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Chapter 4
Microarray Gridding
4.1 Introduction
The discovery of microarray technology in 1995 has opened new avenues for
investigating gene expressions (Schena et al., 1995) and introduced new information
problems (Fenstemacher, 2005; MacMullen et al., 2005). Researchers have developed
several microarray image processing methods and modeling techniques that are
specific to DNA microarray analysis (Quackenbush, 2001) with the objective to draw
biologically meaningful conclusions (Bajcsy et al., 2004; Baldi et al., 2001; Golub et
al., 1999; Moore, 2000). However, the analysis of DNA microarray data consists of
several processing steps (Goryachuv et al., 2001) that can significantly deteriorate the
quality of gene expression information, and hence lower our confidence in any
derived research result. Thus, understanding microarray image processing steps
(Bajcsy, 2006) becomes critical for performing optimal microarray data analysis and
deriving biologically meaningful conclusions. Microarray image analysis consists of
several steps, of which the first critical step is referred to as addressing or gridding
(Brandle et al., 2003). This is the process of identifying the areas within an image that
contain a single spot, which represents the gene and identifying which subgrid and then
which row and column within that subgrid, the spot belongs to. Although this process
may seem relatively straightforward, it is complicated since the quality of images
suffers from the existence of noise (dust on the slide), artifacts (inner holes and
* Some parts of the material in this chapter are appeared / communicated in the following research papers:
1. Skew Correction and Noise Reduction for Automatic Gridding of Microarray Images,
International Journal of Computer Science and Information Security, Vol. 8(4), pp: 326-334,
2010.
2. Automatic Technique for Gridding of Skewed and Noisy Microarray Images, Journal of
Computational Intelligence in Bioinformatics, Vol. 3(2), pp: 185-198, 2010.
3. Automatic Gridding of Noisy Microarray Images Based on Coefficient of Variation,
International Journal of Computer Science Issues.(communicated)
Microarray Gridding 68
scratches) and uneven background, while some spots are poorly contrasted and ill-
defined. In addition, spots vary in size and position due to the presence of noise during
the sample preparation and hybridization processes. Thus there may be rotations,
misalignments and local deformations of the ideal rectangular grid (Bajcsy, 2005).
4.2 Proposed Techniques for Gridding
We propose three techniques for automatic gridding of skewed and noisy microarray
images. In the first method, the microarray image is skew corrected, noise removed
using adaptive thresholds computed on various segments, spatial topology of spots
detected, gridding performed and finally grids are refined.
In the second method the microarray image is skew corrected, noise removed using
adaptive thresholds computed on various segments, spatial topology of spots detected,
bounding boxes are drawn over the spots.
In the third method, the projection profiles of the binarized image are obtained, noise
removed using morphological operations. The unduly non uniform distance between
grid lines in noisy microarray images are corrected using coefficient of variation (CV)
of the successive differences in the gridding locations.
Figure 4.1 shows the block diagram which describes the salient stages of the proposed
methods for automatic gridding of noisy microarray images.
Microarray Gridding 69
Figure 4.1: Stages of automatic gridding of noisy microarray images
4.2.1 Skew Detection and Correction
This section describes the first stage of microarray gridding, skew detection and
correction. In this section an approach for skew detection and correction of
microarray images based on corner positions of the subgrid is presented.
Skew Detection
First step in this process is to convert the RGB image to gray scale image. Figure 4.2
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 image rowwise. The
very first pixel in the image is assigned the coordinate address (topx, topy). Scan the
gray scale image columnwise. The very first pixel in the image is assigned the
Microarray Gridding 70
coordinate address (leftx, lefty). xmid is the mid value of columns and ymid is the
mid value of rows.
If topx < xmid and lefty > ymid the skew is clockwise (Figure.4.2)
If topx > xmid and lefty < ymid the skew is anticlockwise (Figure.4.3)
Figure 4.2: Parameters for clockwise skew detection
Figure 4.3: Parameters for anticlockwise skew detection
The clockwise skew angle can be found using the formula
Φ = (atan topx – leftx ) / (lefty – topy)
The anticlockwise skew angle can be found using the formula
Φ = (atan lefty – topy ) /( topx - leftx)
Skew Correction
The new coordinate address xx and yy are computed as given below.
Skew correction for clockwise tilt:
It is required to perform rotation about (leftx, lefty) by Φ in anticlockwise direction.
xx = (leftx + x-leftx) * cos (Φ ) – (y-lefty) * sin(Φ )
yy =( lefty + x-leftx) * sin (Φ ) + (y-lefty) * cos(Φ )
Microarray Gridding 71
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 and y varies from 1 to number of rows
The minxx and minyy are computed and translated to (0,0). The new image Ll with
the coordinate address is given below:
xx1=xx-minxx
yy1=yy-minyy is the skew corrected image.
Figures 4.4 and 4.5 (Image ID: 62919) shows the clockwise skewed image and skew
corrected image.
Figure 4.4: Clockwise Skewed Image ID: 62919
Figure 4.5: Skew Corrected Image ID: 62919
Microarray Gridding 72
Table 4.1: Estimated angle (φ) and execution time (τs) of the proposed skew correction
technique
Image ID Estimated angle
in degrees (Φ)
Execution time
in seconds (τs)
1c7b060rex2 2.0651 13.14
1c4bo64rex2 2.5323 12.12
s62919 4.8253 15.15
40031 3.7653 13.54
4.2.2 Adaptive Threshold Computation and Filtering
Threshold computation and filtering technique is used to filter insignificant spots so
that automatic gridding procedure becomes easier. Filtering is performed in 2 steps
which have been described in section 3.2.2.1. Subsequent to filtering, gridding is
performed.
4.2.3 Automatic Gridding Process
In this section, a novel approach for automatic gridding of skewed and noisy
microarray images is presented.
4.2.3.1 Spatial Topology Method
Automatic gridding is performed in 3 steps which are described in the 3 subsections
below:
Determination of position of grid lines
For each connected component in the filtered image, rmin, rmax, cmin, cmax are
determined as shown in Figure 4.6. 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 are done on image ID (62919).
Microarray Gridding 73
rmin:
rmax:
Figure 4.6: Computation of rmin, rmax, cmin & cmax of a spot
The steps below describe determination of horizontal grid lines.
1) The rmin array is sorted in ascending order
sorted_ rmin:
Microarray Gridding 74
2) The differences of successive rmin values in the sorted rmin array are calculated.
diff_rmin:
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 3 in diff_rmin array. The third
element of rmin array is 9. Hence examination of diff_rmin suggests a grid line at row
9. Similarly it is understood that successive values of grid rmin.
grid_ rmin:
Similarly grid_rmax is determined. Shown below are sorted_rmax, diff_rmax,
grid_rmax values.
sorted_ rmax:
diff_rmax:
grid_ramx:
Microarray Gridding 75
Finally, positions of horizontal gridlines are determined by finding average of rows
suggested by grid_rmin and grid_rmax contents. Thus horizontal gridlines are placed
at rows 9, 25 [(25+25)/2], 41 [(38+43)/2], 57 [(55+60)/2]…etc.
In a similar manner vertical gridlines are positioned using sorted_cmin, diff_cmin,
grid_cmin, sorted_cmax diff_cmax, grid_cmax.
Grid Refinement Algorithm
The algorithm described in the section before, will draw 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 several consecutive rows or columns. In these
images, there will be irregular spacing between gridlines. Figure 4.7, 4.8 show sparse
gridding in horizontal and vertical direction. In such cases the refinement algorithm
suggested can be used to draw additional / missing grid lines. Grid refinement process
is used 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 4.9 shows both horizontal (figure 4.7) and vertical (figure 4.8) gridlines placed
before refinement process. Figure 4.10 is the gridding result obtained after refinement.
Observe that there are more grid lines here when compared to figure 4.9. Figures 4.11
and 4.12 show gridding done by projection profiles and standard deviation methods.
Observation reveals that, these have less and nonuniform grid lines.
The results are summarized in the table 4.2. Table 4.2 shows comparison of proposed
method with projection profile algorithm and standard deviation algorithm to perform
gridding. The comparison was performed on 10 sets of microarray images and it is
evident that proposed method performs better than other existing approaches.
Expected number of rows and columns are inferred by the number of connected
components across each row and column.
Microarray Gridding 76
Table 4.2: Performance comparison of proposed spatial topology method with other
approaches
Method Image ID Expected
Number
of Rows
Expected
Number of
Columns
Number
of Rows
obtained
Number of
Columns
obtained
Total
Error
(%)
Gridding
using
Standard
Deviation
62919 29 30 27 27 8.474576
22593 17 15 21 15 12.5
37993 29 29 27 29 3.448276
34212 20 21 21 21 2.439024
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
Gridding
using
Projection
Profile
62919 29 30 27 29 5.084746
22593 17 15 20 15 9.375
37993 29 29 26 26 10.34483
34212 20 21 20 21 0
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
Gridding
using
Proposed
method
62919(SMD) 29 30 29 30 0
22593(SMD) 17 15 17 15 0
37993(UNC) 29 29 29 29 0
34212(UNC) 20 21 20 21 0
34217(UNC) 18 23 18 23 0
34143(UNC) 22 23 23 23 2.222222
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
Microarray Gridding 77
Figure 4.7: Filtered image with sparse horizontal grid lines
Figure 4.8: Filtered image with sparse vertical grid lines
Figure 4.9: Gridding of noisy microarray image before refinement process
Microarray Gridding 78
Figure 4.10: Gridding of noisy microarray image after refinement process
Figure 4.11: Gridding of noisy microarray image by projection profile method
Figure 4.12: Gridding of noisy microarray image by standard deviation method
Microarray Gridding 79
4.2.3.2 Bounding Box Method
In this approach, the procedure of adaptive threshold computation and filtering is
discussed in 3.2.2.1 is used. Subsequently, the procedure of spatial topology
computation discussed in section 4.2.3.1 is used. Instead of drawing grid lines as
discussed in 4.2.3.1, rectangular grid (Bounding box) is constructed around each spot
as shown in figure 4.13.
Figure 4.13: Coordinate system of the spot for rectangular grid
Construction of rectangular grid
Consolidated rmin, rmax, cmin and cmax are used to build the grid structure. Figure
4.13, describes the coordinate system for the grid structure using above mentioned
values. Point A coordinates (grid_rmin, grid_cmin) represents top left corner, B
coordinates (grid_rmin, grid_cmax) represents top right corner, C coordinates
(grid_rmax, grid_cmax) represents bottom right corner and finally D coordinates
(grid_rmax, grid_cmin) represents bottom left corner of the rectangular grid. The
major advantage of the proposed method is that the next stage of the microarry image
analysis, segmentation can be performed easily and with minimum errors.
Figure 4.14 shows one subgrid of noisy microarray image. As discussed in section
3.2.2.1, Adaptive threshold is used to perform filtering. Figure 4.15 shows filtered
image of figure 4.14 and the observation reveals that, most of the contaminated
(insignificant, noisy) pixels are removed. Figure 4.16 shows noisy microarray image
and in figure 4.17 shown is the filtered image using proposed approach. Figure 4.18,
4.19 and 4.20 shows the gridding of the noisy microarray images using the proposed
Bounding Box method.
Microarray Gridding 80
The results are summarized in the table 4.3. Table 4.3 shows the comparison of
proposed Bounding Box method with projection profile and standard deviation
methods to perform gridding. The comparison was performed on 10 sets of
microarray images and it is evident that proposed method performs better than other
existing approaches. Actual number of connected components are inferred by the
number of connected components across each row and column.
Figures 4.21 and 4.22 show gridding done by projection profiles and standard
deviation methods. Observation reveals that, these have nonuniform grid lines.
Figure 4.14: Subgrid of noisy microarray image, Image ID: 32919
Figure 4.15: Filtered image using adaptive threshold, Image ID: 32919
Microarray Gridding 81
Figure 4.16: Subgrid of noisy microarray image, Image ID: 35964
Figure 4.17: Filtered image using adaptive threshold, Image ID: 35964
.
Figure 4.18: Gridding of noisy microarray image using proposed Bounding Box method,
Image ID: 38052
Microarray Gridding 82
Figure 4.19: Gridding of noisy microarray image using our method, Image ID: 75186
Figure 4.20: Gridding of noisy microarray image using our method, Image ID: 37010
Figure 4.21: Gridding of noisy microarray image by projection profile method
Microarray Gridding 83
Figure 4.22: Gridding of noisy microarray image by standard deviation method
Table 4.3: Performance comparison of proposed Bounding Box method with other methods
Method Image ID Actual Number
of connected
components
Number of
components
obtained
Error (%)
Standard
deviation
62919(SMD) 871 750 13.89
22593(SMD) 255 215 15.68
37993(UNC) 841 750 10.82
34212(UNC) 420 350 16.66
34217(UNC) 414 348 15.94
34143(UNC) 506 430 15.01
34134(UNC) 529 440 16.82
52694(SMD) 812 680 16.25
57852(SMD) 783 660 15.70
66357(SMD) 812 678 16.50
Projection
profile
62919(SMD) 871 800 8.15
22593(SMD) 255 225 11.76
37993(UNC) 841 785 6.65
34212(UNC) 420 375 10.71
34217(UNC) 414 368 11.11
34143(UNC) 506 450 11.06
34134(UNC) 529 480 9.26
52694(SMD) 812 740 8.86
57852(SMD) 783 700 10.60
66357(SMD) 812 690 15.02
Proposed 62919(SMD) 871 831 4.5
22593(SMD) 255 235 7.84
37993(UNC) 841 810 3.68
34212(UNC) 420 390 7.14
34217(UNC) 414 389 6.036
34143(UNC) 506 480 5.1383
34134(UNC) 529 500 5.4820
52694(SMD) 812 800 1.4778
57852(SMD) 783 750 4.21455
66357(SMD) 812 790 2.70
Microarray Gridding 84
4.2.3.3 Coefficient of Variation method
Automatic gridding of noisy microarray images is performed in 5 steps which are
described in the subsections below. Figure 4.23 shows the block diagram which
describes the salient stages of the proposed Coefficient of variation method for
automatic gridding of noisy microarray images.
Figure 4.23: Stages of automatic gridding of noisy Microarray images
4.2.3.3.1 Basic method of vertical and Horizontal Projection Profiles.
Let the size of the given gray scale image matrix be m x n where m is the number of
rows and n is the number of columns. Let intensity in noise free gray scale image be F
(i, j) at row i and column location j. Then the vertical projection profile P is calculated
using:
P (j) = ∑ i=1to m F (i, j) , for j=1,2,..n (1)
A typical vertical profile for a 4 x 4 subarray is shown in Figure 4.24. The locations of
regional minima (valley points) of the profile give the column positions of the vertical
grid lines (Figure 4.24).
Microarray Gridding 85
Due to the presence of noise in the subarray, a valley (region between adjacent peaks)
of the vertical profile may contain more than one local minimum. This causes
ambiguity in determining the location of the vertical grid line in that valley region.
Therefore the vertical profile signal should be processed further to uniquely determine
the position of vertical grid lines. This disadvantage is overcome by our proposed
method where projection profiles are obtained after binarizing the subarray image.
4.2.3.3.2 Coefficient of Variation method
In the proposed method, the projection profiles are first transformed into the
corresponding 2D binary images and then further processed to achieve efficient
automatic gridding.
Binarization
Binarization is converting the given gray scale image into its equivalent two level
quantized black and white image. Let F be the gray scale image matrix of size m x n
and T be the threshold level. The spots of the subarray have higher pixel intensity than
the background region. Therefore the spots can be segmented by binarizing the
subarray image using a suitable threshold. Then the binary map B of F is given by,
(2)
Figure 4.24: 4x4 subarray and its vertical profile
Microarray Gridding 86
In the resulting binary image, 1’s represent the pixels whose intensities are greater
than the threshold level and 0’s the other set of pixels. Thus, 1’
s represent the
foreground and 0’s the background. Now consider the vertical projection profiles
after binarization. A valley region (interval between adjacent foreground columns) of
a noise free subarray is represented by all 0’s. Therefore the corresponding vertical
profile (sum of the column values) has zero magnitude in the valley region as shown
in Figure 4.25. Thus the spot region and the valley region can be clearly separated.
Vertical Projection Profile as an image
In our method, the projection profiles obtained after binarization are converted into
corresponding images as described below. After binarization the vertical projection
profile is given by,
V (j) = ∑ i =1 to m G (i, j), for j=1, 2...n (3)
Figure 4.26(a) shows the histogram of the foreground pixels in columns. Observe the
pyramid like structure in Figure 4.26(a).
From Pyramids Extended to Bounding Boxes
The pyramids are enclosed in vertically extended bounding boxes as shown in Figure
4.26(b). The width of each extended bounding box is equal to the base width of the
corresponding pyramid. The heights of the boxes are extended from bottom of the
image all the way to the top for easy manipulation. Here, the heights of the boxes are
Figure 4.25: 4x4 subarray and its vertical profile after binarization
Microarray Gridding 87
immaterial whereas the width and the horizontal spacing’s between the adjacent boxes
determine the vertical grid lines. In general, almost equally spaced vertical boxes
represent the spot columns of the subarray. The black bars of Fig. 4.26(b) separate the
successive spot columns of the subarray. Therefore, the vertical bisectors of black
bars are the vertical gridlines. But because of noise, distortion and mixed distribution
of foreground-background intensities, certain pre-processing is required to remove the
noise and other irregularities to get the correct result.
Figure 4.26 (a) Histogram of subarray in Figure 4.25 (b) Extended Bounding Box image
Drawing vertical grid lines from extended bounding box image
The algorithm given here is proposed for vertical grid line determination in case of
noisy microarray images.
Algorithm
1. Select a suitable gray threshold level.
2. Binarize the subarray using this threshold.
3. Get the vertical profile.
4. Convert the profile into its equivalent binary profile image.
5. Find the bounding boxes of all the profile pyramids by vertically extending them.
6. Draw vertical bisectors for the black bars of the extended bounding box image to
get the vertical grid lines
Horizontal gridlines are obtained similarly using the horizontal profile.
Gridding in noisy Microarray images
Noise in the image produce false spurious, missing and misplaced ridges and valley
regions in the projection profiles and in turn generate spurious, missing and misplaced
grid lines. The effect of subarray irregularities on false gridding can be controlled by
proper selection of threshold level for binarization. A high threshold level suppresses
Microarray Gridding 88
many pixels, from the foreground. This results in false valleys in the profile. Figure
4.27(a) is binarized subarray using a high threshold. Observe that, there are few pixels
in the foreground. Figure 4.27(b) is the vertical profile of array in Figure 4.27(a).
Figure 4.27(c) is the extended bounding. Figure 4.27(d) shows the ill spaced vertical
grid lines.
Figure 4.27: Effect of high threshold Binarization (a) Binarized subarray
(b) Vertical Profile image (c) Extended box profile (d) Incorrect vertical gridding
A low threshold binarization retains most of the pixels in the background
region. Therefore the adjacent spot columns will merge and the bases of the pyramids
touch each other. This results in merged white bars and missing black bars in the box
profile image as shown in Figure 4.28. Here, the first two pyramids touch each other.
Therefore, the connected components labelling technique used in our method
generates single white bar for these two spot columns. Also the valley between them
has disappeared in Figure 4.28(b) and 4.28(c). This results in incorrect gridding as
depicted in Figure 4.28(d).
Figure 4.28: Effect of low threshold Binirization (a) Binarized subarray (b) Vertical Profile
image (c) Extended box profile (d) Incorrect vertical gridding
Both over thresholding and under thresholding result in irregular spacing of gridlines
(figures 4.27(d) and 4.28(d)). The correct threshold is that level which generates
almost equally spaced grid lines. The proposed procedure for adjusting grid locations
in case of unduly non uniform grid lines is given as follows:
a b c d
a b c d
Microarray Gridding 89
Let x(i) denote the horizontal coordinate value of the i th
grid line for i=1,2,...,k where
k is the total number of vertical gridlines as shown in figure 4.29.
Let d(j) represent the separation (space) between successive gridlines, for j=1,2,...(k-
1) where,
d(j) = x(j+1) − x(j) (4)
For an ideal subarray, spatial separations d(j)’s all equal. Under this condition, the
coefficient of variation (ratio of standard deviation to mean) for d (j)’s, is zero. In a
practical subarray, d(j)’s are very nearly equal and the coefficient of variation (CV) is
less. The coefficient of variation (CV) for d(j)’s is a measure of the diversity among
the values of d(j)’s. When the binarization threshold level varies the corresponding
d(j)’s also vary and hence the resulting CV’s also vary. The best threshold is that
value which yields minimum CV. This gives the best gridline distribution. Therefore,
in the proposed method, binarization threshold level is varied in steps, from a low
value to a high value and the corresponding CV’s are calculated for each threshold
value. Then that threshold value which results in minimum CV is chosen as the best
candidate for binarization and the resulting gridlines give the best gridding for that
subarray. The algorithm is given below.
Figure 4.29 Vertical gridlines with their marked separations, d(j)’s
0 x(1) x(2) x(3) x(k-1) x(k)
d(2) d(1) d(k-1)
Microarray Gridding 90
Algorithm: Determination of the correct threshold level for binarization and the
best gridding
Normalize the gray levels of the image in the range 0 to1.
Choose a suitable lower threshold value TL (1%), suitable upper threshold value TH
(85%) and an appropriate increment value ΔT (5%).
1. Set T to its initial value as T = TL.
2. Set the iteration count ic=1.
3. Binarize the subarray, get the vertical grid lines and x(i)’s for this T using the
algorithm.
4. Determine d(j)’s as given by Eq. (4) for this set of grid lines.
5. Calculate the Coefficient of Variation CV(ic) for this set of d.
6. Increment T as T = T+ΔT, where ΔT is the increment term.
7. If T > TH go to step 9, else
8. Set the iteration counter ic to its next value as ic=ic+1 and go back to step 3.
9. Determine the minimum among CV’s. Find the iteration count at which it occurs
and get the corresponding value of T. For this T, get x(i)’s, the locations of vertical
grid lines, as in Algorithm .
The horizontal gridlines are similarly obtained using the horizontal profile image.
4.2.3.3.3 Experimental Results
In this section the performance of the proposed approach is evaluated on noisy
microarray images from SMD (Stanford Microarray Database). The algorithm was
executed on Pentium Centrino Duo processor with 2 GB RAM. For a subarray (18,
18), of an image id (37010), the CV versus T values are shown in Table 4.6. Here, TL
= 0.1, TH = 0.85 and ΔT = 0.05. From Table 4.4, we see that minimum CV is 0.030,
occuring at iteation 4 and the corresponding threshold value (T) is 0.25. Figure 4.30(a)
shows the gridding of the subarray image (37010) using proposed method and figures
4.30(b) and 4.30(c) show the gridding of the same image with the standard deviation
and projection profile methods. All grid lines in figure 4.30(a) are drawn more or less
equally spaced and no grid line is drawn over the spots. Observe in figures 4.30(b),
4.30(c) there are grid lines running through the spots.
Microarray Gridding 91
Table 4.4: Determination of grid lines
Iteration
Count ( ic )
Threshold
Level ( T )
Coefficient of
Variation ( CV ) Remarks
1 0.10 0.314 T = TL
2 0.15 0.033
3 0.20 0.037
4 0.25 0.030 CV minimum
5 0.30 0.033
6 0.35 0.040
7 0.40 0.045
8 0.45 0.051
9 0.50 0.250
10 0.55 0.252
11 0.60 0.252
12 0.65 0.338
13 0.70 0.338
14 0.75 0.336
15 0.80 0.343
16 0.85 0.515 T = TH
Microarray Gridding 92
Figure 4.30 (a): Gridding of noisy microarray image using Coefficient of variation method
Figure 4.30 (b): Gridding of noisy microarray image by standard deviation method
Figure 4.30 (c): Gridding of noisy microarray image by projection profile method
Microarray Gridding 93
4.3 Conclusion
In this chapter, three novel methods for automatic gridding of noisy, skewed
microarray image are presented. In the first method, spatial topology technique was
used to automatically grid skewed, noisy microarray images. The results of our
experiment on skewed noisy microarray images on SMD and UNC are encouraging.
The skew correction algorithm depends on determination of coordinate addresses of
just two positions of the image. The noise removal is done through adaptive
thresholding which makes processes effective. Finally the gridding is performed
based on spatial topology of spots. In the second method, rectangular grid (Bounding
box) was used on each spot to automatically grid noisy, skewed microarray images.
The noise removal is performed through adaptive thresholding, the entire process is
robust, in the presence of noise, skew, artifacts and weakly expressed spots. Finally
the gridding is performed by drawing Bounding Box surrounding the spots in the grid.
In the third method, the projection profiles of the binarized image are obtained, noise
removed using morphological operations. The unduly non uniform distance between
grid lines in noisy microarray images are corrected using coefficient of variation (CV)
of the successive differences in the gridding locations.
To summarize the stages of the proposed methods when executed in sequence, it is
effective and computationally simple.