主講人 : 張緯德 1. image segmentation ◦ ex: edge-based, region-based image representation...

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Image segmentation, Representation, and

Description主講人 :張緯德

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Image segmentation◦ ex: edge-based, region-based

Image representation ◦ ex: Chain code , polygonal approximation

signatures, skeletons Image description

◦ ex: boundary-based, regional-based Conclusion

OUTLINE

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Image segmentationedge-based: point, line, edge detection

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There are three basic types of gray-level discontinuities in a digital image: points, lines, and edges

The most common way to look for discontinuities is to run a mask through the image.

We say that a point, line, and edge has been detected at the location on which the mask is centered if ,where

edge-based segmentation(1)

R T1 1 2 2 9 9......R w z w z w z

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edge-based segmentation(2) Point detection

a point detection mask

Line detection

a line detection mask

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Edge detection: Gradient operation

x

y

fG xG f

y

f

12 2 2( ) x yf mag f G G

1( , ) tan ( )y

x

Gx y

G

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Edge detection: Laplacian operation

2 22

2 2

f ff

x y

2

22 2

2 24

( )r

rh r e

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Image segmentationRegion-base: SRG, USRG, Fast scanning

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Region growing: Groups pixels or sub-region into larger regions.◦step1:

Start with a set of “seed” points and from these grow regions by appending to each seed those neighboring pixels that have properties similar to the seed.

◦step2: Region splitting and merging

region-based segmentationSRG(1)

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Advantage:◦ With good connectivity

Disadvantage:◦ Initial seed-points:

different sets of initial seed-point cause different segmented result

◦ Time-consuming problem

region-based segmentationSRG(2)

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Unseeded region growing:◦no explicit seed selection is necessary, the

seeds can be generated by the segmentation procedure automatically.

◦It is similar to SRG except the choice of seed point

region-based segmentationUSRG(1)

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Advantage:◦ easy to use◦ can readily incorporate high level knowledge of

the image composition through region threshold

Disadvantage:◦ slow speed

region-based segmentationUSRG(2)

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region-based segmentationfast scanning(1)

Fast scanning Algorithm: ◦ The fast scanning

algorithm somewhat resembles unseeded region growing

◦ the number of clusters of both two algorithm would not be decided before image passing through them.

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Last step:

◦ merge small region to big region

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Advantage:◦ The speed is very fast◦ The result of segmentation will be intact with

good connectivity

Disadvantage:◦ The matching of physical object is not good

It can be improved by morphology and geometric mathematic


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region-based segmentationfast scanning-improved by morphology dilation erosion

{ | for some a A and b B}NA B c E c a b { for every }NA B x E x b A b B !

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region-based segmentationfast scanning-improved by morphology dilation erosion

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region-based segmentationfast scanning-improved by morphology

Erosion=>Dilation Dilation=>Erosion

opening closing

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region-based segmentationfast scanning-improved by Geometric

Mathematic

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region-based segmentationfast scanning-improved by Geometric

Mathematic

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region-based segmentationapplication

Muscle Injury Determination

How to judge for using image segmentation?

Use fast scanning algorithm to segment it.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

X

Y

The quadratic regression equation

Image of the unhealthy muscle fiberImage of the healthy muscle fiber

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Representationchain code, polynomial approximation,

signature, skeletons

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Representationchain code

4-direction

8-direction

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Representationpolynomial approximations

Merging Techniques Splitting Techniques

1S

2S

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Representation signature

Distance signature of circle shapes

Distance signature of rectangular shapes

θr

Ar(θ )

4

2

3

4

5

4

3

2

7

4

2

θ

Ar(θ )

4

2

3

4

5

4

3

2

7

4

2

θ

2A

A

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Representationskeletons

Step1:◦ (a)◦ (b)◦ (c) ◦ (d)

Step2:◦ (c’)◦ (d’)

12 ( ) 6N p

1( ) 1T p

4 6 8 0p p p

2 4 6 0p p p

2 4 8 0p p p

2 6 8 0p p p

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Descriptorsboundary descriptor: Fourier descriptor,

polynomial approximation

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Boundary DescriptorsFourier descriptors (1)

Step1:

Step2: (DFT)

Step3: (reconstruction) if a(u)=0 for u>P-1

Disadvantage:◦ Just for closed boundaries

( ) ( ) ( )s k x k jy k

1 2 /

0

1( ) ( )

K j uk K

ka u s k e

K

1 2 /

0( ) ( )

P j uk K

us k a u e

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What’s the reason that previous Fourier descriptors can’t be used for non-closed boundaries?

How can we use the method to descript non-closed boundaries?

(a)linear offset (b)odd-symmetric extension

•Original segment

s1(k)

(x0, y0)

(xK1, yK1) s2(k)

(b) Linearoffset

s3(k)

(c) Odd symmetric extension

Step 2

Step 3

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The proposed method is used not only for non-closed boundaries but also for closed boundaries.

Why we used proposed method to descript closed boundaries rather than previous method?

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Boundary Descriptorspolynomial approximation(1)

Lagrange Polynomial Cubic Spline Interpolation

0 ,0 , ,0

( ) ( ) ( ) ( ) ( ) ( ) ( )n

n n n n k n kk

P x f x L x f x L x f x L x

0 1 1,

0 1 1

( ) ( )( ) ( )( )

( ) ( )( ) ( )k k n

n kk k k k k k n

x x x x x x x xL x

x x x x x x x x

( 1)

0 1

( ( ))( ) ( ) ( )( ) ( )

( 1)!

n

n

f xf x P x x x x x x x

n

( ) ( )e f x P x

x

S(x)

0x 1x 2x 3x 4x 5x 6x 7nx

0S

1S

4S

5S6S

1 1 1 1

' '1 1 1

" "1 1 1

( ) ( ) ( )

( ) ( )

( ) ( )

j j j j j

j j j j

j j j j

S x f x S x

S x S x

S x S x

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Proposed method(1)◦ Step1: rotate the

boundary and let two end point locate at x-axis

◦ Step2: use second order polynomial to approximate the boundary

( )f x

x

( ')f x

'x

( ')f x

'x

y

0 'x

1 'nx a

b

( , )2

ab

(0,0)( ,0)a

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4ˆ ( ' )

2

b ay x b

a

212 2

20

4ˆ' ' ( ' )

2

n

j jj

b ae y y y x b

a

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Proposed method(2)

◦ If the boundary is closed, how can we do?

◦ Step1: use split approach divide the boundary to two parts.

◦ Step2: use parabolic function to fit the boundary.

1 'y

2 'y

1y

2y

1y

2y

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DescriptorsRegional descriptors: Topological, Texture

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Regional DescriptorsTopological

E = V - Q + F = C – H

◦ E: Euler number

◦ V: the number of vertices◦ Q: the number of edges◦ F: the number of faces◦ C: the number of connected component◦ H: the number of holes

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Regional DescriptorsTexture

Statistical approaches◦ smooth, coarse, regular

nth moment:

◦ 2th moment: is a measure of gray level

contrast(relative smoothness)

◦ 3th moment: is a measure of the skewness

of the histogram

◦ 4th moment: is a measure of its relative

flatness

◦ 5th and higher moments: are not so easily related to

histogram shape

1

0( ) ( ) ( )

L nn i iiu z z m p z

1

0( )

L

i iim z p z

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Image segmentation◦ speed, connectivity, match physical objects or

not… match physical objects:

morphological: how to choose foreground or background?

geometric mathematic: wrong connection

Representation & Description ◦ Boundary descriptor:

rotation, translation, degree of match boundary, closed or non-closed boundary

Conclusion

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[1] R.C. Gonzalez, R.E. Woods, Digital Image Processing second edition, Prentice Hall, 2002

[2] J.J. Ding, W.W. Hong, Improvement Techniques for Fast Segmentation and Compression

[3] J.J. Ding, Y.H. Wang, L.L. Hu, W.L. Chao, Y.W. Shau, Muscle Injury Determination By Image Segmentation

[4] J.J. Ding, W.L. Chao, J.D. Huang, C.J. Kuo, Asymmetric Fourier Descriptor Of Non-Closed segments

Reference

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主講人 : 張緯德 1. image segmentation ◦ ex: edge-based, region-based image representation...

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