Sector Mean with Individual Cal and Sal Components in Walsh Transform Sectors as Feature Vectors for CBIR

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Sector Mean with Individual Cal and Sal Components in Walsh Transform Sectors as Feature Vectors for CBIR Powered By Docstoc
					                                                        (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                              Vol. 8, No. 7, October 2010




    Sector Mean with Individual Cal and Sal
Components in Walsh Transform Sectors as Feature
               Vectors for CBIR
                       H. B. Kekre                                                            Dhirendra Mishra
        Senior Professor, Computer Engineering                                    Associate Professor, Computer Engineering
        MPSTME,SVKM‟S NMIMS University,                                           MPSTME, SVKM‟S NMIMS University,
                   Mumbai, INDIA                                                               Mumbai, INDIA
                 hbkekre@yahoo.com                                                      dhirendra.mishra@gmail.com


Abstract- We have introduced a novel idea of conceiving                 much smaller in size than the original image, typically of the
complex Walsh transform for sectorization of transformed                order of hundreds of elements (rather than millions). The
components. In this paper we have proposed two different                second task is similarity measurement (SM), where a
approaches for feature vector generation with consideration of          distance between the query image and each image in the
all sal components and all cal components separately. Both
                                                                        database using their signatures is computed so that the top
these approaches are experimented with the extra components
of zero-cal and highest-sal. Two similarity measures such as            closest images can be retrieved.[7-9]. There are various
sum of absolute difference and Euclidean distance are used and          approaches which have been experimented to generate the
results are compared. The cross over point performance of               efficient algorithm for CBIR like FFT sectors [4-6],
overall average of precision and recall for both approaches on          Transforms [15][17], Vector quantization[12], bit truncation
different sector sizes are compared. The individual sector mean         coding [13][14]. In this paper we have introduced a novel
of Walsh sectors in all three color planes are considered to            concept of complex Walsh transform and its sectorization
design the feature vector. The algorithm proposed here is               for feature extraction (FE).Two different similarity measures
worked over database of 1055 images spread over 12 different
                                                                        namely sum of absolute difference and Euclidean distance
classes. Overall Average precision and recall is calculated for
the performance evaluation and comparison of 4, 8, 12 & 16
                                                                        are considered. The performances of these approaches are
Walsh sectors. The use of Absolute difference as similarity             compared.
measure always gives lesser computational complexity and
consideration of only all cal components with augmentation of
zero-cal approach with sum of absolute difference as similarity                           II. WALSH TRANSFORM
measure of feature vector has the best retrieval performance.
Index Terms- CBIR, Walsh Transform, Euclidian Distance,                 Walsh transform [17] matrix is defined as a set of N rows,
Absolute Difference, Precision, Recall
                                                                        denoted Wj, for j = 0, 1, .... , N - 1, which have the
                                                                        following properties:
                  I.    INTRODUCTION
                                                                                 Wj takes on the values +1 and -1.
With the huge growth of digital information the need of its                      Wj[0] = 1 for all j.
management requires need of storage and utilization in                           Wj x WTk=0, for j ≠ k and Wj x WkT =N, for j=k.
efficient manner. This has lead to approach like content                         Wj has exactly j zero crossings, for j = 0, 1, ., N-1.
based image search and retrieval to be used. Content-based                       Each row Wj is either even or odd with respect to
image retrieval into automatic retrieval of images from a                       its midpoint.
database by color, texture and shape features. The term has
been widely used to describe the process of retrieving
                                                                        Walsh transform matrix is generated using a Hadamard
desired image on the basis of features (such as colors,
                                                                        matrix of order N. The Walsh transform matrix row is the
texture and shape) that can be automatically extracted from
                                                                        row of the Hadamard matrix specified by the Walsh code
the images themselves. The typical CBIR system [1-6]
                                                                        index, which must be an integer in the range [0, ..., N - 1].
performs two major tasks. The first one is feature extraction
                                                                        For the Walsh code index equal to an integer j, the
(FE), where a set of features, called image signature or
                                                                        respective Hadamard output code has exactly j zero
feature vector, is generated to accurately represent the
                                                                        crossings, for j = 0, 1, ... , N - 1.
content of each image in the database. A feature vector is



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                                                                                                    ISSN 1947-5500
                                                       (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                               Vol. 8, No. 7, October 2010



Kekre‟s Algorithm[10] to generate Walsh Transform from                 sectors are further divided into 8, 12 and 16 sectors. We
Hadamard matrix [17] is illustrated for N=16.However the               have proposed two different approaches for feature vector
algorithm is general and can be used for any N = 2 k where k           generation namely sector mean of only sal components and
is an integer.                                                         only cal components value of all the vectors in each sector
                                                                       with augmentation of extra highest-sal, zero-cal components
                                                                       and without augmentation of extra highest-sal, zero-cal
Step 1:                                                                components with sum of absolute difference and Euclidean
Arrange the „N‟ numbers in a row and then split the row at             distance [7-9] [11-14] as similarity measures. Performances
„N/2‟, the other part is written below the upper row but in            of all these approaches are compared using both similarity
reverse order as follows:                                              measures.
0   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15                                A.Four Walsh Transform Sectors:
15 14 13 12 11 10 9 8                                                  To get the angle in the range of 0-360 degrees, the steps as
Step 2:                                                                given in Table 1 are followed to separate these points into
                                                                       four quadrants of the complex plane. The Walsh transform
We get two rows, each of this row is again split in „N/4‟ and          of the color image is calculated in all three R, G and B
other part is written in reverse order below the upper rows as         planes. The complex rows representing sal components of
shown below.                                                           the image and the real rows representing cal components
0   1 2 3                                                              are checked for positive and negative signs. The sal and cal
15 14 13 12                                                            Walsh values are assigned to each quadrant. as follows:
7   6 5    4
                                                                              TABLE I.    FOUR WALSH SECTOR FORMATION
8   9 10 11
                                                                            Sign of Sal   Sign        of    Quadrant Assigned
This step is repeated until we get a single column which
                                                                                          Cal
gives the ordering of the Hadamard rows according to
sequency as given below:                                                         +             +               I (0 – 90 Degrees)
0 ,15, 7, 8, 3,12,4,11,1,14,6,9,2,13,5,10                                        +               -          II ( 90 – 180 Degrees)
Step 3:                                                                          -               -          III( 180- 270 Degrees)
According to this sequence the Hadamard rows are arranged                        -             +            IV(270–360 Degrees)
to get Walsh transform matrix. Now a product of Walsh
matrix and the image matrix is calculated. This matrix
contains Walsh transform of all the columns of the given               The equation (1) is used to generate individual components
image.                                                                 to generate the feature vector of dimension 12 considering
                                                                       three R, G and B Planes in the sal and cal density
Since Walsh matrix has the entries either +1 or -1 there is            distribution approach. However, it is observed that the
no multiplication involved in computing this matrix. Since             density variation in 4 quadrants is very small for all the
only additions are involved computational complexity is                images. Thus the feature vectors have poor discretionary
very low.                                                              power and hence higher number of sectors such as 8, 12 and
                                                                       16 were tried. In the case of second approach of feature
           III. FEATURE VECTOR GENERATION
                                                                       vector generation i.e. individual sector mean has better
                                                                       discretionary power in all sectors.Sum of absolute difference
The proposed algorithm makes novel use of Walsh                        measure is used to check the closeness of the query image
transform to design the sectors to generate the feature                from the database image and precision and recall are
vectors for the purpose of search and retrieval of database            calculated to measure the overall performance of the
images. The complex Walsh transform is conceived by                    algorithm.
multiplying all sal functions by j = √-1 and combining them
with real cal functions of the same sequency. Thus it is               B.   Eight Walsh Transform Sectors:
possible to calculate the angle by taking tan-1 of sal/cal.
However the values of tan are periodic with the period of π            Each quadrants formed in the previous obtained 4 sectors
radians hence it can resolve these values in only two sectors.         are individually divided into 2 sectors each considering the
To get the angle in the range of 0-360 degrees we divide               angle of 45 degree. In total we form 8 sectors for R,G and B
these points in four sectors as explained below. These four            planes separately as shown in the Table 2. The percentage




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                                                                                                     ISSN 1947-5500
                                                               (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                 Vol. 8, No. 7, October 2010



density distribution of sal and cal in all 8 sectors are
determined using equation (1) to generate the feature vector.
                                                                                      IV.    RESULTS AND DISCUSSION
                                                                           The sample Images of the database of 1055 images of 12
       TABLE 2. EIGHT WALSH SECTOR FORMATION                               different classes such as Flower, Sunset, Barbie, Tribal,
Quadrant of 4             Condition         New sectors Formed             Puppy, Cartoon, Elephant, Dinosaur, Bus, Parrots, Scenery,
Walsh sectors                                                              Beach are shown in the Figure 1.The algorithm is tested by
                                                                           taking 5 query images from each class and then averaging
    I (0 – 90 0 )          Cal >= Sal            I (0-45 Degrees)
                                                                           the performance in terms of precision and recall over all the
                            Sal > Cal           II (45-90 Degrees)         classes.
  II ( 90 – 1800 )         |Sal | > |Cal|      III(90-135 Degrees)
                          |Cal| >= |Sal|    IV(135-180 Degrees)
                    0
 III ( 180- 270 )         |Cal| >= |Sal|    V (180-225 Degrees )
                           |Sal| > |Cal|    VI (225-270 Degrees)
                    0
 IV ( 270 – 360 )          |Sal| > |Cal|          VII (270-315
                                                   Degrees)
                          |Cal| >= |Sal|          VIII (315-360
                                                    Degrees )

C. Twelve Walsh Transform Sectors:
Each quadrants formed in the previous section of 4 sectors
are individually divided into 3 sectors each considering the
angle of 30 degree. In total we form 12 sectors for R,G and
B planes separately as shown in the Table 3. The percentage
density distribution of sal and cal in all 12 sectors are
determined using equation (1) to generate the feature vector
       TABLE 3. TWELVE WALSH SECTOR FORMATION
 4 Quadrants            Condition                  New sectors
             0
   I (0 – 90 )            Cal >= √3 * Sal             I (0-30 0)
                        1/√3 cal <=sal<= √3          II (30-60 0)
                                 cal
                             Otherwise               III (60-90 0)
 II ( 90 – 1800)          Cal >= √3 * Sal           IV (90-120 0)
                         1/√3 |cal| <=|sal|<=       V (120-150 0)
                               √3 |cal|
                             Otherwise              VI (150-1800)
 III(180-2700 )           |Cal|>= √3 * |Sal|       VII (180-2100 )
                        1/√3 cal <=|sal|<= √3      VIII(210-240 0)
                                 |cal|
                                                                                        Figure 1. Sample Image Database
                             Otherwise              IX (240-270 0)
   IV ( 270 –             |Cal|>= √3 * |Sal|        X (270-300 0)
     3600)
                         1/√3 |cal| <=|sal|<=      XI (300-330 0 )
                               √3 |cal|
                             Otherwise             XII (330-360 0)         Figure 2. Query Image




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                                                                                                       ISSN 1947-5500
                                                     (IJCSIS) International Journal of Computer Science and Information Security,
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The dinosaur class image is taken as sample query image as
shown in the Figure 2. The first 21 images retrieved in the
case of sector mean in 12 Walsh sector used for feature
vectors and Absolute difference as similarity measure is
shown in the Figure 3. It is seen that all images retrieved
among first 21 images are of same class of query image i.e.
dinosaur.
                                                                      Figure 3: First 21 Retrieved Images based on individual
                                                                     sector mean with augmentation of zero-cal and highest-sal
                                                                     components of 12 Walsh Sectors with Absolute Difference
                                                                      as similarity measures for the query image shown in the
                                                                                              Figure 2.

                                                                    Once the feature vector is generated for all images in the
                                                                    database a feature database is created. A query image of
                                                                    each class is produced to search the database. The image
                                                                    with exact match gives minimum sum of absolute difference.
                                                                    To check the effectiveness of the work and its performance
                                                                    with respect to retrieval of the images we have calculated the
                                                                    precision and recall as given in Equations (1) and (2)
                                                                    below:
                                                                                Number of relevant images retrieved
                                                                    Precision=----------------------------------------------          (1)
                                                                                  Total Number of images retrieved


                                                                               Number of relevant images retrieved
                                                                    Recall= ------------------------------------------------- (2)
                                                                           Total number of relevant images in database


                                                                    The Figure 4 – Figure 7 shows the Overall Average
                                                                    Precision and Recall performance of mean of only sal
                                                                    components of each sectors in 4, 8, 12 and 16 Walsh
                                                                    Transform sectors with absolute Difference respectively.
                                                                    Figure 8 – Figure 11 shows the overall average cross over
                                                                    performance of individual sector mean of only cal
                                                                    components in 4, 8, 12 and 16 Walsh sectors. The
                                                                    comparison bar chart of cross over points of overall average
                                                                    of precision and recall for 4, 8, 12 and 16 sectors of with
                                                                    augmentation of extra zero-cal and highest-sal components
                                                                    with individual sector mean w.r.t. two different similarity
                                                                    measures namely        Euclidean distance and Absolute
                                                                    difference is shown in the Figure 12 and Figure13. It is
                                                                    observed that performance of 12 sectors with extra
                                                                    components of zero-cal and highest-sal with consideration of
                                                                    only cal components of each sector is the best. The
                                                                    performance of absolute difference is quite closed to
                                                                    Euclidean distance.




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Figure 4: Overall Average Precision and Recall performance
    of Sector mean with only sal component in 4 Walsh
   Transform sectors with Absolute Difference(AD) and              Figure 6: Overall Average Precision and Recall performance
      Euclidian Distance (ED) as similarity measures.                 of Sector mean with only sal component in 12 Walsh
                                                                      Transform sectors with Absolute Difference(AD) and
                                                                         Euclidian Distance (ED) as similarity measures.




Figure 5: Overall Average Precision and Recall performance         Figure 7: Overall Average Precision and Recall performance
    of Sector mean with only sal component in 8 Walsh                 of Sector mean with only sal component in 16 Walsh
   Transform sectors with Absolute Difference(AD) and                 Transform sectors with Absolute Difference(AD) and
      Euclidian Distance (ED) as similarity measures.                    Euclidian Distance (ED) as similarity measures.




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Figure 8: Overall Average Precision and Recall performance
                                                                        Figure 10: Overall Average Precision and Recall
    of Sector mean with only cal component in 4 Walsh
                                                                   performance of Sector mean with only cal component in 12
   Transform sectors with Absolute Difference(AD) and
                                                                   Walsh Transform sectors with Absolute Difference(AD) and
      Euclidian Distance (ED) as similarity measures.
                                                                         Euclidian Distance (ED) as similarity measures.




Figure 9: Overall Average Precision and Recall performance              Figure 11: Overall Average Precision and Recall
    of Sector mean with only cal component in 8 Walsh              performance of Sector mean with only cal component in 16
   Transform sectors with Absolute Difference(AD) and              Walsh Transform sectors with Absolute Difference(AD) and
      Euclidian Distance (ED) as similarity measures.                    Euclidian Distance (ED) as similarity measures.




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                                                                   only cal for feature vector generation with sum of absolute
                                                                   difference as similarity measuring parameter. These results
                                                                   are compared with Euclidian distance as similarity measure.
                                                                   Both thease approaches are experimented with and without
                                                                   augmentation of extra component of zero-cal and highest-
                                                                   sal. The cross over point performance of overall average of
                                                                   precision and recall for both approaches on all applicable
                                                                   sectors are compared. It is found that the sector mean of
                                                                   only cal component with augmentation of extra component
                                                                   of zero-cal and highest-sal always gives the best outcome of
                                                                   retrieval as shown in the bar chart of the figure 13. It is also
                                                                   observed that sum of absolute difference is found
                                                                   economical similarity measuring parameter. Using Walsh
                                                                   transform and absolute difference as similarity measuring
                                                                   parameter reduces the computational complexity reducing
                                                                   the search time and calculation of feature vector [8][9].
                                                                                           REFERENCES

   Figure 12: Comparison of Overall Precision and Recall           [1]    Kato, T., “Database architecture for content based
cross over points based on individual sector mean in Walsh                image retrieval in Image Storage and Retrieval
 4, 8, 12 and 16 sectors with Absolute Difference (AD) and                Systems” (Jambardino A and Niblack W eds),Proc
       Euclidean Distance (ED) as similarity measure.                     SPIE 2185, pp 112-123, 1992.
                                                                   [2]    John Berry and David A. Stoney “The history and
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                                                                          Gaensslen, Eds., pp. 1-40. CRC Press Florida, 2nd
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                                                                   [3]    Emma Newham, “The biometric report,” SJB
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                                                                   [4]    H. B. Kekre, Dhirendra Mishra, “Digital Image
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                                                                          Information            communication            and
                                                                          technology(NCICT 10) 5TH & 6TH March
                                                                          2010.SVKM‟S NMIMS MUMBAI
                                                                   [5]    H.B.Kekre, Dhirendra Mishra, “Content Based
                                                                          Image       Retrieval using Weighted      Hamming
                                                                          Distance Image         hash Value” published in the
                                                                          proceedings of        international conference on
                                                                          contours of computing        technology pp. 305-309
                                                                          (Thinkquest2010) 13th & 14th March 2010.
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  Figure 13: Comparison of Overall Precision and Recall                   Search & Retrieval using FFT Sectors of Color
cross over points based on individual sector mean in Walsh                Images” published in International Journal of
4, 8, 12 and 16 sectors with Absolute Difference (AD) and                 Computer Science and Engineering (IJCSE) Vol.
      Euclidean Distance (ED) as similarity measure.                      02,No.02,2010,pp.368-372         ISSN    0975-3397
                                                                          available                   online                at
                  .V.   CONCLUSION                                        http://www.enggjournals.com/ijcse/doc/IJCSE10-
                                                                          02-     02-46.pdf
The Innovative idea of using complex Walsh transform 4, 8,
                                                                   [7]    H.B.Kekre, Dhirendra Mishra, “CBIR using upper
12 and 16 sectors of the images to generate the feature
                                                                          six FFT Sectors of Color Images for feature vector
vectors for content based image retrieval is proposed. We
                                                                          generation” published in International Journal of
have proposed two different approaches using only sal and



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         Engineering and Technology(IJET) Vol. 02, No.                         Advances in Computing, Communication and
         02, 2010, 49-54 ISSN 0975-4024 available online                       Control (ICAC3-2009), pp.: 384-390, 23-24 Jan
         at                                                                    2009, Fr. Conceicao Rodrigous College of Engg.,
         http://www.enggjournals.com/ijet/doc/IJET10-02-                       Mumbai. Available online at ACM portal.
         02-06.pdf                                                      [ 16 ] H.B.Kekre, Tanuja K. Sarode, Sudeep D. Thepade,
[8]      H.B.Kekre, Dhirendra Mishra, “Four walsh                              “DCT Applied to Column mean and Row Mean
         transform sectors feature vectors for image retrieval                 Vectors of Image for Fingerprint Identification”,
         from image databases”, published in international                     International Conference on Computer Networks
         journal of computer science and information                           and Security, ICCNS-2008, 27-28 Sept 2008,
         technologies (IJCSIT) Vol. 1 (2) 2010, 33-37 ISSN                     Vishwakarma Institute of Technology, Pune.
         0975-9646           available         online        at         [ 17 ] H.B.Kekre, Sudeep Thepade, Archana Athawale,
         http://www.ijcsit.com/docs/vol1issue2/ijcsit201001                    Anant Shah, Prathmesh Velekar, Suraj Shirke, “
         0201.pdf                                                              Walsh transform over row mean column mean
[9]      H.B.Kekre, Dhirendra Mishra, “Performance                             using image fragmentation and energy compaction
         comparison of four, eight and twelve Walsh                            for image retrieval”, International journal of
         transform sectors feature vectors for image retrieval                 computer       science      and       engineering
         from image databases”, published in international                     (IJCSE),Vol.2.No.1,S2010,47-54.
         journal     of     Engineering,       science     and          [ 18 ] H.B.Kekre, Vinayak Bharadi, “Walsh Coefficients
         technology(IJEST) Vol.2(5) 2010, 1370-1374                            of the Horizontal & Vertical Pixel Distribution of
         ISSN      0975-5462          available    online    at                Signature Template”, In Proc. of Int. Conference
         http://www.ijest.info/docs/IJEST10-02-05-62.pdf                       ICIP-07, Bangalore University, Bangalore. 10-12
[ 10 ]   H.B.Kekre, Dhirendra Mishra, “Density distribution                    Aug 2007.
         in Walsh Transform sectors as feature vectors for
         image retrieval”, International journal of computer
         application (IJCA), ISSN NO. 975-8887, Vol.4,                                     AUTHORS PROFILE
         No.6, July 2010, pp-30-36.available online at
         http://www.ijcsonline.org/archives/volume4/number                                 Dr. H. B. Kekre has received B.E.
         6/829-1072.                                                                       (Hons.) in Telecomm. Engg. from
[ 11 ]   Arun Ross, Anil Jain, James Reisman, “A hybrid                                    Jabalpur University in 1958, M.Tech
         fingerprint matcher,” Int’l conference on Pattern                                 (Industrial Electronics) from IIT
         Recognition (ICPR), Aug 2002.                                                     Bombay in 1960, M.S.Engg. (Electrical
[ 12 ]   A. M. Bazen, G. T. B.Verwaaijen, S. H. Gerez, L.                                  Engg.) from University of Ottawa in
         P. J. Veelenturf, and B. J. van der Zwaag, “A                  1965 and Ph.D.(System Identification) from IIT Bombay in
         correlation-based fingerprint verification system,”            1970. He has worked Over 35 years as Faculty and H.O.D.
         Proceedings of the ProRISC2000 Workshop on                     Computer science and Engg. At IIT Bombay. From last 13
         Circuits, Systems and Signal Processing,                       years working as a professor in Dept. of Computer Engg. at
         Veldhoven, Netherlands, Nov 2000.                              Thadomal Shahani Engg. College, Mumbai. He is currently
[ 13 ]   H.B.Kekre, Tanuja K. Sarode, Sudeep D. Thepade,                Senior Professor working with Mukesh Patel School of
         “Image Retrieval using Color-Texture Features                  Technology Management and Engineering, SVKM‟s
         from        DCT on VQ Codevectors obtained by                  NMIMS University vile parle west Mumbai. He has guided
         Kekre‟s Fast        Codebook Generation”, ICGST                17 PhD.s 150 M.E./M.Tech Projects and several
         International Journal       on Graphics, Vision and            B.E./B.Tech Projects. His areas of interest are Digital signal
         Image Processing (GVIP),          Available online at          processing, Image Processing and computer networking. He
         http://www.icgst.com/gvip                                      has more than 300 papers in National/International
[ 14 ]   H.B.Kekre, Sudeep D. Thepade, “Using YUV                       Conferences/Journals to his credit. Recently ten students
         Color Space to Hoist the Performance of Block                  working under his guidance have received the best paper
         Truncation Coding for Image Retrieval”, IEEE                   awards. Currently he is guiding 8 PhD. Students. Two of his
         International Advanced Computing Conference                    Students have recently completed Ph. D. He is life member
         2009 (IACC‟09), Thapar University, Patiala,                    of ISTE and Fellow of IETE.
         INDIA, 6-7 March 2009.
[ 15 ]   H.B.Kekre, Sudeep D. Thepade, “Image Retrieval
         using Augmented Block Truncation Coding
         Techniques”, ACM International Conference on



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                    Dhirendra S.Mishra has received his
                   BE (Computer Engg) degree from
                   University     of      Mumbai       in
                   2002.Completed his M.E. (Computer
                   Engg) from Thadomal shahani Engg.
                   College, Mumbai, University of Mumbai.
                   He is PhD Research Scholar and working
as Assistant Professor in Computer Engineering department
of Mukesh Patel School of Technology Management and
Engineering, SVKM‟s NMIMS University, Mumbai,
INDIA. He is life member of Indian Society of Technical
education (ISTE), Member of International association of
computer science and information technology (IACSIT),
Singapore, Member of International association of
Engineers (IAENG). His areas of interests are Image
Processing, Operating systems, Information Storage and
Management




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