Segmentation and Perceptual Grouping Kaniza (Introduction to Computer Vision, 11.1.04)

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


• Closure• Closure• Common Fate

Gestalt Principles


• 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)



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

Documents

Segmentation and Perceptual Grouping Kaniza (Introduction to Computer Vision, 11.1.04)