SIMPLICITY & COMPLETION Walter Gerbino University of Trieste, - - PowerPoint PPT Presentation

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SIMPLICITY & COMPLETION Walter Gerbino University of Trieste, - - PowerPoint PPT Presentation

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SIMPLICITY & COMPLETION Walter Gerbino University of Trieste, Italy VBM2006 - Montevideo why completion? perception depends on stimulus information and internal constraints when the stimulus is incomplete, perception reflects

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SIMPLICITY & COMPLETION

Walter Gerbino University of Trieste, Italy

VBM2006 - Montevideo

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  • perception depends on stimulus

information and internal constraints

  • when the stimulus is incomplete,

perception reflects internal constraints

why completion?

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  • amodal completion & occlusion
  • beyond contours
  • retinal constraints
  • approximation vs. interpolation

topics

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different kinds

  • f completion
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virtual unifications

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

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amodal “covered” completions

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but Michotte also discussed

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les compléments amodaux “à decouvert”

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lampshade for crossfusers

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in monocular conditions

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simplicity and 3D

  • spheres simpler than disks
  • spheres: why not in 2-circle patterns?
  • minimizing interobject distance,

shape, and global structure

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eggs

(Tse, 1999)

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a continuum

  • virtual unifications
  • amodal uncovered surfaces
  • amodal covered surfaces
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amodal completion as a process

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two hypotheses

  • completed objects are recognized

despite partial evidence

  • completions are generated as

parts of a full object model

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modeling hypothesis

  • amodal parts are produced
  • completion is pre-categorical
  • completion is constrained

(by simplicity, among

  • ther things)
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contours

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not /abefil.../cdghk.../ we perceive /acegi.../bdfhl.../

+ +

(Wertheimer, 1921, §27)

line segmentation

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with closed adjacent contours

front behind + front behind +

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(Wertheimer, 1921, §29-30)

good continuation

local gc local gc + similarity similarity alone simplicity local gc vs. symmetry similarity?

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Consider a curve corresponding to a simple mathematical function, large enough to allow

  • bservers 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

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minimizing the length

  • f modal

illusory contours

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Petter’s rule

easier than

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Petter’s rule & undulation

(modified from Kanizsa, 1984, 1991)

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  • length minimization explains

direction

  • width dissimilarity explains
  • ccurrence

stratification

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undulation persists

(also when width is balanced)

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control for contrast polarity

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control for orientation

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minimal local depth

  • the grey bar on the right looks undulated,

though consistent with Petter’s rule

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minimal depth

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surfaces

(perceived modal area)

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less is more

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(Kanizsa & Gerbino, 1982)

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  • bjects
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cylinder on a block

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cylinder into a block

  • obliquity or non-parallelism?
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  • blique cylinder on a block
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3D penetration

  • amodal continuation
  • explained by form regularization
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joint undeterminacy

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pencil in the block

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two possibilities

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  • doubly owned (metaphysical)
  • totally or partially empty
  • divided among the two objects
  • belonging to one object only

the undeterminate intersection volume

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past experience?

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  • rientation
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surfaces

(minimal amodal area)

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equivalent solutions at the contour level

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equivalent solutions at the contour level

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estimating the vertex

  • f an occluded angle

(Fantoni, Bertamini, & Gerbino, 2005)

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concave vs. convex angles

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average localization= 80%

84% 84% 74% 77%

concave symmetric convex symmetric convex asymmetric concave asymmetric

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retinal constraints

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46 (2006) 3142–3159

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probe localization paradigm

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retinal gap= 1.6 deg retinal gap= 0.8 deg

79% 61% 59% 88%

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the field model

(Fantoni & Gerbino, 2003; Gerbino & Fantoni, 2005)

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GC field MP field

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CHAINED VECTOR SUMS

FREE PARAMETER: GC-MP contrast = GCmax - MPmax GCmax + MPmax

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approximation

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interpolation approximation

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  • rounding due to the minimization
  • f the amodal contour
  • good continuation is irresistible

(Gerbino 1978)

  • shape approximation and contrast

(Fantoni, Gerbino, & Kellman, submitted)

why a deformation?

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local effect

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a byproduct of g.c.

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approximation & contrast

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approximation distorts visible contours

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approximation & surface torsion

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with occluder without occluder

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∆RMS= RMSwithout - RMSwith

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  • amodal completion is mediated

by internal models

  • modeling by approximation

can distort modal parts

conclusions

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thanks

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Completion phenomena are theoretically important because they reveal how the visual system overcomes the local gaps of optic information. Gestalt theorists proposed that amodal completion is driven by a tendency towards simplicity. I will discuss strengths and weaknesses of such an idea and refer to specific cases of 2D and 3D completion, supporting the following specific hypotheses: surface-level processes integrate contour-level processes; retinal constraints play a non trivial role; approximation explains the perceived shape of partially occluded surfaces better than interpolation.