Image segmentation, Representation, and Description
description
Transcript of Image segmentation, Representation, and Description
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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-based segmentation(3)
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-based segmentation(4)
Edge detection: Laplacian operation
2 22
2 2
f ff
x y
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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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region-based segmentationfast scanning(2)
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region-based segmentationfast scanning(3)
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
region-based segmentationfast scanning(4)
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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
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X
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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 )
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θ
Ar(θ )
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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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Boundary DescriptorsFourier descriptors (2)
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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Boundary DescriptorsFourier descriptors (3)
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
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( 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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Boundary Descriptorspolynomial approximation(2)
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
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4ˆ ( ' )
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4ˆ' ' ( ' )
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Boundary Descriptorspolynomial approximation(3)
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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