ukci05 5-7 september 1 applicability of fuzzy clustering for the identification of upwelling areas...

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

1

,

nu

u

u

n

iiku

x

x

x

cncc

n

n

uuu

uuu

c

21

11211

21

1

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