segmentation and perceptual grouping kaniza (introduction to computer vision, 11.1.04)
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Segmentation and Perceptual Grouping
Kaniza
(Introduction to Computer Vision, 11.1.04)
The image of this cube contradicts the optical image
Perceptual Organization
• Atomism, reductionism:– Perception is a process of decomposing an
image into its parts.– The whole is equal to the sum of its parts.
• Gestalt (Wertheimer, Köhler, Koffka 1912)– The whole is larger than the sum of its parts.
Gestalt: apparent motion
Gestalt: apparent motion
Gestalt Principles
• Proximity
Gestalt Principles
• Proximity• Proximity• Similarity
Gestalt Principles
• Proximity• Similarity
• Proximity• Similarity• Continuity
Gestalt Principles
• Closure• Proximity• Similarity• Continuity
Gestalt Principles
• Proximity• Similarity• Continuity
• Closure• Closure• Common Fate
Gestalt Principles
• Proximity• Similarity• Continuity
• Closure• Common Fate• Simplicity
• Closure• Common Fate
Mona Lisa
Mona Lisa
Smooth Completion
• Isotropic
• Smoothness
• Minimal curvature
• Extensibility
Elastica:
2min ( )k s ds
Elastica
• Scale invariant (Weiss, Bruckstein & Netravali)
• Approximation (Sharon, Brandt & Basri)
2 21 2 1 24( )
2min ( )l k s ds
(Sharon, Brandt & Basri)
Hough Transform
Hough Transform
Curve Salience
Saliency Network
Encourage
• Length
• Low curvature
• Closure
(Shashua & Ullman)
Saliency Network(Shashua & Ullman)
Tensor Voting
• Every edge element votes to all its circular edge completions
• Vote attenuates with distance: e-αd
• Vote attenuates with curvature: e-βk
• Determine salience at every point using principal moments
(Guy & Medioni)
Tensor Voting(Guy & Medioni)
Stochastic Completion Field
• Random walk:
• In addition, a particle may die with probability:
2
cos
sin
(0, )
x
y
N
1/ re
(Mumford; Williams & Jacobs)
Stochastic Completion Fields
• Most probable path:
with
2
2
( )
1
21
log( 2 )
k s ds ds
r
(Mumford; Williams & Jacobs)
Stochastic Completion Fields(Mumford; Williams & Jacobs)
Stochastic Completion Fields(Mumford; Williams & Jacobs)
Stochastic Completion Fields(Mumford; Williams & Jacobs)
Shortest Path(Hu, Sakoda & Pavlidis)
Snakes
• Given a curve Г(s)=(x(s),y(s)), define:1
0
int
22 2
int 2
( ( ))
( ( ))
( , )
( ) ( )
image ext
image
E s ds
E s E E E
E I x y
E s ss s
(Kass, Witkin & Terzopolous)
Snakes: Curve Evolution
Snakes: Curve Evolution
Thresholding
Histogram
0 50 100 150 200 250
0
200
400
600
800
1000
1200
Thresholding
Thresholding
125
15699
Image Segmentation
Camouflage
Minimum Cut(Wu & Leahy)
Texture Examples
Filter Bank(Malik & Perona)
Normalized Cuts(Malik et al.)
Segmentation by Weighted Aggregation
A multiscale algorithm:• Optimizes a global measure• Returns a full hierarchy of segments• Linear complexity• Combines multiscale measurements:
– Texture– Boundary integrity
(Galun, Sharon, Brandt & Basri)
Segmentation by Weighted Aggregation(Galun, Sharon, Brandt & Basri)
Leopards
And More…
Malik’s Ncuts