A Novel Graph based Fuzzy Clustering Technique for ......A Novel Graph based Fuzzy Clustering Technique for Unsupervised Classi cation of Remote Sensing Images Biplab Banerjee and

A Novel Graph based Fuzzy Clustering Technique forUnsupervised Classification of Remote Sensing Images

Biplab Banerjee and B. Krishna Mohan

Satellite Image Analysis Lab,Centre of Studies in Resources Engineering,

Indian Institute of Technology Bombay,biplab.banerjee,[email protected]

The work was partially carried out when the first author was an intern at the RemoteSensing Lab, University of Trento, Italy

December 10, 2014

Banerjee and Mohan (CSRE,IIT Bombay) Unsupervised image classification December 10, 2014 1 / 18

Overview

1 Background

2 Problem definition

3 Proposed methodology

4 Experimental results

5 Conclusion


Background perspective

Image segmentation refers to the problem of grouping the pixels of animage into mutually exclusive regions.

Clustering based methods are very popular in segmenting remotesensing images [1].

pixel based segmentation → Object based segmentation.

Graph based clustering techniques are simple, robust, preserves thespatial topology [2].

Minimum spanning tree provides a simple clustering framework inO(K ) for producing K clusters.

Simple clustering techniques like K -means, fuzzy c-means can beused with graph topology for faster convergence [3].

For Fuzzy c-means, the local means may converge to the global meandue to the weighted averaging.


Clustering as a self learning problem

Maximum likelihood classifier, X = x1,1, x1,2, . . . xR,S,Ω = ω1, ω2, . . . , ωN

xr ,c ∈ ωk ⇔ argmaxωl∈Ω

(P(ωl )p(xr ,c |ωl )) (1)

According to the law of large numbers, the land-cover classes areGaussian distributed.

We need to estimate mean, standard deviation and the priorprobability for each class.

Some training samples per class/cluster are needed for the estimation.

A hierarchy of clustering techniques are applied to the image toobtain those training samples.


Broad overview


MST (T ) based over-clustering of image graph G

MST based clustering

Sort the edges of T in descending order of the corresponding edgeweights.

Delete top KO edges. It will generate KO + 1 sub-trees where thepixels (nodes) of each sub-tree correspond to a cluster.

X is now over-segmented into KO clusters. Several objects of eachcluster are likely to be present in the over-segmented image.

Let us consider Rover = R1,R2, . . . ,RMto represent the regionsfound from this step.


Proposed graph based fuzzy clustering

GR is a complete graph with regions as nodes, UN×M = αk,i(1 ≤ k ≤ N , 1 ≤ i ≤ M), µi is the mean spectral value of Ri

Ck =

M∑i=1αm

kiµi

M∑i=1αm

ki

(2)

αki =1

M∑j=1

( ||µi−Ck ||||µi−Cj || )

2m−1

(3)

Our modification in this respect

Instead of considering the L2 norm for ||µi − Ck || in the Euclideanspace, the smallest distance between two nodes in GR is considered.

Dijkstra’s shortest path algorithm is used for this purpose.


Proposed graph based fuzzy clustering

Convergence criterion (F )

Sum of the mean edge weights of every cluster (F1).

Sum of mean weights of the edges spanning different clusters (F2).

F =F1

F2(4)


Estimate of the initial cluster parameters and parameterupdate by EM

From each cluster, pixels lying within the δ% of the maximum pairwisedistance within the cluster is considered to form the training set.

Parameter update using EM

P l+1i (ωi ) =

1

R × S

∑xr,s∈X

P l (ωi )pl (xr ,s |ωi )

P l (xr ,s)(5)

µl+1i =

∑xr,s∈X

P l (ωi )pl (xr,s |ωi )P l (xr,s )

xr ,s∑xr,s∈X

P l (ωi )pk (xr,s |ωi )P l (xr,s )

(6)

Σl+1i =

∑xr,s∈X

P l (ωi )pl (xr,s |ωi )(xr,s−µl+1i )2

Pl (xr,s )∑xr,s∈X

P l (ωi )pl (xr,s |ωi )P l (xr,s )

(7)


Sardinia multi-spectral LandSat-5 image taken on Sept’95

11Ack: Prof Lorenzo Bruzzone, University of Trento, for sharing this data.


Scatter plot of the land-cover classes (2nd and 5th

dimensions)


Comparison of classification accuracy

Cluster (Underlying Land Cover) # of samples FCM based clustering (%) Hierarchical clustering (%) Proposed method(%)

Cluster1 (Pasture) 470 44.12 45.37 67.61

Cluster2 (Forest) 128 93.71 93.78 93.08

Cluster3 (Urban) 408 92.43 92.64 90.69

Cluster4 (Water) 804 100.00 100.00 100.00

Cluster5 (Vineyard) 179 60.68 58.54 68.31

Cluster6 (Burned area) 176 96.65 95.74 95.65

Overall 2165 72.85 74.61 83.32

The classification performance of a supervised ML classifier trained onmanually selected set of samples (87.45%).


The effect of the graph based FCM over traditional FCMwith random centroid initialization

Figure: The FCC image of the IRS-1B LISS III image of Mumbai, India



Figure: The scatter plot of the test samples with reference labels for the IRS data



Figure: The scatter plot of the test samples after the proposed graph-fuzzyclustering for the IRS data (around 50 iterations)



Figure: The scatter plot of the test samples after the FCM clustering for the IRSdata (around 115 iterations)


Conclusion

A novel multi-level unsupervised classification of remote sensingimages is proposed.

The proposed graph-fuzzy clustering is consistent, has betterconvergence rate than its traditional counterpart.

The proposed framework identifies a set of reliable samples perclusters that can be used as the prospective training data for them.

The future endeavor is based on selecting the number of clusterautomatically from the graph-fuzzy model.

Semi-supervised clustering and Semi-supervised clustering.


The End


T. Blaschke, “Object based image analysis for remote sensing,” ISPRSjournal of photogrammetry and remote sensing, vol. 65, no. 1, pp.2–16, 2010.

P. F. Felzenszwalb and D. P. Huttenlocher, “Efficient graph-basedimage segmentation,” International Journal of Computer Vision,vol. 59, no. 2, pp. 167–181, 2004.

L. Galluccio, O. Michel, P. Comon, and A. O. Hero III, “Graph basedk-means clustering,” Signal Processing, vol. 92, no. 9, pp. 1970–1984,2012.


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A Novel Graph based Fuzzy Clustering Technique for ......A Novel Graph based Fuzzy Clustering Technique for Unsupervised Classi cation of Remote Sensing Images Biplab Banerjee and