# Microarray Spot Finding Example
Date: 2004-08-09

<introduction>

This example shows a simple method for locating spots on a microarray and extracting the intensties of the spots. It can be downloaded from MATLAB Central. http://www.mathworks.com/matlabcentral

</introduction>

## Contents

- Start with clean slate
- Read image file
- Crop specified region
- Display red & green layers
- Convert RGB image to grayscale for spot finding
- Create horizontal profile
- Estimate spot spacing by autocorrelation
- Remove background morphologically
- Segment peaks
- Locate centers
- Determine divisions between spots
- Transpose and repeat
- Put bounding boxes around each spot
- Segment spots from background by thresholding
- Apply logarithmic transformation then threshold intensities
- Try local thresholding instead
- Logically combine local and global thresholds
- Fill holes to solidify spots
- Label spot masks by bounding box
- Extract first spot for measurement
- Measure spot intensity & releative expression level
- Remove background, calculate again and compare measurements
- Set up graphical display for results
- Repeat measurement for all spots
- Export spot data to Excel spreadsheet

## Start with clean slate

    clear           %empty workspace (no variables)
    close all       %no figures
    clc             %empty command window

## Read image file

MATLAB can read many standard image formats including TIFF, GIF and BMP using the `imread` command. In addition, the Image Procesing Toolbox provides support for working with specialized image file formats such as DICOM. This microarray image was stored as a J-PEG file. The image is much larger than the screen size, so `imshow` scales it down to fit and let's you know with a warning message.

    x = imread('MicroArraySlide.JPG');
    imageSize = size(x)
    screenSize = get(0,'ScreenSize')

    iptsetpref('ImshowBorder','tight')
    imshow(x)
    title('original image')

    imageSize =
            3248        1248           3
    screenSize =
               1           1        1024         768
    Warning: Image is too big to fit on screen; displaying at 42% scale.

## Crop specified region

Next we use `imcrop` to extract a region of interest. You can repeat this for all print-tip blocks for a full microarray study.

    y = imcrop(x,[622 2467 220 227]);
    f1 = figure('position',[40 46 285 280]);
    imshow(y)

## Display red & green layers

This image was stored in RGB format. We are only interested in the red and green planes. To extract the red plane, simply index layer 1. For the green plane, layer 2. Custom colormaps make visualization more intuitive. Notice that spot shapes are not necessarily the same in both colors.

    f2 = figure('position',[265 163 647 327]);
    subplot(121)
    redMap = gray(256);
    redMap(:,[2 3]) = 0;
    subimage(y(:,:,1),redMap)
    axis off
    title('red (layer 1)')
    subplot(122)
    greenMap = gray(256);
    greenMap(:,[1 3]) = 0;
    subimage(y(:,:,2),greenMap)
    axis off
    title('green (layer 2)')

## Convert RGB image to grayscale for spot finding

Initially we care more about where the spots are located than their red and green intensities. Converting from RGB color to grayscale allows us to focus first on spot locations.

    z = rgb2gray(y);
    figure(f1)
    imshow(z)

## Create horizontal profile

We are looking for a regular grid of spots so we start by looking at the mean intensity for each column of the image. This will help us identify where the centres of the spots are and where the gaps between the spots can be found.

    xProfile = mean(z);
    f2 = figure('position',[39 346 284 73]);
    plot(xProfile)
    title('horizontal profile')
    axis tight

## Estimate spot spacing by autocorrelation

Ideally the spots would be periodicaly spaced consistently printed, but in practice they tend to have different sizes and intensities, so the horizontal profile is irregular. We can use autocorrelation to enhance the self similarity of the profile. The smooth result promotes peak finding and estimation of spot spacing. The Signal Processing Toolbox allows easy computation of the autocorrelation function using the `xcov` command.

    ac = xcov(xProfile);                        %unbiased autocorrelation
    f3 = figure('position',[-3 427 569 94]);
    plot(ac)
    s1 = diff(ac([1 1:end]));                   %left slopes
    s2 = diff(ac([1:end end]));                 %right slopes
    maxima = find(s1>0 & s2<0);                 %peaks
    estPeriod = round(median(diff(maxima)))     %nominal spacing
    hold on
    plot(maxima,ac(maxima),'r^')
    hold off
    title('autocorrelation of profile')
    axis tight

    estPeriod =
        19

## Remove background morphologically

We can use the spacing estimate to help design a filter to remove the background noise from the intensity profile. We do this with the `imtophat` function from the Image Processing Toolbox. The `strel` command creates a simple rectangular 1D window or line shaped structuring element.

    seLine = strel('line',estPeriod,0);
    xProfile2 = imtophat(xProfile,seLine);
    f4 = figure('position',[40 443 285 76]);
    plot(xProfile2)
    title('enhanced horizontal profile')
    axis tight

## Segment peaks

Now that we have clean and anchored gaps between the peaks, we can number each peak region with the `bwlabel` command. These regions were segmented by thresholding with `im2bw`. The threshold value was automatically determined by statistical properties of the data using `graythresh`. This is a good example of image processing techniques are often useful for 1D data analysis.

    level = graythresh(xProfile2/255)*255
    bw = im2bw(xProfile2/255,level/255);
    L = bwlabel(bw);
    f5 = figure('position',[40 540 285 70]);
    plot(L)
    axis tight
    title('labelled regions')

    level =
        16

## Locate centers

We can extract the centroids of the peaks. These correspond to the horizontal centres of the spots. This is a common blob analysis or feature extraction task that can be done with `regionprops`.

    stats = regionprops(L);
    centroids = [stats.Centroid];
    xCenters = centroids(1:2:end)
    figure(f5)
    hold on
    plot(xCenters,1:max(L),'ro')
    hold off
    title('region centers')

    xCenters =
      Columns 1 through 8
       23.0000   41.0000   60.0000   79.0000   98.0000  119.5000  137.0000  156.0000
      Columns 9 through 10
      175.0000  193.5000

## Determine divisions between spots

The midpoints between adjacent peaks provides grid point locations.

    gap = diff(xCenters)/2;
    first = xCenters(1)-gap(1);
    xGrid = round([first xCenters(1:end)+gap([1:end end])])
    figure(f2)
    for i=1:length(xGrid)
      line(xGrid(i)*[1 1],ylim,'color','m')
    end
    title('vertical separators')

    xGrid =
        14    32    51    70    89   109   128   147   166   184   203

## Transpose and repeat

We just did the analysis on the vertical grid. Now we want to do the same for the horizontal spacing. To do this, we simply transpose the image and repeat all the steps used above. This time without intermediate graphics display commands in order to summarize the mathematical steps of this algorithm.

    yProfile = mean(z');                        %peak profile
    ac = xcov(yProfile);                        %cross correlation
    p1 = diff(ac([1 1:end]));
    p2 = diff(ac([1:end end]));
    maxima = find(p1>0 & p2<0);                 %peak locations
    estPeriod = round(median(diff(maxima)))     %spacing estimate
    seLine = strel('line',estPeriod,0);
    yProfile2 = imtophat(yProfile,seLine);      %background removed
    level = graythresh(yProfile2/255);          %automatic threshold level
    bw = im2bw(yProfile2/255,level);            %binarized peak regions
    L = bwlabel(bw);                            %labeled regions
    stats = regionprops(L);
    centroids = [stats.Centroid];               %centroids
    yCenters = centroids(1:2:end)               %Y parts only
    gap = diff(yCenters)/2;                     %inner region half widths
    first = yCenters(1)-gap(1);

    % list defining vertical boundaries between spot regions
    yGrid = round([first yCenters(1:end)+gap([1:end end])])

    estPeriod =
        20
    yCenters =
      Columns 1 through 8
       24.0000   43.5000   64.0000   83.5000  104.5000  123.5000  144.5000  164.0000
      Columns 9 through 10
      183.0000  203.5000
    yGrid =
        14    34    54    74    94   114   134   154   174   193   214

## Put bounding boxes around each spot

We have now found the rectangular grid. Using pairs of neighboring grid points we can form bounding box regions to address each spot individually. The position and size coordinates of each bounding box were tabulated for convenience into a 4-column matrix called `ROI`, which stands for regions of interest.

    figure(f1)
    imshow(z)
    line(xGrid'*[1 1],yGrid([1 end]),'color','b')
    line(xGrid([1 end]),yGrid'*[1 1],'color','b')
    [X,Y] = meshgrid(xGrid(1:end-1),yGrid(1:end-1));
    [dX,dY] = meshgrid(diff(xGrid),diff(yGrid));
    ROI = [X(:) Y(:) dX(:) dY(:)];
    % first few rows of ROI table
    ROI(1:5,:)

    ans =
        14    14    18    20
        14    34    18    20
        14    54    18    20
        14    74    18    20
        14    94    18    20

## Segment spots from background by thresholding

Applying a single threshold level to the whole image so all spots are detected equally is generally a good idea. However, in this case is doesn't work so well due to large differences in spot brightness.

    fSpots = figure('position',[265 163 647 327]);
    subplot(121)
    imshow(z)
    title('gray image')
    subplot(122)
    bw = im2bw(z,graythresh(z));
    imshow(bw)
    title('global threshold')

## Apply logarithmic transformation then threshold intensities

One way to equalize large variations in magnitude is by transforming intensity values to logarithmic space. This works much better but some weak spots are still missed.

    figure(fSpots)
    subplot(121)
    z2 = uint8(log(double(z)+1)/log(255)*255);
    imshow(z2)
    title('log intensity')
    subplot(122)
    bw = im2bw(z2,graythresh(z2));
    imshow(bw)
    title('global threshold')

    Warning: Conversion rounded non-integer floating point value to nearest uint8 value.

## Try local thresholding instead

Alternatively, the bounding boxes can be used to determine local threshold values for each spot. The code is a little more sophisticated, requiring looping and indexing. Unfortunately, the results are mixed. Weak spots showed up well but spots with bright perimeters were as bad as the original global threshold before log space transformation.

    figure(fSpots)
    subplot(122)
    bw = false(size(z));
    for i=1:length(ROI)
      rows = round(ROI(i,2))+[0:(round(ROI(i,4))-1)];
      cols = round(ROI(i,1))+[0:(round(ROI(i,3))-1)];
      spot = z(rows,cols);
      bw(rows,cols) = im2bw(spot,graythresh(spot));
    end
    imshow(bw)
    title('local threshold')

## Logically combine local and global thresholds

Since both have their merits, let's combine the best of both approaches. This can be done using logial operation on the binary masks. These spot segmentation results are indeed much better.

    figure(fSpots)
    subplot(121)
    bw = im2bw(z2,graythresh(z2));
    for i=1:length(ROI)
      rows = round(ROI(i,2))+[0:(round(ROI(i,4))-1)];
      cols = round(ROI(i,1))+[0:(round(ROI(i,3))-1)];
      spot = z(rows,cols);
      bw(rows,cols) = bw(rows,cols) | im2bw(spot,graythresh(spot));
    end
    imshow(bw)
    title('combined threshold')
    subplot(122)
    imshow(z)
    title('linear intensity')

## Fill holes to solidify spots

The silhouettes of some spots still contained pinholes. The whole image could be filled using a single call to `imfill` but this may not be a good idea. Notice that some spots run together. If four mutually adjacent spots (sharing a common corner) were all joined at their edges then a single function call would incorrectly fill in the common corner as well. To avoid that possibility, it's good insurance to fill each spot one bounding box region at a time by looping. Indeed, the spot segmentation now looks quite good.

    figure(fSpots)
    subplot(121)
    warning off MATLAB:intConvertOverflow
    for i=1:length(ROI)
      rows = round(ROI(i,2))+[0:(round(ROI(i,4))-1)];
      cols = round(ROI(i,1))+[0:(round(ROI(i,3))-1)];
      bw(rows,cols) = imfill(bw(rows,cols),'holes');
    end
    imshow(bw)
    title('filled pinholes')

## Label spot masks by bounding box

If the gridding went well, all spots should be a single color. The results here are pretty good. There is still room for improvement.

TODO List:

- Due to slightly irregular spacing, for some spots a few pixels were mislabeled. With additional processing, the algorithm could be extended to reclassify these stray pixels.

- The crescent shaped spot in row 8, column 4 could be completed to be more circular by using the 'ConvexImage' return value from `regionprops`.

- The few stray pixels that are not attached to any spots could be removed as well.

However, in this case the spot segmentation is good enough to proceed.

    L = zeros(size(bw));
    for i=1:length(ROI)
      rows = ROI(i,2)+[0:(ROI(i,4)-1)];
      cols = ROI(i,1)+[0:(ROI(i,3)-1)];
      rectMask = L(rows,cols);
      spotMask = bw(rows,cols);
      rectMask(spotMask) = i;
      L(rows,cols) = rectMask;
    end
    map = [0 0 0; 0.5+0.5*rand(length(ROI),3)];
    figure(f1)
    imshow(L+1,map)

## Extract first spot for measurement

We will now examine the first spot closely to see how we can measure its red and green intensities, and ultimately quantify its gene expression value. The measurement technique can then be repeated for all spots.

    rect = ROI(1,:);                            %[X Y dX dY]
    spot = imcrop(y,rect);                      %region around spot
    figure(f1)
    imshow(spot,'notruesize')

## Measure spot intensity & releative expression level

We now simply calculate the nominal intensity over the spot for both the red and green layers. A measure of gene expression level can then be calculated from the two color intensities. Here a simple log-ratio measurement is shown. Other more robust measures could be used instead. You could also perform some analysis of the quality of the spot.

    mask = imcrop(L,rect)==1;
    for i=1:2
      layer = spot(:,:,i);
      intensity(i) = double(median(layer(mask)));
    end
    intensity
    expressionLevel = log(intensity(1)/intensity(2))

    intensity =
        32    81
    expressionLevel =
       -0.9287

## Remove background, calculate again and compare measurements

If you noticed, the background intensity around the spot was not zero. This could bias results. To see how much difference it makes, we can perform background subtraction around all spots, again using `imtophat` but this time in 2D on the image using a disk shaped structuring element. Then we can calculate color intensities and relative expression level again to see what effect background bias had on the measurement. In this case the measurement shows more downregulation with background removed.

    seDisk = strel('disk',round(estPeriod));
    spot2 = imtophat(spot,seDisk);
    for i=1:2
      layer = spot2(:,:,i);
      intensity(i) = double(median(layer(mask)));
    end
    intensity
    expressionLevel = log(intensity(1)/intensity(2))

    intensity =
        14    70
    expressionLevel =
       -1.6094

## Set up graphical display for results

It is helpful to see red and green intensity values overlayed onto the respective color images to gain confidence that measured intensities make sense. It is also be helpful to overlay quantitative expression levels onto the original image to provide additional visual assurance of measurement results. The rectangular grid also helps correlate measured values between images. The flexibility of MATLAB's powerful Handle Graphics engine allow custom graphics like this to be set up quickly and easily.

    f7 = figure('position',[52 94 954 425]);
    ax(1) = subplot(121);
    subimage(y(:,:,1),redMap)
    title('red intensity')
    ax(2) = subplot(122);
    subimage(y(:,:,2),greenMap)
    title('green intensity')
    f8 = figure('position',[316 34 482 497]);
    ax(3) = get(imshow(y,'notruesize'),'parent');
    title('gene expression')
    for i=1:3
      axes(ax(i))
      axis off
      line(xGrid'*[1 1],yGrid([1 end]),'color',0.5*[1 1 1])
      line(xGrid([1 end]),yGrid'*[1 1],'color',0.5*[1 1 1])
    end

## Repeat measurement for all spots

We now repeat the spot extraction and intensity calculation for all the spots in the grid. Here the measured values were tabulated as additional columns beside the ROI positions for each spot into a new matrix called `spotData`.

    figure(f7), figure(f8)
    spotData = [ROI zeros(length(ROI),5)];
    for i=1:length(ROI)
      spot = imcrop(y,ROI(i,:));                            %raw image
      spot2 = imtophat(spot,seDisk);                        %background removed
      mask = imcrop(L,ROI(i,:))==i;                         %spot mask
      for j=1:2
        layer = spot2(:,:,j);                               %color layer
        intensity(j) = double(median(layer(mask)));
        text(ROI(i,1)+ROI(i,3)/2,ROI(i,2)+ROI(i,4)/2,sprintf('%.0f',intensity(j)),...
          'color','y','HorizontalAlignment','center','parent',ax(j))
        rawLayer = spot(:,:,j);
        rawIntensity(j) = double(median(layer(mask)));
      end
      expression = log(intensity(1)/intensity(2));
      text(ROI(i,1)+ROI(i,3)/2,ROI(i,2)+ROI(i,4)/2,sprintf('%.2f',expression),...
        'color','w','HorizontalAlignment','center','parent',ax(3))
      drawnow
      spotData(i,5:9) = [intensity(:)' expression rawIntensity(:)'];
    end

## Export spot data to Excel spreadsheet

MATLAB can write to many standard formats. We will use `xlswrite` to save the `spotData` to an Excel workbook.

TODO list:

- prepend column names first (see `xlswrite` doc example using cell arrays)

- programmatically open spreadsheet in Excel (see `winopen` doc)

    xlswrite('microarray.xls',spotData)