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SIMPLICITY & COMPLETION
Walter Gerbino
University of Trieste, Italy
VBM2006 - Montevideo
perception depends on stimulus
information and internal constraints
when the stimulus is incomplete, perception reflects internal constraints
why completion?
amodal completion & occlusion
beyond contours
retinal constraints
approximation vs. interpolation
topics
different kinds of completion
virtual unifications
The horseman, 1918(Bart van der Leck, 1876-1958)
amodal “covered” completions
but Michotte also discussed
les compléments amodaux“à decouvert”
lampshade for crossfusers
in monocular conditions
simplicity and 3D
spheres simpler than disks
spheres: why not in 2-circle patterns?
minimizing interobject distance,
shape, and global structure
eggs (Tse, 1999)
a continuum
virtual unifications
amodal uncovered surfaces
amodal covered surfaces
amodal completionas a process
two hypotheses
completed objects are recognized
despite partial evidence
completions are generated as
parts of a full object model
modeling hypothesis
amodal parts are produced
completion is pre-categorical
completion is constrained
(by simplicity, among other things)
contours
not /abefil.../cdghk.../
we perceive /acegi.../bdfhl.../
+
+
(Wertheimer, 1921, §27)line segmentation
with closed adjacent contours
front behind+
frontbehind +
(Wertheimer, 1921, §29-30)good continuation
local gc local gc + similarity similarity alone
simplicity local gc vs. symmetry similarity?
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
minimizing the length of modal
illusory contours
Petter’s rule
easier than
Petter’s rule & undulation (modified from Kanizsa, 1984, 1991)
length minimization explains
direction
width dissimilarity explains
occurrence
stratification
undulation persists (also when width is balanced)
control for contrast polarity
control for orientation
minimal local depth
the grey bar on the right looks undulated, though consistent with Petter’s rule
minimal depth
surfaces(perceived modal area)
less is more
(Kanizsa & Gerbino, 1982)
objects
cylinder on a block
cylinder into a block
obliquity or non-parallelism?
oblique cylinder on a block
3D penetration
amodal continuation
explained by form regularization
joint undeterminacy
pencil in the block
two possibilities
doubly owned (metaphysical)
totally or partially empty
divided among the two objects
belonging to one object only
the undeterminate intersection volume
past experience?
orientation
surfaces(minimal amodal area)
equivalent solutionsat the contour level
equivalent solutionsat the contour level
estimating the vertexof an occluded angle
(Fantoni, Bertamini, & Gerbino, 2005)
concave vs. convex angles
average localization= 80%84%
84%
74%
77%
concavesymmetric
convexsymmetric
convexasymmetric
concaveasymmetric
retinal constraints
46 (2006) 3142–3159
probe localization paradigm
retinal gap= 1.6 deg retinal gap= 0.8 deg
79%
61%
59%
88%
the field model(Fantoni & Gerbino, 2003; Gerbino & Fantoni, 2005)
GC field MP field
CHAINED VECTOR SUMS
FREE PARAMETER: GC-MP contrast = GCmax - MPmax
GCmax + MPmax
approximation
interpolation approximation
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?
local effect
a byproduct of g.c.
approximation & contrast
approximation distorts
visible contours
approximation &
surface torsion
with occluder without occluder
RMS= RMSwithout - RMSwith
amodal completion is mediated by internal models
modeling by approximation can distort modal parts
conclusions
thanks
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.