Serendipity
b8a8ff2bc6
实现内容： - 网格划分：投影分析 + 自相关估周期 + 白顶帽去背景 + 质心提取 - 三种阈值分割：人工阈值、Otsu自动阈值、迭代阈值 - TV去噪（Chambolle投影算法） - 后处理：去小连通域 + 保留最大连通域 - 完整可视化：网格叠加、阈值对比、收敛曲线、分割结果 参考MATLAB代码：NewGridAndCV/demo_GriddingAndCV.m
409 lines
15 KiB
Matlab
409 lines
15 KiB
Matlab
%% Microarray Spot Finding Example
|
|
% 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
|
|
%
|
|
% Copyright 2004-2010 RBemis The MathWorks, Inc.
|
|
|
|
%% 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')
|
|
|
|
%% 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]);
|
|
y=imread('test.tif');
|
|
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
|
|
|
|
%% 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')
|
|
|
|
%% 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')
|
|
|
|
%% 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')
|
|
|
|
%% 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])])
|
|
|
|
%% 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)
|
|
figure()
|
|
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)); %xGrid和yGrid中存储了分格子的数据
|
|
[dX,dY] = meshgrid(diff(xGrid),diff(yGrid));
|
|
ROI = [X(:) Y(:) dX(:) dY(:)];
|
|
% first few rows of ROI table
|
|
ROI(1:5,:)
|
|
|
|
%% 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')
|
|
|
|
%% 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) %最终的分割结果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))
|
|
|
|
%% 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))
|
|
|
|
%% 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)
|