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

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 internal constraints

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

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 completion as 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

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

with closed adjacent contours front behind + behind front +

good continuation (Wertheimer, 1921, §29-30) local gc local gc + similarity similarity alone simplicity local gc vs. symmetry similarity?

a definition (Wertheimer, 1921, §29-30) 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.

minimizing the length of modal illusory contours

Petter’s rule easier than

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

stratification  length minimization explains direction  width dissimilarity explains occurrence

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

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

past experience?

orientation

surfaces (minimal amodal area)

equivalent solutions at the contour level

equivalent solutions at the contour level

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

concave vs. convex angles

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

retinal constraints

46 (2006) 3142–3159

probe localization paradigm

retinal gap= 1.6 deg retinal gap= 0.8 deg 79% 61% 88% 59%

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

GC field MP field

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

approximation

interpolation approximation

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

local effect

a byproduct of g.c.

approximation & contrast

approximation distorts visible contours

approximation & surface torsion

with occluder without occluder

∆ RMS= RMS without - RMS with

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

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.