ukci05 5-7 september 1 applicability of fuzzy clustering for the identification of upwelling areas...
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UKCI’05 5-7 September 1
Applicability of Fuzzy Clustering for Applicability of Fuzzy Clustering for thethe
Identification of Upwelling Areas on Identification of Upwelling Areas on
Sea Surface Temperature ImagesSea Surface Temperature Images Susana Nascimento, Fátima M. Sousa,
Hugo Casimiro Dmitri Boutov
2Instituto de Oceanografia
Faculdade de Ciências
Universidade de Lisboa,
PORTUGAL
1
Centro de Inteligência Artificial
Dep. InformáticaFaculdade de Ciências e Tecnologia
Universidade Nova de LisboaPORTUGAL
UKCI’05 5-7 September 2
Overview
Introduction to the problem of Upwelling Recognition
Sea Surface Temperature (SST) Image Segmentation by Fuzzy Partitional Clustering
Methodology
Experimental Study
Ongoing Work
UKCI’05 5-7 September 3
Upwelling Event
What is Upwelling?
It is a mass of deep, cold, and nutrient-rich seawater that rises close to the coast.
Upwelling occurs when winds parallel to the coast induce a net mass transport of surface seawater in a 90º direction, away from the coast, due to the Coriolis force. Deep waters rise in order to compensate the mass deficiency that develops along the coastal area.
Why is Upwelling so important? Brings nutrient-rich deep waters close to the ocean
surface, creating regions of high biological productivity. Strong impact on fisheries, and global oceanic climate
models
http://oceanexplorer.noaa.gov/explorations/02quest/background/upwelling/upwelling.html
UKCI’05 5-7 September 4
Upwelling Event in the Coastal Waters of Portugal
SST image of an upwelling event obtained on 04AUG1998 (n14_98216_0422_sst); (b) upwelling boundary manually contoured; (c) upwelling areas automatically retrieved.
Ground truth image
UKCI’05 5-7 September 5
Why an Automatic System for Upwelling Recognition?
Satellite Station of Instituto de Oceanografia (IO) of FC-UL Reception AVHRR thermal infrared Images since 1991
100 images per Upwelling Epoc (June-September) An expert chooses, by visual inspection, the best image of a day
reception and treatment of 3-4 images a day.
Until now, the areas covered by upwelling waters including cold filaments, have been contoured by hand.
The method is very subjective and depending on the skill and practice of the expert.
UKCI’05 5-7 September 6
Data
AVHRR thermal infrared images are received and processed by IO Station with SeaSpace software package TeraScan producing SST images.
Sea Surface Temperature (SST) images
720 400 matrix with each entry a temperature value in degrees Celsius with 1Km2 spatial resolution.
X
Y
UKCI’05 5-7 September 7
Distinct Groups of Images
(G1) well-defined upwelling events
(G2) images where upwelling is evident but there are areas with no temperature information (covered with clouds or noise);
SST images divided into 5 groups according to different “upwelling situations”.
(G5) Images lacking the upwelling event
(G4) 3-day sequence of an upwelling event
(G3) Upwelling event not well-defined;
UKCI’05 5-7 September 8
Nature of the problem is Fuzzy
Unsupervised segmentation does not require training data.
Expert´s can take advantage of visualization skills and interpretability of fuzzy membership values.
Why SST Image Segmentation by Fuzzy Clustering?
Upwelling frontier
UKCI’05 5-7 September 9
Methodology
Feature Extraction
Image compression/data quantization
Fuzzy Clustering Segmentation
Accuracy Assessment
Fuzzy Clustering
VisualizationFuzzy
Partition
Pixel aggregation
Region quantization
UKCI’05 5-7 September 10
Fuzzy Clustering
k-means vs Fuzzy c-means FCM AO Algorithms
Fuzzy c-Means (FCM)
• Validity Guided (re)Clustering
• Adaptive variants
• ...
Parameters 1. sharpness exponent m, 2. number of clusters ‘c’
FCM FeaturesData representation: objects are vectors of measured values.
Clusters shape: different geometric prototypes; norms or scalar products.
Clusters size: use of adaptive distance or adaptive algorithms.
Clusters validity: optimal number of classes through validity functionals,
clusters merging/splitting or by using a hierarchical approach.
Final fuzzy partition: can be defuzzied; fuzzy partition should not be discarded
Method: fuzzy objective function minimization; two step iterativeprocedure that continually decreases the value of the objective function
FCM FeaturesData representation: objects are vectors of measured values.
Clusters shape: different geometric prototypes; norms or scalar products.
Clusters size: use of adaptive distance or adaptive algorithms.
Clusters validity: optimal number of classes through validity functionals,
clusters merging/splitting or by using a hierarchical approach.
Final fuzzy partition: can be defuzzied; fuzzy partition should not be discarded
Method: fuzzy objective function minimization; two step iterativeprocedure that continually decreases the value of the objective function
UKCI’05 5-7 September 11
Spatial Visualization of Fuzzy c-Partition
U=[uik]
max membership value
0,99 0,99 0,59 0,93 0,57 1,00 1,00 0,94 0,94 3 3 3 2 2 1 1 1 1 1
0,99 0,99 0,94 0,94 1,00 1,00 0,90 1,00 1,00 3 3 3 2 1 1 1 1 1 1
0,99 0,99 0,94 0,94 0,90 0,90 0,90 0,90 0,90 3 3 3 1 1 1 1 1 1 1
0,97 0,99 0,93 1,00 0,90 0,90 1,00 1,00 1,00 + 3 3 3 2 1 1 1 1 1 1
0,99 0,99 0,57 1,00 1,00 1,00 1,00 1,00 1,00 3 3 3 1 1 1 1 1 1 1
0,99 0,59 0,57 0,94 0,94 1,00 1,00 1,00 1,00 3 3 2 1 1 1 1 1 1 1
0,99 0,99 0,99 0,94 0,94 1,00 0,57 0,94 1,00 3 3 3 3 2 1 1 1 1 1
0,99 0,99 0,99 0,94 0,93 0,57 0,57 0,57 1,00 3 3 3 3 2 2 1 1 1 1
0,99 0,99 0,99 0,99 0,94 0,94 0,94 0,57 0,57 3 3 3 3 3 2 2 2 1 1
0,97 0,97 0,97 0,97 0,99 0,99 0,94 0,57 0,57 3 3 3 3 3 3 3 2 1 1
(uik, i)
1,1
3,32
3,31
2
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,
nu
u
u
n
iiku
x
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cncc
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xxx
UKCI’05 5-7 September 12
Ground truth imageOceanographer´s evaluation
Accuracy Assessment Assessment
cluster validation
cXB
SST image
cMR
Matching rate
cE
Fuzzy segmentation + visualization module
Image matching
c=2c=3
c=4
UKCI’05 5-7 September 13
Clustering Validation
Small values of XB for compact and well-separated clusters.
2
1 1
22
min jiji
c
i
n
kikik
n
u
cXBvv
vx
Xie-Beni (compactness and sepation) Index
Other validation indexes Partition coeficient Partition entropy Davies-Bouldi ...
Other Validation approaches Adaptive algorithms totally
unsupervised ...
UKCI’05 5-7 September 14
Consider two c-partitions P(1) , P(2) of X
1. Maximal intersection
2. Matching rate of mapping P(1) P(2)
3. Matching rate of mapping P(2) P(1)
4. Matching rate, MR
Image Matching
1. Defuzzify c-partition
2. Merge clusters
3. Measure matching rate
, 1)1( PCi 2)2( PC j
.,,2,1:max )2()1()2(max
)1( cjCCCC jij
ji
X
CC
match
c
iji
1
)2(max
)1(
12
2112 ,max matchmatchMR
Compare segmented and ground-truth images.
UKCI’05 5-7 September 15
Experimental Study
Main Goal
To identify the upwelling event using fuzzy clustering• analyse the enhancement of the upwelling areas
To evaluate the number of clusters that better identifies the phenomena in a SST image.
• validation index
To evaluate how closely the obtained segmentation reproduces the shape of the areas covered with upwelling waters.
• matching rate between fuzzy c-partition of SST and corresponding ‘ground truth’.
UKCI’05 5-7 September 16
Experimental StudyReception of AVHRR thermal infrared
Images
Selection of SST Images and provide
GT Images
Image pre-processingNormalization
Fuzzy Clustering Image Segmentation
c=2, 3,..., 4
Ground truth assessment Clustering Validation
Fuzzy partition Visualization
Oceanographer´sEvaluation
Used 16 SST images for all five groups represented
Change in the mean temperature of the main clusters is not significant beyond four clusters (i.e. c > 4).
for each c the FCM had been run from 10 distinct initialisations with sharpness parameter m= 2.0.
UKCI’05 5-7 September 17
Summary of Results
The FCM c-partitions for c=3, c=4 very closely represent the upwelling areas for all images of groups G1, G2, G3, G4
The upwelling areas correspond to the subset of clusters with the lowest mean temperatures
The segmented results for the images with no upwelling, also lack the characteristic shape of the upwelling areas
For 79% of segmented images, the FCM algorithm closely reproduces the shape of the areas covered with upwelling waters.
The matching rate MR of selected partitions with GT images varied between 90% and 97%.
The Xie-Beni index selects the correct number of clusters for 71% of images
UKCI’05 5-7 September 18
Ongoing and Future Prospects
Feature Selection o Temperature + spatial coordinates: no appearent improvmentso Temperature + Distance to coast: an option
Distinguish Upwelling from no-UpwellingAnalysing the clusters of lowest mean temperature of two
consecutive partitions Pc , Pc+1 : they splitThe behavior only occurs consistently for the days with Upwelling
Spatio-temporal Analysis of Upwelling Eventso Compare two consecutive partitions Pc , Pc+1 wrt
o Mean temperature differences (i.e. cluster prototypes)
o Change of membership assignment of points along the frontal boundaries - cut analysis
Hybridization of FCM + GA´s on cluster validation
UKCI’05 5-7 September 19
Automatic Eddy Recognition and its Spatio-Temporal Tracking through Fuzzy Clustering
Image Pre-processing to get edge enanhmento Image Filters + Normalization
Feature extraction Segmentation using fuzzy clustering
o e.g. Gath-Geva algorithm
Developing Dynamical versions of Fuzzy Clustering and their adaptation to model Eddy Tracking
Eddies are energetic swirling Eddies are energetic swirling currents found all over the oceancurrents found all over the ocean
o any temperatureany temperatureo distinct shapesdistinct shapes
UKCI’05 5-7 September 20
Remote Detection of Mediterranean Water Eddies in the Northeast Atlantic (RENA)
RENA Project
Funding
Fundação para a Ciência e Tecnologia (FCT)
European Space Agency (ESA)
UKCI’05 5-7 September 21
UKCI’05 5-7 September 22
Fuzzy c-Means Clustering
4c Membership Values
Weighted Fuzzy c-Means
22ik k iD
Ax vdistance
1mdegree offuzzification
1
1 ,c
iki
u k
constraint
Stepest descent constraint AO Algorithm
Optimization of the performance index
c
i
n
kik
mikkm
VUDuwVUJ
1 1
2
),(,min
weight ,...,2,1kw
Given c= # of groups
UKCI’05 5-7 September 23
System Arquitecture
OceanCutCookieGUI
VGC1
VGC2
VGC3
Matching rate
Fuzzy Clustering algorithms
FCM
Segmentation Module
Parameterization and Visualization Interface
Pre-processing Module Validation Module
NormalizationCompression by
histogram
Xie-Beni Index
UKCI’05 5-7 September 24
Objective
Automatic Identification of Eddy Patterns in Remote Sensed Satellite Images.
Problem Illustration
UKCI’05 5-7 September 25
Architecture
Pre-Processing
Fuzzy Clustering
Histogram
Feature Extraction Feature Selection
ANNClassifier Training
Evolutionary Algorithm
Embedded Approach
Structural (i.e. shape, orientation, size)
oceanographic properties
Segmentation Classification
Spiral Description
?
Windowing
SOM
• Law´s method• Oriented gradients
• Histogram
• Grid method
Data Quantization
Data Filtering
UKCI’05 5-7 September 26
Task: Fuzzy Segmentation
Unsupervised segmentation does not require training data
Linguistic / visualization interpretability of fuzzy membership functions by the experts.
Rule-based Segmentation Extraction of Fuzzy IF-THEN rules
UKCI’05 5-7 September 27
Why Fuzzy Image Segmentation?
Fuzzy membership functions provide natural means to model the ambiguity of patterns present in these images.
n12_01104_0602
What is a segment ?
UKCI’05 5-7 September 28
• HistogramSpatial connectedness
• Grid method
Data Quantization
Region quantization
Data points aggregation
• central value
<x, y, t, w>
<t, w>
UKCI’05 5-7 September 29
Compressed Image by histogram
UKCI’05 5-7 September 30
Fuzzy c-Means Clustering
4c Membership Values
Weighted Fuzzy c-Means
22ik k iD
Ax vdistance
1mdegree offuzzification
1
1 ,c
iki
u k
constraint
Stepest descent constraint AO Algorithm
Optimization of the performance index
c
i
n
kik
mikkm
VUDuwVUJ
1 1
2
),(,min
weight ,...,2,1kw
Given c= # of groups
UKCI’05 5-7 September 31
Fuzzy Partition Visualization
Membership matrix
Maximum membership
Threshold membership ( )
Defuzzification
[0.7 0.2 0.1] [0.7 0.0 0.0]
[0.7 0.2 0.1] [0.7 0.0 0.0]
[0.5 0.3 0.2] [0.0 0.0 0.0]
= 0.6
= 0.6
[0.7 0.2 0.1] [1.0 0.0 0.0]
Color mapping
60.21.19.
20.30.50.
55.25.20.
25.65.10.
10.70.20.
c c c 321
UKCI’05 5-7 September 32
Original image
Fuzzy Membership by thresholdingMax Fuzzy Membership Partition
Defuzzified Partition
UKCI’05 5-7 September 33
Evaluate Segmentation Quality
Goal: Accurate quantitative evaluation of image Segmentations.
• Detection Accuracy: matching between ‘reference optimal segmentation’ of ‘ ground-truth ’ eddies and segmented ones.
• Select Validity Functional
UKCI’05 5-7 September 34
Validity-Oriented Clustering
Two main problems
(P1) Objective function may not be a good estimator of “true” classification quality (as defined by the expert)
(P2) Objective function often admits many suboptimal solutions.
Strategy
algorithm that evaluates generated partitions by a ‘quality measure’
Modify bad partitions and improve their quality
UKCI’05 5-7 September 35
Ongoing Work
1. Study of techniqes to evaluate segmentation quality.
2. Segmentation from other feature vectors.
3. Development of a totaly unsupervised FCM algorithm the number of clusters is determined by a validation functional.
Validity measure based on cluster compactness and separation
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