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.