Segmentation 268

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Segmentation 268

Segmentation

Image Processing & Computer Vision Lecture

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Segmentation 269

Image Processing & Computer Vision

Introduction

-. Introduction

-. Automatic Thresholding Methods

-. Region Representation

-. Split and Merge

-. Region Growing


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Introduction (cont.)

n Segmentation problem

Partition an imageI into homogeneous regions.

n Description:

Given an imageI and a homogeneity predicateP(), find a partition S ofthe imageI into a set ofNregionsRi such that

ng)partitionie(exhaustiv1

IRN

i

i=

=

U

ng)partitioni(exclusivefor,0 jiRR ji =I

property)ty(homogenei,)(

,)(

==

jiFalseRRP

iTrueRP

ji

i

U

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Introduction (cont.)

n Attributes orP()

Intensity, texture, color, motion, etc.

n Qualitative guideline

Uniform & homogeneous

Simple region interior

Significantly different adjacent regions

Simple and accurate boundary

n Techniques

Threshold-based segmentation

Region-based segmentation

Boundary extraction


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n P-tile segmentation method

Simply use the size information of

the object

Suppose the object occupies about

p% of the image area, then setthreshold to assignp% of the pixelsto the object

n Mode method

Assume Gaussian distribution forthe object and background withsimilar size

Then, detect the peaks and thevalleys, and set the threshold by

the valley point

Bayes decision theory

h

xP %

T

h

xgi gk gj

T

( ) ( )=

=255

areaimageentireTx

pxh

Histogram

Intensity

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Segmentation 273



Peakness detection algorithm for

threshold selection:

Find two local maxima gi and gjwhich are some distance apart

Find the lowest point gk betweengi and gj

Determine the peakness definedas min(h(gi ),h(gj))/h(gk)

Find the highest peaknesscombination(g

i

, gj

, gk

), and setthe threshold T= gk

Segmentation result with T=90


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Threshold-based segmentation (cont.)

n Practical problems of global

thresholding techniques

Noise

Uneven illumination problem

Original Text Threshold=90

Threshold=150 Threshold=230

Uneven illumination problem

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n Iterative threshold selection method

Refines the threshold iteratively using the statistics of the segmented

regions in the previous iteration.

Algorithm:

1. Set initial threshold T (the average intensity of the image)

2. Partition the image into two regions R1 and R2using T

3. Determine the means1 and2 of R1 and R2, respectively.

4. Update new threshold T= (1 +2 )/2.5. Repeat steps 2-4, until the means1 and2 in successive iterations do not

change.


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n Adaptive thresholding method

Partition the image intomxm

subimages

Select a threshold Tijfor each

subimage based on its histogram

Threshold levels for each pixel aredetermined by interpolation

between the block centers

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n Variable thresholding

(background normalization)

Approximate the background

intensity by simple functionsuch as plane or biquadratic

Then normalize the

background by subtractingthe fitted function to theimage

Now, a global thresholdingtechnique can be applied to

segment the normalizedimage

22fyexydxcybxaI +++++=


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n Double Thresholding

Single threshold segmentation failswhen the same intensities belong toeither objects or the background.

Save marginal histogram region forthese intensities and decideassignment by consideringgeometric properties.

Double thresholding algorithm

1. Select two thresholds T1 and T2

2. Partition the image into three regionsR1, R2 and R3 using T1 and T2

3. For each pixel in the middle regionR2, assign it to R1 if it is a neighborof R1

4. Repeat until no changes inreassigning

5. Reassign any pixel left in R2 to R3

Double thresholding example

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Segmentation 279



n Ostu s method (N=2)

Determine thresholdTwhich minimizes the within-class variation while

maximizes the between-class variation s.t.,

where

22 /BW

JMinimize =

)(0110

2

2

11

2

00

2

=

+=

B

W

222

WBT +=

=

=1

0

0

2

0

2

0 )()(T

x

xpx

=

=255

1

2

1

2

1 )()(Tx

xpx

=

=1

0

0 )(T

x

xp

=

=255

1)(

Tx

xp

=

=

=

1

0

1

0

0 )()(T

x

T

x

xhxxh

=

==

25 525 5

1 )()(TxTx

xhxxh

=

=255

0

)()()(x

xhxhxp


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Region-based Segmentation

n Quad Tree representation of

regions

Tree-structure representationof recursive subregions

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n Region Adjacency Graphs (RAG)

represent region and mutual relationships

node: regions

arcs: boundary between regions


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n Region Split and Merge

The basic idea: break the image into a

set of disjoint regions which arecoherent within themselves

Top-down approach

Algorithmic Steps:

1. Start with the entire image as a singleregion.

2. For each region Ri. If P(Ri)=FALSE,then split Ri into four subregions.

3. If for any adjacent subregions Rj andRk, P(RjU Rk)=TRUE, then mergethem into a single region.

4. Repeat until no further split and mergetake place.

R1 R2

R41 R42

R44R43R3

R1 R2

R41 R42

R43R3

R

R1 R2

R3 R4

Whole image First split

Second split Merge

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Segmentation 283


Region-based Segmentation (cont.)

n Region Split and Merge (Cont.)

Modified quadtree structure.

Each non-terminal node in the treehas at most four descendants,

although it may have less due tomerging.

Corresponding quadtree

R

R1

R41 R42 R43

R4R3R2


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n Similarity measures between regions

Mean intensity comparison

If |1 -2 | < Th, then similar. Otherwise dissimilar.

Statistical hypothesis testing

Consider Two regions R1,R2with m1 and m2pixels, respectively

Then, two hypothesesH0andH1 are possible

H0: Both regions belong to the same region

Intensities are from a single Gaussian distribution with( 0,0)

The joint pdf under H0becomes

2

0

2

)(

0

2

)(

1 0

1

0021

)21(

21

20

21

1

20

21

2

0

2

021

21

21

)2(

1

)2(

1

21

)|()|,...,,(

mm

mm

ii

i

e

e

e

HgpHgggp

mm

g

mm

gmm

i

mm

i

imm

+

+

=

+

+

+

=

+

=+

=

=

=

=

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n Similarity measures between regions (cont.)H1 : Two regions are different:

Intensities of each regions are from different Gaussian distribution

with( 1,1) and ( 2,2)

The joint pdf becomes

Define the likely-hood ratio

Then, decide to merge ifL< Th. Otherwise, do not merge.

2

21

2

2

2

1

1121

)21(

2121

2

2

1

12111

)2(

1

)2(

1

)2(

1)|,...,,,...,,(

mm

e

eeHgggggp

mmmm

m

m

m

mmmmm

+

+

++

=

=

21

21

21

21

21

0

021

121

)|,...,,(

)|,...,,(mm

mm

mm

mm

Hgggp

HgggpL

+

+

+ ==


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n Removing Weak Edges (Boundaries)

4Approach 1:

Merge R1 and R2 if

W: length of the weak boundaryS = min(S1,S2): threshold ( =0.5)

>S

W

4Approach 2:

Merge R1 and R2 if

W: length of the weakS = common boundary: threshold ( =0.75)

>S

W

Not merge Merge Not merge Merge

S1

S2

w wS

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n Region Split and Merge Examples

original segmentation

Split and Merge Example


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n Region Growing

Basic Idea: the opposite of the split and merge approach

An initial set of small areas are iteratively merged according tosimilarity constraints.

A bottom up method.

Algorithmic Steps:

1. Start by choosing an arbitrary seed pixel and compare it withneighbouring pixels.

2. Region is grown from the seed pixel by adding in neighboring pixelsthat are similar, increasing the size of the region.

3. When the growth of one region stops we simply choose another seedpixel which does not yet belong to any region and start again.

4. This whole process is continued until all pixels belong to some region.

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n Region Growing (Cont.)

Region growing methods oftengive very good segmentationsthat correspond well to the

observed edges.

However, starting with a

particular seed pixel andletting this region growcompletely before trying other

seeds biases thesegmentation in favor of the

regions which are segmentedfirst.


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n Region Growing (cont.)

Undesirable effects:

Current region dominates the growth process -- ambiguities around edgesof adjacent regions may not be resolved correctly.

Different choices of seeds may give different segmentation results.

Problems can occur if the (arbitrarily chosen) seed point lies on an edge.

simultaneous region growing techniques

Similarities of neighbouring regions are taken into account in the growingprocess.

No single region is allowed to completely dominate the proceedings. .

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n Region Growing (cont.)

Simultaneous region growing technique (cont.)

A number of regions are allowed to grow at the same time.

Similar regions will gradually coalesce into expanding regions.

Easy and efficient to implement on parallel computers

Segmentation results by region growing

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Segmentation 268

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