Efficient Parallel Algorithm For Pix

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Beleghata Canal is shown as another thin line stretching between the top ... PKM algorithm fails to classify the Talis Nala and Beleghata Canal properly.
Editorial Manager(tm) for Geoinformatica Manuscript Draft Manuscript Number: GEIN414 Title: Efficient Parallel Algorithm For Pixel Classification In Remote Sensing Imagery Article Type: Manuscript Keywords: Pixel Classification; Distributed Algorithm; Remote Sensing Imagery; Symmetry Detection; Point-Symmetry Based Distance Measure. Corresponding Author: Dr. Ujjwal Maulik, SMIEEE, Ph D Corresponding Author's Institution: Jadavpur University First Author: Ujjwal Maulik, SMIEEE, Ph D Order of Authors: Ujjwal Maulik, SMIEEE, Ph D; Anasua Sarkar, Doctoral student

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Efficient Parallel Algorithm For Pixel Classification In Remote Sensing Imagery Ujjwal Maulik · Anasua Sarkar

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Abstract An important approach for image classification is the clustering of pixels in the spectral domain. Fast detection of different land cover regions or clusters of arbitrarily varying shapes and sizes in satellite images presents a challenging task. In this article, an efficient scalable parallel clustering technique of multi-spectral remote sensing imagery using a recently developed point symmetry-based distance norm is proposed. The proposed distributed computing time efficient point symmetry based K-Means technique is able to correctly identify presence of overlapping clusters of any arbitrary shape and size, whether they are intra-symmetrical or inter-symmetrical in nature. A Kd-tree based approximate nearest neighbor searching technique is used as a speedup strategy for computing the point symmetry based distance. Superiority of this new parallel implementation with the novel two-phase speedup strategy over existing parallel K-Means clustering algorithm, is demonstrated both quantitatively and in computing time, on two SPOT and Indian Remote Sensing satellite images, as even K-Means algorithm fails to detect the symmetry in clusters. Different land cover regions, classified by the algorithms for both images, are also compared with the available ground truth information. The statistical analysis is also performed to establish its significance to classify both satellite images and numeric remote sensing data sets, described in terms of feature vectors. Keywords Pixel Classification · Distributed Algorithm · Remote Sensing Imagery · Symmetry Detection · Point-Symmetry Based Distance Measure

1 Introduction In the realm of the remote sensing imagery, the pixel classification of a particular land cover region is often posed as clustering in the intensity space of multi-spectral satellite U. Maulik Senior Member, IEEE,Dept of Computer Sc. and Engg, Jadavpur University, Kolkata-700032, India E-mail: [email protected] A. Sarkar LaBRI, University of Bordeaux1, Talence-33400, France E-mail: [email protected]

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images [8]. However some homogeneous regions (like bridges and roads) occupy only a few pixels, while the neighboring regions are significantly large. Thus detection of overlapping clusters of such arbitrary shapes and sizes presents an important challenge in remote sensing pixel classification. Clustering is an unsupervised pattern classification method based on maximum intra-class and minimum inter-class similarity. K-Means [10] is a conventional partitional clustering method with heuristic global optimization criteria. Given n points in d-dimensional space Rd , the problem is to determine a set of k centroids(z1 , z2 , · · · , zK ) for disjoint clusters C1 , C2 , · · ·P , CK , P to minimize the mean squared distance norm in K 2 the crisp partitioning metric: i=1 xj ∈Ci D (xj , zi ), where D(xj , zi ) denotes Euclidean distance of pattern xj from centroid zi . Yet K-Means algorithm fails to detect the symmetry in clusters. Symmetry is a pre-attentive inherent feature to recognize and reconstruct shapes and objects, even in the remote sensing multi-spectral domain. Therefore Bandyopadhyay et. al [3, 4] recently proposed dps , point-symmetry(P S) based proximity norm to detect any convex/non-convex shaped overlapping intra- and inter-symmetrical clusters properly. Point Symmetry-Based K-Means(Sym) method is used for high-resolution satellite image pixel classification with high-throughput spectral data. Therefore a faster pixel classification method detecting point-symmetry is required to analyze them.Kanungo et. al [12] defined a faster non-parallel K-Means to speedup computing, while other distributed approaches were also proposed in different clustering fields [11, 19, 20]. Therefore a two-phase speedup strategy for Sym is implemented in this article, which combination is itself unique in nature in this application domain. In the first speedup phase, an efficient parallel Sym (P arSym) algorithm has been implemented using distributed master-slave paradigm. Subsequently a Kd − tree [5] based data structure is used for nearest neighbor searching to compute P S distance as the second speedup strategy. P arSym clusters remote sensing data effectively, for both set of labeled feature vectors and satellite images with a scalable time-efficiency in its linear relative speedup and time gain %T G over sequential version Sym in Section 3.3. The classification results of a SP OT (Systems Probataire d’Observation de la Terre) image of a part of Kolkata and an IRS (Indian Remote Sensing) satellite image of a part of Mumbai are then compared with available ground truth knowledge qualitatively and also evaluated quantitatively for three cluster validity indices which shows P arSym is superior over well-known parallel K-Means(P KM ) algorithm. Finally statistical tests demonstrate the significance of P arSym over P KM algorithm. 2 Clustering Using Point Symmetry In this section the P S-based non-metric distance norm [3] used in Sym algorithm and next the newly proposed parallel version of Sym, named P arSym algorithm has been discussed along with its complexity analysis. Existing norms for proximity of points like Euclidean, Pearson correlation, Spearman distances etc. can not detect point symmetry. To detect both intra- and intersymmetrical clusters properly, [3, 4] proposed a point symmetry(P S)-based distance measure between any pattern xi , i = 1, 2, ..., N and any reference centroid ck , k = 1, 2, ..., K is: (d + d2 ) × de (xi , ck ) dps (xi , ck ) = 1 (1) 2

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,where dps (xi , ck ) is P S distance and de (xi , ck ) is Euclidean distance between xi and ck . Let x∗i = (2 ∗ ck − xi ) be the symmetrical point of xi , then d1 and d2 represent Euclidean distances between x∗i and its first and second nearest neighbors.

2.1 Kd-tree Based Nearest Neighbor Computation K−d tree is a space-partitioning data structure for organizing points in a K-dimensional space, considering only splitting planes perpendicular to the coordinate axes. Approximate Nearest Neighbor(AN N ) is a library in C + + [16], implementing Kd − tree data structure for this in arbitrarily high dimension. To speed up the computation intensive search of d1 and d2 - the first two nearest neighbors of x∗i for computing dps (xi , ck ) in Eq. 1, AN N computes k = 2-nearest neighbors for a query point q = x∗i using an array of distances dists with a maximum approximation upper bound set to 0 and stores their indices in nnidx array.

2.2 Parallel Clustering Using Point Symmetry Based on P Sdistance norm in Eq. 1, a new Parallel Point Symmetry-Based K-Means (P arSym) clustering method is proposed here. 2.2.1 Algorithms P arSym algorithm have been implemented in a distributed master-slave paradigm. Among M distributed nodes, master M0 ensures load balancing and other m = M − 1 nodes act as slaves. The P arSym algorithm in Fig. 1 composed of 3 phases - initial horizontal partitioning of universal dataset with N elements and C attributes, parallely-computed local centroids updation using K-Means method and parallel point N symmetry-based fine-tuning. The horizontally partitioned data set becomes a m ×C matrix. After initial random cluster assignment, each slave performs centroids updation on local partitioned data and returns its local assignment to M0 . Subsequently M0 merges them into global cluster assignment, using the union-find data structure with an average runtime of inverse Ackermann’s function, which will be redistributed to continue optimization. The final fine-tuning phase utilizes P S distance in Eq. 1. Each point is reassigned to a new cluster only if its symmetrical point resides inside that cluster and the minimal P S distance between the point and its new cluster centroid, is greater than a user-specified threshold value θ, which is computed as the maximum nearest neighbor distance [3, 4]. The nearest neighbor distances d1 and d2 are parallely computed first using AN N library. Then P S distance based cluster assignment corrections of local points in m slave nodes are computed and finally collected in M0 . This leads to convergence to stop execution. 2.2.2 Complexity Analysis The time complexity of P arSym algorithm, as illustrated in Figure 1, is analyzed below:

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4 Step 1 : Initialization on master node M0 : 1.1: Horizontal partitioning of N elements ). to m = M − 1 slave nodes: SCAT T ER(GLOBAL DAT A, LOCAL DAT A, N m 1.2: Assign an element xi ∈ Cluster Ck ∀i = 1, · · · , N such that |Ck | ≥ 1 ∀k = 1, · · · , K. Step 2 : Parallel computation of centroids towards convergence : 2.1: In M0 : BROADCAST (GLOBAL CLU ST ERS, N ). 2.2: On m slave nodes : Compute centroids ck ∀k = 1, · · · , K and execute 1 pass of K −M eans method on LOCAL DAT A to update ck . N ). 2.3: In M0 : ALL GAT HER(LOCAL CLU ST ERS, GLOBAL CLU ST ERS, m If centroids ck ∀k = 1, · · · , K converge then go to Step 3 else go to Step 2. Step 3 : Parallel fine-tuning phase : Step 3.1 : Parallel θ computation with P S distance : 3.1.1: In M0 : ALL GAT HER(LOCAL θ, GLOBAL θ, m). 3.1.2: Compute θ = Maximum nearest neighbor distance ∀i = 1, · · · , N using GLOBAL θ and BROADCAST (θ, 1). Step 3.2 : Parallel point symmetry-based centroids updation : N 3.2.1: On m slave nodes : For xi , ∀i = 1, · · · , m compute d1 , d2 using Kd − tree data structure and then minimum-value criterion k ∗ = Arg mink=1,···,K dps (xi , ck ), where dps (xi , ck ) is computed using Eq 1. If dps (xi , ck ∗ ) < θ and xi 6∈ Ck∗ , then assign xi ∈ Ck∗ . else compute k ∗ = Arg mink=1,···,K de (xi , ck ), where de = ||xi − ck || and assign xi ∈ Ck∗ . 3.2.2: In M0 : ALL GAT HER(LOCAL CHAN GES, GLOBAL CHAN P GES). i∈S (t)

Xi

k , ∀k = Compute new P S-distance corrected centroids : ck (t + 1) = |Sk (t)| 1, · · · , K,where Sk (t) = {xi |xi ∈ Ck at time t}. Step 3.3 : Continuation : In M0 , if no pattern changes its cluster, then stop, else go to Step 3.

Fig. 1: Steps of Parallel Sym (P arSym) Algorithm

1. ‘Initialization’ - The time complexity is given by: Tpartition = Constant 2. ‘Parallel centroids computation’ - If maxrepeat = number of repetitions to N elements, time complexity is: Tcluster = converge K centroids on m slaves for m N N O( m ∗ K + K) ∗ maxrepeat ≃ O( m ∗ K), N ≫ maxrepeat. 3. ‘Fine-tuning phase’ (a) ‘Parallel θ computation’ - The parallel computation cost for θ with K−d tree based nearest neighbor search is: Tθ = O(log N m ). (b) ‘Parallel point symmetry-based centroids updation’ - If repeat sym = number of repetitions to converge to parallely compute d1 , d2 and to compute N centroids, the time complexity is: TP S = O(( N m ∗ K ∗ log m ) ∗ repeat sym) + N N O(K) ≃ O( m ∗ K ∗ log m ), N ≫ repeat sym. So total complexity for the fine-tuning phase is : Tf ine tuning = Tθ +TP S = O(log N m )+ N N N ∗ K ∗ log ) ≃ O( ∗ K ∗ log ). Therefore total time complexity of P arSym O( N m m m m N algorithm becomes: TP AR = Tpartition + Tcluster + Tf ine tuning ≃ O( N m ∗ K) + O( m ∗ N N N K ∗ log m ) ≃ O( m ∗ K ∗ log m ). The sequential time complexities of P KM [21] and Sym [3] algorithms are shown in Table 1. The parallel time complexity of P arSym N is O( N m ∗ K ∗ log m ), which theoretically yields a linear speedup curve. In P arSym the communication cost with SCAT T ER, BROADCAST and ALL GAT HER collective operations incurs O(N ∗ log m). If T1 and TP show the execution times on one and P processors of datasizes N and N ∗ P respectively, then their ratio is called Scaleup [13].Table 1 shows the scaleup comparisons for both P KM and P arSym algorithms with their criteria to reach the ideal ratio 1.

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Table 1: Computation Costs and Scaleup Comparisons Method Computation TimeCommunication Time K − M eans O(N ∗ K 2 ) 2

) O( N∗K m

P KM Sym P arSym

Scaleup O(N∗K 2 )

O(K 2 )

O(N 2 ∗ K)

-

N O( N ∗ K ∗ log m ) m

O(N ∗ logm)

Criterion for Scaleup ≥ 1 N ≫ K2

2

)+O(K 2 ) O( N ∗K m

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O(N 2 ∗K) N ∗K∗log N )+O(N∗logm) O( m m

N N ≫ log m + logm

3 Application To Pixel Classification The parallel P arSym algorithm is implemented using Message Passing Interface(M P I) [18] on IBM p690 Regatta Server, with 16 Power 4+ processors[1.3 GHz clock speed]. All execution times are obtained through M P I W time() function in seconds in Section 3.3. To compare parallel K-Means(P KM ) [21] method is also implemented. Jm [6], XB [22] and I [14] validity indices evaluate the effectiveness of P arSym over P KM quantitatively. The efficiency of P arSym is also verified visually from the clustered images considering ground truth information of land cover areas.

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Fig. 2: Scatter Plots of Numneric Remote Sensing Data Sets - (a) IRS image of Mumbai having 198 points and 6 classes and (b) SP OT image of Kolkata having 932 points and 7 classes.

3.1 Classification Of Numeric Remote Sensing Data Two numeric satellite image data obtained from SP OT (part of Kolkata) and IRS (part of Mumbai) have been classified here. A numeric image data contains some image pixels where land cover types denote class labels and band intensity values serve as feature values. Abscence of pixel locations looses the spatial information. 1. ‘SP OT with 932 samples’ This is a 3 channel data set [2] (green, red, near infrared (N IR) bands) with 932 samples of 7 classes. Fig. 2b) shows the scatter plot with complex overlapping clusters.

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Table 2: Validity Indices Values of a) Classified Numeric Remote Sensing Data Sets and b)Classified Satellite Images Provided by P arSym and P KM Algorithms Index Jm XB I Index Jm XB I

IRS with 198 samples SP OT with 932 samples P KM P arSym P KM P arSym 410.653 404.282 1106.428 1105.526 51.91 38.23 225.277 221.765 371.023 426.179 14.598 15.132 (a) Kolkata SP OT Mumbai IRS P KM P arSym P KM P arSym 717054.109 635569.295 607753.674 492319.115 12432.671 11169.933 18522.469 16931.822 487.237 514.247 280.637 380.193 (b)

2. ‘IRS with 198 samples’ This data set has 198 samples and 3 bands:green, red and near infrared (N IR) [2]. Fig. 2a) shows the scatter plot of this data with overlapping clusters for 6 classes. Table 2a) presents the performance of both P KM and P arSym algorithms on SP OT and IRS image datasets respectively for minimizing Jm , minimizing XB and maximizing I cluster validity indices. For SP OT numeric image of Kolkata, Jm , XB and I indices values produced by P KM and P arSym algorithms are (1106.428, 225.277, 14.598) and (1105.526, 221.765, 15.132) respectively. Similarly for numeric Mumbai IRS image data, P KM and P arSym algorithms provide respectively (410.653, 51.91, 371.023) and (404.282, 38.23, 426.179) values for Jm , XB and I indices. Therefore it has been observed that P arSym algorithm is able to provide better scores than P KM for both SP OT and IRS numeric remote sensing data sets for all cluster indiaces.

3.2 Satellite Image Pixel Classification This section provides the descriptions of two satellite images(size 512X512) and the experimental results obtained by both P KM and P arSym algorithms on them. 3.2.1 SP OT image of Kolkata The SP OT image of Kolkata [2] is available in three bands viz. green, red and near infrared bands in the multispectral mode with distribution of the pixels in the feature space as shown in Figure 3a). Figure 3b) shows the original SP OT image of Kolkata in the near infrared band with histogram equalization with 7 classes: turbid water (TW), pond water (PW), concrete (Concr.), vegetarian (Veg), habitation (Hab), open space (OS), and roads (including bridges)(B/R). The river Hooghly cuts through the image, with two distinct black patches of water bodies below it on left bank, one namely Khidirpur Dock(right). In its right side the very thin line, between the river and the bottom edge of image, is a canal called the Talis Nala. Beleghata Canal is shown as another thin line stretching between the top edge and the middle of left edge. Figures 3c) and 3d) respectively show the classified SP OT images of Kolkata using P KM and P arSym algorithms for K = 7. In Figure ?? P KM algorithm fails to classify the Talis Nala and Beleghata Canal properly. However

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Fig. 3: Pixel Classification on SP OT image of Kolkata.(a) Data distribution of Kolkata SP OT image in the Feature Space.(b) Original Kolkata SP OT image in the near infrared band with histogram equalization. Classified Kolkata images (with K = 7) obtained by (c)P KM and (d)P arSym algorithms respectively.

P arSym clustering is able to separate almost all the regions well. Both Talis Nala and Beleghata Canal are rightly classified into T W class. Moreover P KM wrongly detects Khidirpur Dockyard in P W and Concr classes, where P arSym succeeds to detect it properly. The quantitative evaluation of the segmented Kolkata SP OT image by P KM and P arSym algorithms is shown in Table 2b) for Jm , XB and I indices. P arSym provides better classification with smaller XB = 11169.933 value, as P KM provides XB = 12432.671. Similarly minimized Jm = 635569.674 reported for P arSym is better than Jm = 717054.109 provided by P KM . Interestingly for maximized I index, P arSym produces larger value of I = 514.247, while P KM produces smaller value of I = 487.237. All these values show the superiority of P arSym algorithm over P KM in goodness of the clustering solutions. 3.2.2 IRS image of Mumbai The IRS image of Mumbai [15] was obtained using the Linear Imaging Self-Scanning System II sensor, available in four bands viz. blue, green, red and near infrared bands. The distribution of pixels in first 3 feature space of this image is shown in Figure 4a). Figure 4b) shows the original IRS image of Mumbai with histogram equal-

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Fig. 4: Pixel Classification on IRS image of Mumbai. (a) Data distribution of IRS image of Mumbai in the Feature Space. (b) Original IRS image of Mumbai in the near infrared band with histogram equalization. Classified Mumbai images obtained by (c) P KM and (d) P arSym algorithms respectively.

ization. According to the available ground knowledge [15], there are 7 classes - concrete(Concr), open spaces(OS1,OS2), vegetation(Veg), habitation(Hab) and turbid water(TW1,TW2). The city is surrounded on 3 sides by the Arabian sea. Near the bottom right corner, there are several islands including Elephanta island. The dockyard is situated on south-east shown as three fingers. The segmented Mumbai IRS images obtained by P KM and P arSym algorithms respectively are shown in Figures 4c) and 4d)(K = 7). In Figure 4c), P KM partitions the Arabian sea into three regions, while in Figure 4d) P arSym classifies it into two distinguishable classes T W 1 and T W 2 with different spectral properties. The islands and dockyard have been correctly identified by P arSym algorithm with a high proportion of OS, V eg and Hab classes as expected. The southern heavily industrialized Mumbai has been classified primarily as belonging to Hab and Concr classes. These indicate that P arSym algorithm detects the overlapping arbiraty shaped regions significantly better than P KM . Table 2b) shows the quantitative evaluation of Jm , XB and I indices for the classified Mumbai IRS images provided by P KM and P arSym algorithms. As shown, P KM provides Jm = 607753.674 value, while P arSym provides smaller Jm = 492319.115. Similarly P arSym provides smaller XB = 16931.822 compared to XB = 18522.469 for P KM . For maximizing I index, P arSym also provides larger I = 380.193 value than

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Table 3: Time Comparisons of a) SP OT (With 932 Samples) And IRS (With 128 Samples) Images and b)Kolkata SP OT and Mumbai IRS Images For P arSym Algorithm Data

Methods P

Execution Time S TG PartitionClusterFine-tuningTotal % Time Time Time Time IRS Sequential 1 – 0.009 0.092 0.1011.00 0.00 198 samples Parallel 2 0.003 0.008 0.067 0.0781.2922.41 4 0.003 0.008 0.031 0.0412.4759.55 8 0.002 0.007 0.021 0.0293.4270.79 12 0.002 0.006 0.014 0.0224.5578.01 SP OT Sequential 1 – 0.078 0.339 0.4171.00 0.00 932 samples Parallel 2 0.011 0.067 0.263 0.3401.2318.46 4 0.009 0.058 0.062 0.1283.2569.22 8 0.008 0.054 0.038 0.1004.1776.03 12 0.006 0.050 0.018 0.0755.5982.13 (a) Data Methods P Execution Time S TG PartitionClusterFine-tuning Total % Time Time Time Time Kolkata Sequential 1 – 46.006 1315.346 1361.3811.00 0.00 SP OT Parallel 2 2.717 36.842 971.392 1010.9511.3525.74 4 2.675 34.662 567.951 605.288 2.2555.54 8 2.652 31.285 255.531 289.468 4.7078.74 12 2.637 22.368 207.404 232.409 5.8682.93 MumbaiSequential 1 – 47.443 1517.187 1564.6491.00 0.00 IRS Parallel 2 3.150 33.514 1095.405 1132.0691.3827.65 4 3.057 30.383 581.149 614.589 2.5560.72 8 3.053 28.304 284.585 315.942 4.9579.81 12 2.964 23.979 225.361 252.304 6.2083.87 (b)

I = 280.637 provided by P KM . Therefore from all results it is evident that P arSym is quantitatively superior than P KM even in proper parallel pixel classification of the satellite imagery.

3.3 Timing Analysis The experimental results of P arSym algorithm varying the number of processors are provided for remote sensing images and numerical data on Regatta server. Tables 3a)3b) report the runtimes of sequential and parallel version of Sym algorithm, including the partitioning, clustering and fine-tuning phases of the algorithm. The speedup S = T ime(p=1) , is computed to show the scalability of parallel execution on each data set. T ime(p=P ) T ime(p=1)−T ime(p=P )

∗ 100 shows the percentage of time gain with Similarly %T G = T ime(p=P ) the increase in the number of processors. The parallel runtimes of the algorithm is reduced further with the increase in number of processors until the communication overhead arises. Table 3a) shows the speedup ranging from 1.29 to 4.55 and 1.23 to 5.59 respectively for the numerical IRS − 198 and SP OT − 932 data sets, which is superior than the speedup range from 1.159 to 3.804 and from 1.19 to 4.592 respectively for P KM algorithm in Table 5. Similarly, Table 3b) provides the execution times for satellite image data. P arSym algorithm is able to achieve the speedup ranging from

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Table 4: Speedup Comparisons of P KM Algorithm on Different Remote Sensing Data Data Numerical Data Satellite Images

IRS 198 SP OT 932 Kolkata SP OT Mumbai IRS 7 Speedup ( Time(1) / Time(P) )

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P=1 1.00 1.00 1.00 1.00

P=2 1.159 1.191 1.329 1.173

Processors P=4 P=8 1.470 2.459 2.183 3.431 2.065 3.205 1.894 3.042

P=12 3.804 4.592 4.608 4.541

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SPOT−932 SPOT−KolkataIRS−Mumbai Data Sets

Fig. 5: Scalability of P arSym algorithm with varying number of processors and increasing data sizes

1.35 to 5.86 and 1.38 to 6.20 respectively for Kolkata SP OT and Mumbai IRS images. The %T G for this P arSym implementation, is in the range of 25.74% to 82.93% for Kolkata SP OT image, while for the Mumbai IRS image, it is ranging from 27.65% to 83.87%. This shows an increasing order of speedup and %T G with increasing of the number of processors, which proves the necessity of parallelization for the pointsymmetry based clustering on those high resolution multi-spectral satellite image data. Figures 6a), 6b), 6c) and 6d) show the improvement in the runtimes for P arSym algorithm on two numerical data and two satellite image data respectively, as P is increased from 2 to 12 while keeping the datasize constant. The speedup of P arSym algorithm on each image data in bar chart in Figure 5 shows higher scalability is with increase in the number of processors. The large image data Mumbai IRS (512X512 pixels), shows the highest scalability of 6.20 times with P = 12, forming a linear speedup curve with other timing results in spite of the communication overhead. Similar results for other data sets also show that P arSym algorithm succeeds in the scalability of parallel execution times.

3.4 Test for Statistical Significance A non-parametric statistical significance test called W ilcoxon′ s rank sum for independent samples has been conducted at 5% significance level [9]. Two groups have been created with the performance scores XB produced by 10 consecutive runs of both P KM and P arSym algorithms on each data set. From the medians of each group on all datasets in Table 5a), it is observed that P arSym provides better median values than

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Fig. 6: Timing analysis of P arSym algorithm. Performance with varying datasizes and increasing number of processors for(a) SP OT − 932,(b) IRS − 198,(c) KolkataSP OT and (d)M umbaiIRS data sets.

Table 5: a) Median Values of Performance Parameter XB over 10 Consecutive Runs on Different Algorithms and b) P -values Produced by Rank Sum while Comparing P arSym with P KM Algorithm Data

Median P KM 85.792 960.104 28063.000 61655.000

Numerical IRS 198 Data SP OT 932 Satellite Kolkata SP OT Images Mumbai IRS (a)

Values P arSym 67.742 888.346 11170.000 18522.000

Data H Numerical IRS 198 1 Data SP OT 932 1 Satellite Kolkata SP OT 1 Images Mumbai IRS 1 (b)

P-values P 5.50E-4 1.79E-4 1.59E-5 4.73E-5

P KM . Table 5b) shows the P -values and H-values produced by W ilcoxon′ s rank sum test for comparison of two groups, P arSym and P KM . All the P -values reported in the table are less than 0.005 (5% significance level).For KolkataSP OT image, comparative P -value of rank sum test between P KM and P arSym is very small 1.59E − 5, indicating the performance metrics produced by P arSym to be statistically significant and not occurred by chance. Similar results are obtained for all other datasets. Hence, all results establish the significant superiority of P arSym over P KM algorithm.

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4 Conclusion In this article, the problem of faster pixel classification of satellite images into different land cover regions is posed as one of parallel clustering method in the intensity space. Consequently an efficient scalable parallel point symmetry based clustering technique has been proposed for classifying remote sensing imagery. This method is able to identify any types of clusters irrespective of its shape, size, convexity as long as clusters possess the point symmetry property, which even parallel K-Means algorithm fails to detect. The efficiency of the P arSym algorithm is demonstrated over numerical remote sensing data in terms of linear speedup and %T G over its sequential runtime without using an All-to-All communication pattern. Superiority of the new P arSym clustering technique over the widely used P KM algorithm is established for one SP OT image of a part of the city of Kolkata and one IRS image of Mumbai, both qualitatively and quantitatively. Statistical tests also establish the statistical significance of P arSym over P KM algorithm. As a scope of future research, the time-efficiency of P arSym algorithm may be improved further using the bounded-collision parallel memory-mapping scheme for effective utilization of cluster memory [7, 17]. Moreover, incorporation of spatial information in the feature vector as this is found to be effective in pixel classification [1] in P arSym method, in lieu of intensity values at different spectral bands constitutes an important direction for farther research.

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*Author Biographies-Ujjwal Maulik

Dr. Ujjwal Maulik did his BS in Physics and Computer Science in 1986 and 1989 respectively,and MS and Ph.D in Computer Sciencein 1991 and 1997 respectively. He is currently a professor in the Department of Computer Science and Technology, Jadavpur University. He has served as the Head of the Computer Science and Technology School of the Government Engineering College in Kalyani, India, during 1996-1999. Dr. Maulik has worked in the Center for Adaptive Systems Application, Los Alamos, New Mexico, USA in 1997, University of New South Wales, Sydney, Australia in 1999, University of Texas at Arlington, USA in 2001, University of Maryland Baltimore County in 2004, Fraunhofer Institute, AiS, Germany in 2005 and Tsinghua University, China in 2007 and University of Rome, Italy in 2008 and German Cancer Research Center, Heidelberg, Germany in 2010. He received the fellowships from International Center for Pure and Applied Mathematics, CIMPA, France, in 1994, 1996 and 2006, and International Center for Theoretical Physics (ICTP), Italy in 2007. He has edited two books titled ?Advanced methods for knowledge discovery from complex data?, published by Springer, UK in 2005 and ?Analysis of biological data: A soft computing approach? published by World Scientific in 2007 and also preparing another book titled ?Computational Intelligence and Pattern Analysis in Biology Informatics? from John Wiley and Sons,2010. He is a co-author of more than hundred and twenty five technical articles in international journals, book chapters and conference/workshop proceedings. He has served on the program committees of many International Conferences, and has delivered many invited talks and tutorials around the world. He has served as the Program Chair of the Conference on Intelligent Computing and VLSI, 2001 held in Kalyani, India, and Tutorial Co-Chair, World Congress on Lateral Computing, 2004 held in Bangalore, India. His research interests include Computational Intelligence, Pattern Recognition, Data Mining, Bioinformatics and Parallel and Distributed Systems. Dr. Maulik is a Fellow of the Institution of Electronics and Telecommunication Engineers (IETE), India and Institution of Engineers(IE), India, a senior member of Institute of Electrical and Electronics Engineers (IEEE), USA.

*Author Biographies-Anasua Sarkar

Anasua Sarkar has passed her M.E. with specialization in Embedded System and now is pursuing Ph.D. on bioinformatics in Jadavpur University. She is also pursuing her doctoral research in Magnome-INRIA group, Genolevures Consortium, LaBRI, University Bordeaux 1, France under EMMA Fellowship for another dual Ph D degree. She is professionally a lecturer of Information Technology Department at Government College of Engineering and Leather Technology, Kolkata with 9 years of teaching experience. She was coordinator of a National Level seminar on 'Knowledge Discovery and Data Mining - Identifying potential information' held at GCETTS in 2006. Anasua has pursued a variety of interests over her career, including compiler theory, database theory, embedded systems, parallel computing, automata theory and computer algorithms. She was is a member of Magnome-INRIA group, MaBioVis group, ISTE in 2003-2004. She was HOD-InCharge of IT and CSE depts. for about 6 months in GCETTS. She has already published a paper on Xilinx FPGA in Kindler, Indian Institute of Army Management, Kolkata.She also has published papers in Fundamenta Informatica, Kindler-Journal of Indian Institute of Army Management, Kolkata and a book Chapter in the book 'Computational Intelligence and Pattern Analysis in Biology Informatics' of Willey and Sons Publication. She also has completed four more research work in bioinformatics, clustering, parallel and distributed system, phyloenetic analysis with publications. She also is a reviewer of IEEE SMC-C journal.

*Author Photographs-Ujjwal Maulik

*Author Photographs-Anasua Sarkar