SIMPLICITY & COMPLETION Walter Gerbino University of Trieste, Italy VBM2006 - Montevideo.
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Transcript of SIMPLICITY & COMPLETION Walter Gerbino University of Trieste, Italy VBM2006 - Montevideo.
![Page 1: SIMPLICITY & COMPLETION Walter Gerbino University of Trieste, Italy VBM2006 - Montevideo.](https://reader035.fdocuments.us/reader035/viewer/2022062518/56649e8a5503460f94b8ed7c/html5/thumbnails/1.jpg)
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 of 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 completionas 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 other 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+
frontbehind +
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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 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
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minimizing the length of 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
occurrence
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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objects
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cylinder on a block
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cylinder into a block
obliquity or non-parallelism?
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oblique 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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orientation
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surfaces(minimal amodal area)
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equivalent solutionsat the contour level
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equivalent solutionsat the contour level
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estimating the vertexof 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%
concavesymmetric
convexsymmetric
convexasymmetric
concaveasymmetric
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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
of 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.