence to Jacob Feldman .

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Feldman, J., Singh, M., Briscoe, E., Froyen, V., Kim, S., Wilder, J. (2013). An Integrated Bayesian Approach to Shape Representation and Perceptual Organization. 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_4

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  • DOI: https://doi.org/10.1007/978-1-4471-5195-1_4

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5194-4

  • Online ISBN: 978-1-4471-5195-1

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