1. SIMPLICITY & COMPLETION Walter Gerbino University of Trieste, Italy VBM2006 - Montevideo

2.  perception depends on stimulus information and internal constraints  when the stimulus is incomplete, perception reflects internal constraints why completion?

3.  amodal completion & occlusion  beyond contours  retinal constraints  approximation vs. interpolation topics

4. different kinds of completion

5. virtual unifications

6. The horseman, 1918 (Bart van der Leck, 1876-1958)

7. amodal “covered” completions

8. but Michotte also discussed

9. les compléments amodaux “à decouvert”

11. lampshade for crossfusers

13. in monocular conditions

15. simplicity and 3D  spheres simpler than disks  spheres: why not in 2-circle patterns?  minimizing interobject distance, shape, and global structure

18. eggs (Tse, 1999)

19. a continuum  virtual unifications  amodal uncovered surfaces  amodal covered surfaces

20. amodal completion as a process

21. two hypotheses  completed objects are recognized despite partial evidence  completions are generated as parts of a full object model

22. modeling hypothesis  amodal parts are produced  completion is pre-categorical  completion is constrained (by simplicity, among other things)

23. contours

24. not /abefil.../cdghk.../ we perceive /acegi.../bdfhl.../ + + (Wertheimer, 1921, §27) line segmentation

25. with closed adjacent contours frontbehind + frontbehind +

26. (Wertheimer, 1921, §29-30) good continuation local gclocal gc + similaritysimilarity alone simplicitylocal gc vs. symmetrysimilarity?

27. Consider a curve corresponding to a simple mathematical function, large enough to allow observers to recognize the underlying function. Then, add a segment based on a clearly different function and another following the same principle. In general, the latter (not the former) will form a unit with the given curve. (Wertheimer, 1921, §29-30) a definition

28. minimizing the length of modal illusory contours

29. Petter’s rule easier than

30. Petter’s rule & undulation (modified from Kanizsa, 1984, 1991)

31.  length minimization explains direction  width dissimilarity explains occurrence stratification

32. undulation persists (also when width is balanced)

33. control for contrast polarity

34. control for orientation

35. minimal local depth  the grey bar on the right looks undulated, though consistent with Petter’s rule

36. minimal depth

39. surfaces (perceived modal area)

45. less is more

46. (Kanizsa & Gerbino, 1982)

48. objects

49. cylinder on a block

50. cylinder into a block  obliquity or non-parallelism?

51. oblique cylinder on a block

52. 3D penetration  amodal continuation  explained by form regularization

53. joint undeterminacy

55. pencil in the block

56. two possibilities

57.  doubly owned (metaphysical)  totally or partially empty  divided among the two objects  belonging to one object only the undeterminate intersection volume

58. past experience?

60. orientation

61. surfaces (minimal amodal area)

62. equivalent solutions at the contour level

64. estimating the vertex of an occluded angle (Fantoni, Bertamini, & Gerbino, 2005)

66. concave vs. convex angles

67. average localization= 80% 84% 74% 77% concave symmetric convex symmetric convex asymmetric concave asymmetric

68. retinal constraints

69. 46 (2006) 3142–3159

70. probe localization paradigm

71. retinal gap= 1.6 degretinal gap= 0.8 deg 79% 61% 59% 88%

72. the field model (Fantoni & Gerbino, 2003; Gerbino & Fantoni, 2005)

73. GC field MP field

74. CHAINED VECTOR SUMS FREE PARAMETER: GC-MP contrast = GC max - MP max GC max + MP max

75. approximation

76. interpolationapproximation

80.  rounding due to the minimization of the amodal contour  good continuation is irresistible (Gerbino 1978)  shape approximation and contrast (Fantoni, Gerbino, & Kellman, submitted) why a deformation?

81. local effect

82. a byproduct of g.c.

83. approximation & contrast

84. approximation distorts visible contours

90. approximation & surface torsion

91. with occluderwithout occluder

95.  RMS= RMS without - RMS with

96.  amodal completion is mediated by internal models  modeling by approximation can distort modal parts conclusions

97. thanks