Docstoc

Skew Correction and Noise Reduction for Automatic Gridding of Microarray Images

Document Sample
Skew Correction and Noise Reduction for Automatic Gridding of Microarray Images Powered By Docstoc
					                                                         (IJCSIS) International Journal of Computer Science and Information Security,
                                                         Vol. 8, No. 4, July 2010




              Skew Correction and Noise Reduction for
             Automatic Gridding of Microarray Images
Manjunath S S,                                                          Dr. Lalitha Rangarajan
Asistant Professor, Dept of Computer Science                            Reader, Dept of Studies in Computer Science
Dayananda Sagar College of Engineering,                                 University of Mysore, India
Bangalore. India                                                        Email: lali85arun@yahoo.co.in
Email: mnj_ss2002@ yahoo.co.in


Abstract-                                                               spots by assignment of image coordinates to the spots. 2.
Complementary DNA (cDNA) microarrays are a powerful                     Segmentation, separation between the foreground and
high throughput technology developed in the last decade                 background pixels and 3. Intensity extraction, computation
allowing researchers to analyze the behavior and interaction            of the average foreground and background intensities for
of thousands of genes simultaneously. The large amount of               each spot of the array.
information provided by microarray images requires
automatic techniques for efficient processing of microarray             Gridding is an important task that is to be performed as
images to arrive at accurate biological conclusion. Most of the
methods discussed in the literature need different levels of
                                                                        accurately as possible, since it affects the subsequent tasks
human intervention, which inevitably reduces the efficiency             of segmentation, intensity extraction and finally the
and reproducibility of the entire automation process. In this           conclusions derived out of the whole analysis. The
paper a novel approach for automatic gridding of skewed and             available gridding software packages Scanlyze [1], Dappel
noisy microarray images is presented. The microrarray                   [2], Image Gene[3], Genepix and SpotFinder[4] require
image is skew corrected, noise removed using adaptive                   human intervention in order to specify input parameters as
thresholds computed on various segments, spatial topology of            well as to adjust properly the location of the grid lines. The
spots detected, gridding performed and finally grids are                template based approach is most prevalent in the existing
refined. Experiments conducted on selected microarray                   packages which require specfication of parameters such as
images (skewed and noisy) of Stanford and UNC databases
are encouraging
                                                                        spot size, spot spacing and space location. Some software
                                                                        products already incorporate an automatic refinement
Keywords: Microarray, Gridding, Adaptive threshold,                     search for grid location, given size and spacing of spots
Spatial topology, Grid refinement, Skewed images,                       [2,3]. Irregular grids cannot be found with the template
Noisy images.                                                           based approach unless the template is manually adjusted to
                                                                        fit predefined distortions [3]. Automating this part of the
1. Introduction                                                         process is essential because it reduces error in grid that
DNA microarray technology has a large impact in many                    may arise due to inaccurate specification.
application areas, such as diagnosis of human diseases and
treatments (determination of risk factors, monitoring                   The problem of automatic gridding is complicated because
disease stage and treatment progress, etc.), agricultural               microarray images are usually highly contaminated with
development (plant biotechnology), and quantification of                the noise and artifacts of the wet lab processes. Rotations,
genetically modified organisms, drug discovery, and                     misalignment and local deformations of the ideal
design. In cDNA microarrays, a set of genetic DNA probes                rectangular grid can often occur. There is a high need for
(from several hundreds to some thousands) are spotted on                automated methods for microarray gridding which are
a slide. Two populations of mRNA, tagged with                           robust and flexible at the same time.
fluorescent dyes, are then hybridized with the slide spots,
and finally the slide is read with a scanner. The outlined              Some efforts on automatic microarray gridding have been
process produces two images, one for each mRNA                          reported in literature. However most of them impose
population, each of which varies in intensity according to              different kinds of restrictions and are based on stringent
the level of hybridization represented as the quantity of               assumptions. For example, the approaches in Jain et al.[5]
fluorescent dye contained in each spot.                                 and Yan et al.[6] requires that the grid rows and columns
                                                                        are strictly parallel to the x and y image axes. Other
Microarray image processing consists of the following                   approaches, such as described by Carstensen et al.[7] and
sequence of three main tasks 1. Gridding, separation of                 Katzer [8], rely on the Bayesian paradigm to deal with




                                                                  326                               http://sites.google.com/site/ijcsis/
                                                                                                    ISSN 1947-5500
                                                          (IJCSIS) International Journal of Computer Science and Information Security,
                                                          Vol. 8, No. 4, July 2010




uncertainty and noise. Some well-known approaches to
gridding microarray images are based on axis projections
(Deng et al.[9]), or on morphological filtering (Yan et                                                    I/P Raw Microarray
al.[10]). Both of them require user intervention in order to                                                ImageI1 (with Skew & Noise)
manually adjust the grid location. The Hill-Climbing
approach for automatic gridding (Rueda et al.[11]) can                          Perform skew detection & correction
perform gridding properly only if misalignments and                                    resulting in image I2
rotations of the ideal grid are not present. Markov random
field (MRF) (Antoniol et al.[12]) and graph-based grid
approaches (Jung et al.[13]) have been used to perform
gridding. A drawback of these approaches is that they                      Compute adaptive thresholds in segments of
require input parameters. A variety of different                           the image, I2
methodologies have been proposed with the intension to
solve rotation and misalignment problems. Bajcsy [14] has
suggested an exhaustive search of all the expected rotation                Filter the segments using respective thresholds
angles, where as Steinfath [15] has estimated the rotation
angle. A drawback of these approaches is that, it
introduces pixel distortions when the rotation angle is
small. Brandle et al.[16] utilized the discrete Radon                       Detect spatial arrangement of very bright spots
transformation to estimate the angle of rotation. As it is                               resulting in image I3
computationally expensive, the process is accelerated by
constraining the range of rotation angles. Ho et al.[17]
expressed the gridding process as an optimization problem
based on the Jacobi iteration. However, this method is
efficient only when the grids are smoothly distorted.                      Identify grid lines on I3 (fewer since the spots
Giuiliano et al.[18] recommended a gridding procedure                      retained from previous step are less in number)
based on stochastic search algorithms. Although it deals
with rotations effectively, it requires manual intervention
in order to define the radius of the spots.

In spite of the potential importance of gridding approaches                          Refine the grid on the image I2
in microarray image analysis, the existing gridding
methods pay little attention to pre-processing of noisy
microarray images and focus mainly on spot localization
and spot segmentation. The aim of the present study is to                 Figure 1. Stages of automatic gridding of noisy
                                                                                         Microarray image
propose a method that can deal with rotations,
misalignments, and local deformations of the ideal
rectangular grid. It is also noise-resistant and it is efficient
even under adverse conditions such as the appearance of                  The organization of rest of the paper is as follows: In
various spot sizes or the absence of spots.                              section 2, preprocessing techniques such as skew detection
                                                                         and correction, filtering through respective thresholds are
                                                                         described. In section 3 automatic gridding process which
Figure. 1 Shows a block diagram which describes the                      consists of detection of rmin & rmax, detection of cmin &
salient stages of the proposed approach for automatic                    cmax and gridding method are described. Section 4
gridding of microarray images.                                           describes grid refinement algorithm. Section 5 highlights
                                                                         the results of extensive experimentation conducted on
                                                                         some benchmark images. Finally conclusion is discussed
                                                                         in section 6.

                                                                         2. Skew Detection and Correction

                                                                         This section describes the first stage of microarray image
                                                                         gridding, that is skew detection and correction.

                                                                         2.1. Skew Detection




                                                                   327                                 http://sites.google.com/site/ijcsis/
                                                                                                       ISSN 1947-5500
                                                                (IJCSIS) International Journal of Computer Science and Information Security,
                                                                Vol. 8, No. 4, July 2010




First step in this process is to convert the rgb image to gray                           Φ     = atan (lefty – topy ) / (topx - leftx)
scale image. Figure 2. shows the computation of the
parameters topx, topy, leftx, lefty, xmid and ymid which
are required to find the skew angle. Scan the gray scale
                                                                               2.1.2 Skew Correction
image rowwise. The very first pixel in the image is
assigned the coordinate address (topx, topy). Scan the gray                    The new coordinate address xx and yy are computed as
scale image columnwise. The very first pixel in the image                      given below.
is assigned the coordinate address (leftx, lefty). xmid is the
mid value of columns and ymid is the mid value of rows.                        Skew correction for clockwise tilt: It is required to perform
.                                                                              rotation about (leftx,lefty) by Φ in anticlockwise direction .
            If topx < xmid and lefty > ymid the
             skew is clock wise (Figure.2)                                     xx = leftx + ( x-leftx) * cos (Φ ) – (y-lefty) * sin (Φ )
           If topx > xmid and lefty < ymid the                                 yy = lefty + (x-leftx) * sin (Φ ) + (y-lefty) * cos (Φ )
            skew is anticlock wise (Figure.3)
                                                                               Skew correction for anticlockwise:

                                                                               xx = topx + (x-topx) * cos(Φ) + (y-topy) * sin(Φ)

                                                                                yy = topy + (y-topy) * cos(Φ) + (topx-x) * sin(Φ)

                                                                               where
                                                                               x varies from 1 to number of columns
                                                                               y varies from 1 to number of rows

                                                                               The min xx and min yy are computed and translated this to
                                                                               (0,0).The new image Ll with the coordinate address
                                                                               xx1=xx-minxx
                                                                               yy1=yy-minyy is the skew corrected image.

         Figure 2. Parameters for clockwise skew detection                     Figures 4 and 5 (Image ID: 62919) shows the clockwise
                                                                               skewed image and skew corrected image.




        Figure 3. Parameters for anticlockwise skew detection




The clockwise skew angle can be found using the formula
                                                                               Figure 4. Clockwise Skewed Image ID: 62919
         Φ = atan (topx – leftx ) / (lefty - topy)



The anticlockwise skew angle can be found using the
formula



                                                                         328                               http://sites.google.com/site/ijcsis/
                                                                                                           ISSN 1947-5500
                                                          (IJCSIS) International Journal of Computer Science and Information Security,
                                                          Vol. 8, No. 4, July 2010




                                                                              T (i) = (Number of pixels in i th segment)

                                                                                           (Total number of connected
                                                                                            Components)


                                                                         Where i ranges from 1 to 4.
                                                                         For example in the image (ID: 40031) Fig. 6 the number of
                                                                         bright pixels in the four segments are 2462, 1572, 1353,
                                                                         1065. Total number of connected components is 146. The
                                                                         thresholds are 2462/146=17, 1572/146= 11, 1353/146= 10,
                                                                         1065/146=9
                                                                         The results of the proposed filtering process in removing
                                                                         the insignificant spots using the threshold value and
Figure 5. Skew Corrected Image ID: 62919                                 execution time (τf) are reported in Table 2.

TABLE 1: ESTIMATED ANGLE (Φ) AND EXECUTION TIME (ΤS)                     TABLE 2. ESTIMATED THRESHOLD VALUE (AT)
OF THE PROPOSED SKEW CORRECTION TECHNIQUE.
                                                                         AND EXECUTION TIME (ΤF) OF THE PROPOSED
Image ID               Estimated angle      Execution time               FILTERING PROCESS.
                       in degrees (Φ)       in seconds (τs)
   1c7b060rex2                2.0651                13.14                     Noisy Image ID    Thresholds      #spots in    Execution
   1c4bo64rex2                2.5323                12.12                                       on a            the          time(τf) in
      62919                   4.8253                15.15                                       subarray        subarray     seconds
      40031                   3.7653                13.54                                          T1=17
                                                                                                   T2=11           146            10
                                                                                   40031           T3=10
                                                                                 (Stanford)        T4=09
2.2 Adaptive Threshold and Filtering                                                               T1=14
                                                                                   44004           T2=12           777            15
Filtering is performed in 2 steps which are described in the                      (TBDB)           T3=12
                                                                                                   T4=10
2 subsections below. Thresholds on spot size are first
                                                                                                   T1=28
computed on segments of the image. Insignificant spots are                         17931           T2=23           721            13
filtered using these thresholds.                                                 (Stanford)        T3=47
                                                                                                   T4=41
The skew corrected binary image is divided into n                                                  T1=20
segments. Number of segments can be increased                                      39119           T2=18           562             8
                                                                                  (TBDB)           T3=15
depending on the level of noise. The subgrid is divided                                            T4=15
into 4 segments in the proposed approach as follows

                                                                         Execution time for the filtering process is proportional to
1st segment                          2nd segment
                                                                         number of spots in a noisy microarray image. Adaptive
Rows=0 to r/2                       Rows= 0 to r/2
                                                                         thresholds obtained in the previous step are used to filter
Columns=0 to c/2                  Columns= c/2+1 to c
                                                                         insignificant noisy spots in the segments. If the number of
                                                                         pixels in a component are less than threshold value (T(i)) in
3rd segment                          4th segment
                                                                         each segment, then remove the spot (insignificant spot) by
Rows=r/2+1 to r                         Rows= r/2 +1to r
                                                                         setting intensity zero to all pixels in that component. The
Columns= 0 to c/2                    Columns= c/2+1 to c
                                                                         idea behind using adaptive threshold is, if in a subarray
                                                                         should few successive columns or rows have tiny spots
where r is the number of rows and c is number of columns
                                                                         filtering using global threshold will eliminate all these
of skew corrected image.
                                                                         spots. This results in sparse grid lines.
For each segment, the numbers of connected components
                                                                         Shown in Figure. 6 is a noisy microarray image. Fig. 7 is
are computed. The thresholds on spot size in each segment
                                                                         the noise free filtered image.
are calculated using the equation below.
                                                                         .




                                                                   329                               http://sites.google.com/site/ijcsis/
                                                                                                     ISSN 1947-5500
                                                       (IJCSIS) International Journal of Computer Science and Information Security,
                                                       Vol. 8, No. 4, July 2010




                                                                      rmin:




                                                                      rmax:




Figure 6. Noisy Microarray Image ID : 40031




                                                                          Figure 8. Representation of rmin, rmax, cmin & cmax of a spot.




Figure 7. Filtered Microarray Image ID : 40031
                                                                      The steps below describe determination of horizontal grid
                                                                      lines.

3. Automatic Gridding Process                                              1) The rmin array is sorted in ascending order

Automatic gridding is performed in 3 steps which are                       sorted rmin:
described in the 3 subsections below.

3.1 Determination of position of grid lines

 For each connected component in the filtered image, rmin,
rmax, cmin, cmax are determined as shown in Fig 8.
Sorted arrays of rmin values (similarly rmax, cmin, cmax
values) are found. Array of successive differences of rmin
array called diff_rmin also for rmax, cmin, cmax
(diff_rmax, diff_rmin, diff_cmin, diff_cmax) is found. Key
portions of rmin, rmax and diff_rmin, diff_rmax are shown
below. All computations done on image ID (62919).




                                                                330                                http://sites.google.com/site/ijcsis/
                                                                                                   ISSN 1947-5500
                                                      (IJCSIS) International Journal of Computer Science and Information Security,
                                                      Vol. 8, No. 4, July 2010




                                                                          diff_rmax:

 2) The differences of successive rmin values
     in the sorted rmin array are calculated.

diffrmin:




                                                                          grid_ramx:




    3) Sudden change in the difference in rmin values
       indicate the end of previous row of spots and
       beginning of next row of spots.

    4) Observe the sudden change from 0 to 15, at position                Finally, positions of horizontal gridlines are
    3 in diff_rmin array. The third element of rmin array is              determined by finding average of rows suggested by
    9. Hence examination of rmin diff_rmin suggests a                     grid_rmin and grid_rmax contents. Thus horizontal
    grid line at row 9. Similarly it is understood that                   gridlines are placed at rows 9, 25 (25+25/2), 41
    successive values of grid rmin.                                       (38+43/2), 57 (55+60/2)…etc.

    grid rmin:
                                                                          In a similar manner vertical gridlines are positioned
                                                                          using sorted_cmin, diff_cmin, grid_cmin, sorted_cmax
                                                                          diff_cmax, grid_cmax.

                                                                          4. Grid Refinement Algorithm

                                                                          The algorithm described in section before, will
                                                                          determine all grid lines as long as a spot exists on each
                                                                          row and each column of the filtered image. However
                                                                          there may be images where no spots are present in
    Similarly grid_rmax is determined. Shown below are                    several consecutive rows or columns. In these images,
    sorted_rmax, diff_rmax, grid_rmax values.                             there will be irregular spacing between gridlines. In
                                                                          such cases the refinement algorithm suggested , can be
    sorted rmax:                                                          used to draw additional / missing grid lines. Grid
                                                                          refinement process is called to check whether all the
                                                                          gridlines have been drawn. If the differences in the
                                                                          positions of successive rows (i, i+1) is greater than the
                                                                          average of previous spacing of rows(avgrowspace),
                                                                          then the algorithm will draw horizontal lines at every
                                                                          successive avgrowspace beginning from the
                                                                          previously drawn horizontal line, until i+1 or end of
                                                                          rows. Similar procedure is repeated while drawing
                                                                          vertical lines.

                                                                          Figure 11 shows additional gridlines placed on
                                                                          gridded image of figure 9.




                                                               331                               http://sites.google.com/site/ijcsis/
                                                                                                 ISSN 1947-5500
                                                              (IJCSIS) International Journal of Computer Science and Information Security,
                                                              Vol. 8, No. 4, July 2010




Figure 9. Filtered image with horizontal sparse grid lines.



                                                                             Figure 11 .Gridding of noisy microarray image before refinement process




 Figure 10. Filtered image with vertical sparse grid lines




                                                                       332                                http://sites.google.com/site/ijcsis/
                                                                                                          ISSN 1947-5500
                                                     (IJCSIS) International Journal of Computer Science and Information Security,
                                                     Vol. 8, No. 4, July 2010




                                                                    Table 3 shows comparison of proposed method with
4. Experimental Results                                             projection profile algorithm and standard deviation
                                                                    algorithm to perform gridding. The comparison was
In this section the performance of the proposed approach is         performed on 10 sets of microarray images and it is
evaluated on skewed and noisy microarray images from                evident that proposed method performs better than other
SMD (Stanford Microarray Database) and UNC                          existing approaches. Expected number of rows and
(University of North California Microarray Database).The            columns are inferred by the number of connected
images are available for free download from                         components across each row and column.
https://genome.unc.edu.
The algorithm was executed on Pentium 4 proceesor with              .
2 GB RAM. The results are summarized in the table 3




       TABLE 3: COMPARISON OF PERFORMANCE OF PROPOSED APPROACH AND OTHER APPROACHES

Method              Image ID           Expected           Expected              Number of           Number of               Total Error
                                       Number of          Number of             Rows                Columns                 (%)
                                       Rows               Columns               obtained            obtained
Grid Using          62919              29                 30                    27                  27                                 8.474576
Standard            22593              17                 15                    21                  15                                     12.5
Deviation           37993              29                 29                    27                  29                                 3.448276
                    34212              20                 21                    21                  21                                 5.882353
                    34217              18                 23                    18                  23                                        0
                    34143              22                 23                    22                  21                                 4.444444
                    34134              23                 23                    23                  22                                 2.173913
                    52694              28                 29                    23                  28                                 10.52632
                    57852              27                 29                    25                  28                                 5.357143
                    66357              28                 29                    26                  29                                 3.508772
Grid Using          62919              29                 30                    27                  29                                 5.084746
Projection          22593              17                 15                    20                  15                                    9.375
Profile             37993              29                 29                    26                  26                                 10.34483
                    34212              20                 21                    20                  21                                 11.76471
                    34217              18                 23                    21                  24                                 9.756098
                    34143              22                 23                    24                  23                                 4.444444
                    34134              23                 23                    23                  21                                 4.347826
                    52694              28                 29                    26                  29                                 3.508772
                    57852              27                 29                    25                  29                                 3.571429
                    66357              28                 29                    27                  29                                 1.754386
Grid Using          62919(SMD)         29                 30                    29                  30                                        0
Proposed            22593(SMD)         17                 15                    17                  15                                        0
Approach            37993(UNC)         29                 29                    29                  29                                        0
                    34212(UNC)         20                 21                    22                  25                                        0
                    34217(UNC)         18                 23                    18                  23                                        0
                    34143(UNC)         22                 23                    24                  23                                 4.444444
                    34134(UNC)         23                 23                    23                  23                                        0
                    52694(SMD)         28                 29                    28                  29                                        0
                    57852(SMD)         27                 29                    27                  29                                        0
                    66357(SMD)         28                 29                    28                  29                                        0




                                                              333                               http://sites.google.com/site/ijcsis/
                                                                                                ISSN 1947-5500
                                                                   (IJCSIS) International Journal of Computer Science and Information Security,
                                                                   Vol. 8, No. 4, July 2010




                                                                                     Automation, Chengdu, China, 2004, pp. 254–257.
                                                                                  [10] A. W. Liew, H. Yan, and M. Yang, “Robust adaptive spot
                                                                                      Segmentation of DNA microarray images,” Pattern Recognit.,
                                                                                       vol. 36, pp. 1251–1254, 2003.
                                                                                  [11] L. Rueda and V.Vidyadharan, “A hill-climbing approach for
                                                                                  automatic gridding of cdna microarray images,” IEEE/ACM Trans.
                                                                                  Comput. Biol.     Bioinf., vol. 3, no. 1, pp. 72–83, Jan.-Mar. 2006.
                                                                                  [12] G. Antoniol and M. Ceccarelli, “A markov random field approach to
                                                                                         microarray image gridding,” in Proc. IEEE Int. Conf. Pattern
                                                                                  Recognit., Cambridge, U.K., 2004, pp. 550–553.
                                                                                  [13] H. Y. Jung and H. G. Cho, “An automatic block and spot indexing
                                                                                      with k-nearest neighbors graph for microarray image analysis,”
                                                                                  Bioinformatics, vol. 18, no. 1, pp. 141–151, Oct. 2002.
                                                                                  [14] P. Bajcsy, “Gridline: Automatic grid alignment in DNA microarray
                                                                                        scans,” IEEE Trans. Image Process., vol. 13, no. 1, pp. 15–25, Jan.
                                                                                        2004.
                                                                                  [15] M. Steinfath, W. Wruck, H. Seidel, H. Lehrach, U. Radelof, and J.
                                                                                       O’Brien, “Automated image analysis for array hybridization
                                                                                  experiments,” Bioinformatics, vol. 17, no. 7, pp. 634–641, Jul. 1, 2001.
                                                                                  [16] N. Brandle, H. Bischof, and H. Lapp, “Robust DNA microarray
                                                                                  image analysis,” Mach. Vis. Appl., vol. 15, pp. 11–28, 2003.
                                                                                  [17] J. Ho, W. L. Hwang, H. H. S. Lu, and D. T. Lee, “Gridding spot
Figure 12. Gridding of noisy microarray image after refinement process                  centers of smoothly distorted microarray images,” IEEE Trans.
                                                                                  Image Process., vol. 15, no. 2, pp. 342–353, Feb. 2006.
                                                                                  [18] G. Antoniol and M. Ceccarelli, “Microarray image gridding with
                                                                                        stochasticsearch based approaches,” Image Vison Comput., vol. 25,
5. Conclusion                                                                            no. 2, pp. 155–163, Feb. 2007.
In this paper, we have presented a new spatial topology
technique to automatically grid skewed noisy microarray                                                    AUTHORS PROFILE
images. The results of our experiment on skewed                                   Manjunath S.S has received B.E degree in 2000
microarray images on Stanford databases and UNC are                               from Mysore University, Mysore and M.Tech
encouraging. The skew correction algorithm depends on                             degree in 2005 from VTU University, Belgaum,
determination of coordinate addresses of just two positions
                                                                                  Karnataka, India. Currently he is working as a
of the image. The noise removal is done through adaptive
thresholding which makes processes effective. Finally the                         Assistant Professor at Dayananda Sagar College
gridding is performed based on spatial topology of spots.                         of Engineering, Karnataka, India and His
To summarize the three stages of the proposed method                              experience in teaching started from the year
when executed in sequence is effective and                                        2000. Currently his pursuing PhD in mysore
computationally simple.                                                           university. His areas of interests include
                                                                                  microarray image processing, medical image
References                                                                        segmentation and clustering algorithms.
[1] M. B. Eisen, ScanAlyze Nov. 1999 [Online]. Available:
http://rana.lbl. gov/EisenSoftware.htm
[2] J. Buhler, T. Ideker, and D. Haynor, Dapple: Improved techniques              Dr. Lalitha Rangarajan has received Master degrees in
    for finding spots on DNA microarrays UW CSE Tech. Rep. UWTR                   Mathematics from Madras University, India and from the
     2000-08-05, Aug. 2000, pp. 1–12.                                             Department of Industrial Engineering, Purdue University.
[3] Biodiscovery, Inc., ImaGene 2005 [Online]. Available: http://www.             She completed Ph.D in Computer Science from University
     biodiscovery.com/imagene.asp                                                 of Mysore, India. She has been teaching courses in
[4] P. Hegde et al., “A concise guide to cdna microarray analysis,”
     Biotechniques,     vol. 29, no. 3, pp. 548–556, Sep. 2000.
                                                                                  Mathematics, Operations Research and Computer
[5] A. N. Jain, T. Tokuyasu, A. Snijders, R. Segraves, D. Albertso, and           Science, for Master degree students for more than 25
   D. Pinkel, “Fully automatic quantification of microarray image data,”          years. She is presently a Reader at Department of
  Genome Res., vol. 12, pp. 325–332, 2003.                                        Computer Science, University of Mysore, India. Her
[6] A. W. Liew, H. Yan, and M. Yang, “Robust adaptive spot
   Segmentation of DNA microarray images,” Pattern Recognit., vol.
                                                                                  current research interests are Image Retrieval, Feature
    36, pp. 1251–1254, 2003.                                                      Reduction and Bio Informatics. She has more than
[7] K. Hartelius and J. M. Carstensen, “Bayesian grid matching,” IEEE             40 publications in reputed journals and conferences.
   Trans. Pattern Anal. Mach. Intell., vol. 25, no. 2, pp. 162–173, Feb.
   2003.
[8] M. Katzer, F. Kummert, and G. Sagerer, “A Markov random field
   model of microarray gridding,” presented at the ACM Symp. Applied
   Computing 2003.
[9] N. Deng and H. Duan, “The automatic gridding algorithm based on
   Projection     for microarray image,” in Proc. 2004 Int. Conf. Intell.
  Mechatronics




                                                                            334                                 http://sites.google.com/site/ijcsis/
                                                                                                                ISSN 1947-5500

				
DOCUMENT INFO
Description: The International Journal of Computer Science and Information Security is a monthly periodical on research articles in general computer science and information security which provides a distinctive technical perspective on novel technical research work, whether theoretical, applicable, or related to implementation. Target Audience: IT academics, university IT faculties; and business people concerned with computer science and security; industry IT departments; government departments; the financial industry; the mobile industry and the computing industry. Coverage includes: security infrastructures, network security: Internet security, content protection, cryptography, steganography and formal methods in information security; multimedia systems, software, information systems, intelligent systems, web services, data mining, wireless communication, networking and technologies, innovation technology and management. Thanks for your contributions in July 2010 issue and we are grateful to the reviewers for providing valuable comments. IJCSIS July 2010 Issue (Vol. 8, No. 4) has an acceptance rate of 36 %.