FUZZY COLOUR IMAGE FUZZY COLOUR IMAGE SEGMENTATION APPLIED - - PowerPoint PPT Presentation
FUZZY COLOUR IMAGE FUZZY COLOUR IMAGE SEGMENTATION APPLIED SEGMENTATION APPLIED TO ROBOT VISION TO ROBOT VISION J. Chamorro-Martnez D. Snchez B. Prados-Surez Department of Computer Science and Artificial Intelligence. University of
Department of Computer Science and Artificial Intelligence. University of Granada
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Image Segmentation.
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Colour Information Processing.
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Proposed Algorithm.
– Seed points. – Fuzzy Regions.
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Applications
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Conclusions.
Algorithm
Segmentation Technique Region growing based on the distance Region Definition Fuzzy subset of connected pixels Region Construction Based on topographic and colour information. Colour Space HSI Colour Processing Distance measure Membership degree Distance measure
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Image Segmentation = Dividing an image into significant regions.
Pixel Based Techniques Area Based Techniques Edge Based Techniques Histogram Based Clustering Algorithms Growing Region Split & Merge Algorithms
Region: Set of pixels satisfying a class membership function Region: Set of connected pixels satisfying an uniformity condition Region: Set of pixels bounded by a colour contour
There are three groups of techniques, depending
Chosen Method
Fuzzy Region: Fuzzy subset of pixels. Every pixel of the
image has a membership degree to the region.
All the pixels in the image belong to all the regions to a certain degree.
Maximum membership Minimum membership
Membership degrees to the red-bounded region.
Problem: These techniques apply the same combination rule to the whole image. Region growing algorithms must consider the particularities in the comparison of two colours Combining the information of each band in a single value before processing
(ej. gradient)
Analyzing each band separately and combining the results
(ej. histogram of each band and its combination)
Solutions to process colour information.
Solution: To use a colour space which take into account the particularities of the distance between colours, allowing us to define a metric.
HSI colour space: It’s a perceptual colour space with three components (Hue, Saturation, Intensity).
The distance between two colours (pi=[Hi,Si,Ji], pj=[Hj,Sj,Jj]) is defined as a combination of the difference between their components.
There are three chromaticity regions, defined as:
> > ≤ > ≤ Ts Chromatic Ts atic m Semichro Achromatic is I S H P
i i i i i I i i I i I i
S and T I if S and T I if T I if ] , , [ 5 1 = = Ts I MAX T
I
− − + = B G R B G H 2 ) ( 3 arctan
{ }
I B G R S , , min 1− = 3 B G R I + + =
Semichromatic zone Achromatic zone Chromatic zone
− − ≤ − − =
| | 2 | | if | |
j i j i j i H
H H H H H H d π π | |
j i S
S S d − = | |
j i I
I I d − = 255) I (MAX 1 = = I MAX dI d + =
d chromatic are p
p if 2 d d achromatic are p
p if ) , (
S j i 2 H 2 s j i 2
π
j i p
p d 2 2 2 2 1 ) , ( d d j p i p dc + =
Seed points selection is critical in region growing algorithms => Our method is focused for the case
Calculate the Seed Points θ= {s1, s2, s3, ..., sq} Construct the Fuzzy Sets
} , ~ ,... ~ , ~ , ~ { ~
3 2 1 q
S S S S = Θ
Algorithm
Corner Detection Seed Placement
Maybe too many seeds into the same door => too many regions.
Harri’s corner detection method Two seeds are placed at a distance D from each corner, in the direction of its gradient
(one in each way). D = 7 Gradient => Sobel Operator
D = 7 D = 7
Calculate the seed points θ = {s1, s2, s3, ..., sq}
Algorithm
Construct the Fuzzy Sets
} , ~ ,... ~ , ~ , ~ { ~
3 2 1 q
S S S S = Θ
{ }
1 1
, | ) , ( max ) ( cos
+ +
∋ =
r r ij r r ij
p p p p dc t π π
)} ( cost min{ arg
* ij ij
π π = ) ( cos ) , (
* ij j i
t p p dp π =
Optimum path in Πij. It links pi and pj with minimum cost.
πij
*
Colour distance between pr and ps dc(pr,ps) Distance pi→pj. It’s the cost of the optimum path linking them.
dp(pi, pj)
Two consecutive pixels in πij. pr, pr+1 Cost of the path πij linking pi and pj. Cost(π
π π πij)
A given path in Πij.
πij
Set of possible paths linking pi and pj. Π Π Π Πij
Region Growing We have to define:
↓ ↓ ↓ ↓dc (small colour jump) ⇓ ↓ ↓ ↓ ↓Cost(π62) ⇓
π62
* = π62
Path 2 = π62 Path 1 = π62
dp(p6,p2)= Cost(π π π π62)
P8 P7 P6 P5 P4 P3 P2 P1 P0
Big colour difference => ↑ ↑ ↑ ↑dc ⇓ ↑ ↑ ↑ ↑ Cost(π62)
p
! Characteristics of the distance:
– It’s sensitive to the presence of edges (edge => high distance in the consecutive pixels of the path which are on that edge). – It uses colour information (distances between colours). – It also uses topographic information (paths).
! Notation:
– Contour(L) = Pixels in the contour of the region L. – Neighbor(pi) = 8-neighborhood of pi. – Card(L) = Cardinality of the region L.
I = image NxM sv = seed point Inicialization: dp(sv,sv) = 0 L = {sv} While Card(L) ≠ NxM
}) p )\L p ;Neighbor( p ) |Contour(L ,p {dc(p ) ,p (p
j i i j i ) ,p (p
in
j i
∋ ∋ = min arg
)] , ( ), , ( max[ ) , (
in c v in p v
p
p p d s p d s p d =
} {
p L L U =
End
Calculate the seed points θ = {s1, s2, s3, ..., sq}
Algorithm
Membership degree of the pixel pi to the fuzzy region . Set of fuzzy regions: Distance from píxel pi to seed sv.
dp*(pi, sv)
Seed of the region . θ ∋ sv
sv
A fuzzy region.
) (
~ i S
p
v
µ
v
S ~
v
S ~
v
S ~ } ~ ,..., ~ , ~ { ~
2 1 q
S S S = Θ
Θ ~
∑
=
− − =
q k v i p v i p i S
s p d s p d p
v
1 * * ~
) , ( 1 ) , ( 1 ) ( µ
∑
=
=
q v i S
p
v
1 ~
1 ) ( µ
≠ ∋ Θ
) , ( s p and p if 1 ) , (
v i i * v i p v i p
s p d s p d Construct the Fuzzy Sets
} , ~ ,... ~ , ~ , ~ { ~
3 2 1 q
S S S S = Θ
Region Growing We have to define:
Computational Complexity: O(qnK):
The constat C has been fixed to 0.05. The maximum size of a contour is 2N+2M.
Calculate the seed points θ = {s1, s2, s3, ..., sq}
Algorithm
Construct the Fuzzy Sets
} , ~ ,... ~ , ~ , ~ { ~
3 2 1 q
S S S S = Θ
Region Growing We have to define:
O(nK) q times
Compute In the algorithm to calculate dp a new step is included: “Eliminate all the seeds, su, verifying dp(sv,su) < C”
) (
~ i s p
v
µ
} ,..., , {
2 1 n
s s s = Θ
For every seed, sv, in θ End
} ~ ,..., ~ , ~ { ~
2 1 q
S S S = Θ
For every pixel, pi, in I
colour camera
The algorithm has segmented
12 34 14 12 9 30 5 10 4 3 4 8
... regions from ... seeds.
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Although in the examples we can find degradation in the iluminance and zones with different brightness, this method segments the whole door without splitting it in several parts.
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The technique is based on the growth of regions, treated as fuzzy subsets.
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The colour information is processed using a distance measure defined in the HSI colour space.
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The membership function combines colour and topographic information.
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The combination of the proposed colour distance and the growing region process improves the results obtained with the classical techniques.