Applicability of Fuzzy Clustering for the Identification of Upwelling Areas on Sea Surface Temperature Images

1. Centro de Inteligência Artificial Dep. Informática Faculdade de Ciências e Tecnologia Universidade Nova de Lisboa PORTUGAL 2Instituto de Oceanografia Faculdade de Ciências Universidade de Lisboa, PORTUGAL Applicability of Fuzzy Clustering for theIdentification of Upwelling Areas on Sea Surface Temperature Images Susana Nascimento, Fátima M. Sousa, Hugo Casimiro Dmitri Boutov 1

2. Overview • Introduction to the problem of Upwelling Recognition • Sea Surface Temperature (SST) Image Segmentation by Fuzzy Partitional Clustering • Methodology • Experimental Study • Ongoing Work

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

4. Upwelling Event in the Coastal Waters of Portugal Ground truth image SST image of an upwelling event obtained on 04AUG1998 (n14_98216_0422_sst); (b) upwelling boundary manually contoured; (c) upwelling areas automatically retrieved.

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.

6. 720  400 matrix with each entry a temperature value in degrees Celsius with 1Km2 spatial resolution. 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 X Y

7. (G2)images where upwelling is evident but there are areas with no temperature information (covered with clouds or noise); (G1) well-defined upwelling events (G3)Upwelling event not well-defined; (G5) Images lacking the upwelling event (G4)3-day sequence of an upwelling event Distinct Groups of Images • SST images divided into 5 groups according to different “upwelling situations”.

8. Why SST Image Segmentation by Fuzzy Clustering? • 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. Upwelling frontier

9. Region quantization Pixel aggregation Feature Extraction Visualization Fuzzy Partition Accuracy Assessment Fuzzy Clustering Methodology Image compression/data quantization Fuzzy ClusteringSegmentation

10. k-means vs Fuzzy c-means Fuzzy Clustering FCM AO Algorithms • Fuzzy c-Means (FCM) • Validity Guided (re)Clustering • Adaptive variants • ... • Parameters • 1. sharpness exponent m, • 2. number of clusters ‘c’ FCM Features Data 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 iterative procedure that continually decreases the value of the objective function

11. Spatial Visualization of Fuzzy c-Partition (uik, i) U=[uik] max membership value

12. c=2 c=3  c=4 cE Matching rate cMR SST image Accuracy Assessment Fuzzy segmentation + visualization module Ground truth image Oceanographer´s evaluation cluster validation Image matching cXB

13. Clustering Validation • Xie-Beni (compactness and sepation) Index • Other validation indexes • Partition coeficient • Partition entropy • Davies-Bouldi • ... • Other Validation approaches • Adaptive algorithms totally unsupervised • ... Small values of XB for compact and well-separated clusters.

14. Image Matching • Compare segmented and ground-truth images. • Consider two c-partitions P(1) , P(2) of X • Maximal intersection • Matching rate of mapping P(1) P(2) • Matching rate of mapping P(2) P(1) • Matching rate, MR 1. Defuzzify c-partition 3. Measure matching rate 2. Merge clusters

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 theareas covered with upwelling waters. matching rate between fuzzy c-partition of SST and corresponding ‘ground truth’.

16. Reception of AVHRR thermal infrared Images • Image pre-processing • Normalization Fuzzy Clustering Image Segmentation c=2, 3,..., 4 Fuzzy partition Visualization Oceanographer´s Evaluation Clustering Validation Experimental Study • 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 cthe FCM had been run from 10 distinct initialisations with sharpness parameterm= 2.0. Selection of SST Images and provide GT Images Ground truth assessment

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 theareas 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

18. Ongoing and Future Prospects • Feature Selection • Temperature + spatial coordinates: no appearent improvments • Temperature + Distance to coast: an option • Distinguish Upwelling from no-Upwelling Analysing the clusters of lowest mean temperature of two consecutive partitions Pc , Pc+1: they split The behavior only occurs consistently for the days with Upwelling • Spatio-temporal Analysis of Upwelling Events • Compare two consecutive partitions Pc , Pc+1wrt • Mean temperature differences (i.e. cluster prototypes) • Change of membership assignment of points along the frontal boundaries • - cut analysis • Hybridization of FCM + GA´s on cluster validation

19. Automatic Eddy Recognition and its Spatio-Temporal Tracking through Fuzzy Clustering Eddies are energetic swirling currents found all over the ocean • any temperature • distinct shapes • Image Pre-processing to get edge enanhment • Image Filters + Normalization • Feature extraction • Segmentation using fuzzy clustering • e.g. Gath-Geva algorithm • Developing Dynamical versions of Fuzzy Clustering and their adaptation to model Eddy Tracking

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)

22. Fuzzy c-Means Clustering • Weighted Fuzzy c-Means • Optimization of the performance index Given c= # of groups constraint distance Membership Values degree of fuzzification weight Stepest descent constraint AO Algorithm

23. System Arquitecture

24. Objective • Automatic Identification of Eddy Patterns in Remote Sensed Satellite Images. • Problem Illustration

25. Segmentation Classification Pre-Processing Windowing Data Filtering Feature Selection • Law´s method • Oriented gradients Feature Extraction Histogram Structural (i.e. shape, orientation, size) oceanographic properties Data Quantization ANN Classifier Training SOM • Histogram • Grid method Fuzzy Clustering • Evolutionary Algorithm • Embedded Approach ? Spiral Description Architecture

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

27. n12_01104_0602 Why Fuzzy Image Segmentation? • Fuzzy membership functions provide natural means to model the ambiguity of patterns present in these images. • What is a segment ?

28. Data Quantization Region quantization Data points aggregation • Histogram Spatial connectedness • Grid method • central value <x, y, t, w> <t, w>

29. Compressed Image by histogram

30. Fuzzy c-Means Clustering • Weighted Fuzzy c-Means • Optimization of the performance index Given c= # of groups constraint distance Membership Values degree of fuzzification weight Stepest descent constraint AO Algorithm

31. Maximum membership • Threshold membership (  ) • Defuzzification  = 0.6  = 0.6 [0.7 0.2 0.1] [0.7 0.0 0.0] [0.5 0.3 0.2] [0.0 0.0 0.0] [0.7 0.2 0.1] [0.7 0.0 0.0] [0.7 0.2 0.1] [1.0 0.0 0.0] Fuzzy Partition Visualization • Membership matrix Color mapping

32. Original image Defuzzified Partition Max Fuzzy Membership Partition Fuzzy Membership by thresholding

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

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

35. Ongoing Work • Study of techniqes to evaluate segmentation quality. • Segmentation from other feature vectors. • 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