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8/14/2019 Segmentation 268
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Segmentation 268
Segmentation
Image Processing & Computer Vision Lecture
269
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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Image Processing & Computer Vision
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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Image Processing & Computer Vision
Threshold-based segmentation
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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Image Processing & Computer Vision
Threshold-based segmentation
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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Image Processing & Computer Vision
Threshold-based segmentation (cont.)
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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Threshold-based segmentation (cont.)
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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Threshold-based segmentation (cont.)
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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Threshold-based segmentation (cont.)
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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Threshold-based segmentation (cont.)
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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Region-based Segmentation
n Region Adjacency Graphs (RAG)
represent region and mutual relationships
node: regions
arcs: boundary between regions
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Region-based Segmentation
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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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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Region-based Segmentation (cont.)
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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Region-based Segmentation (cont.)
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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Region-based Segmentation (cont.)
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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Region-based Segmentation (cont.)
n Region Split and Merge Examples
original segmentation
Split and Merge Example
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Region-based Segmentation (cont.)
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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Region-based Segmentation (cont.)
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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Region-based Segmentation (cont.)
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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Region-based Segmentation (cont.)
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