MATLAB: Finding inverse cross-correlation

cross_correlationrespirometry

Hello,

I am trying to compute the inverse cross-correlation of two signals ; that is, I have two signal A and B such that A should reach its positive peak when B hits its negative peak, and I want to find the delay between the two. How can I do this in Matlab?

If it helps, I am working with respiratory data, specifically co2 and 02 volume concentrations. Our respirometer starts collecting co2 data about 1-2 seconds before it starts with the o2 – hence the delay we are trying to account for.

edit: I have enclosed a graph of some sample data to be corrected – the blue signal is oxygen concentration and the orange signal is co2 concentration. As you can see, the o2 concentration is delayed (in this case) by about 1.5 seconds, which is caused entirely by our instrumentation. The goal would be to have a function which could calculate the maximal inverse cross-correlation, so that the maxima of one signal match up with the minima of the other.

Thank you!

Best Answer

Although often true, and maybe true for your signals, the best signal overlap is not guaranteed to occur when the cross correlation is maximum. That is a very common misconception. A simple thought experiment should reveal why. That is why I never use it and use normalized cross correlation instead. There is a function for that in the Image Processing Toolbox called normxcorr2(), however it should work for 1-D signals also I believe. I'm attaching a 2D pattern recognition demo (sorry I don't have any 1-D signal demo for it all ready to go).

Related Solutions

MATLAB: Correlation between the two images;

xcorr2 is not the best for finding the object unless you know the exact peak auto correlation value. A much more robust method is to use normxcorr2() where you simply have to look for the max. (If you look for the peak using xcorr2(), it will not necessarily lie where your template occurs in the image, it could be over any old bright part of the image). Here is a demo using normxcorr2:

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
imtool close all;  % Close all imtool figures.
clear;  % Erase all existing variables (which I know Jan hates).
workspace;  % Make sure the workspace panel is showing.
format longg;
format compact;
fontSize = 20;
% Check that user has the Image Processing Toolbox installed.
hasIPT = license('test', 'image_toolbox');
if ~hasIPT
  % User does not have the toolbox installed.
  message = sprintf('Sorry, but you do not seem to have the Image Processing Toolbox.\nDo you want to try to continue anyway?');
  reply = questdlg(message, 'Toolbox missing', 'Yes', 'No', 'Yes');
  if strcmpi(reply, 'No')
    % User said No, so exit.
    return;
  end
end
% Read in a standard MATLAB color demo image.
folder = fullfile(matlabroot, '\toolbox\images\imdemos');
baseFileName = 'peppers.png';
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);
if ~exist(fullFileName, 'file')
  % Didn't find it there.  Check the search path for it.
  fullFileName = baseFileName; % No path this time.
  if ~exist(fullFileName, 'file')
    % Still didn't find it.  Alert user.
    errorMessage = sprintf('Error: %s does not exist.', fullFileName);
    uiwait(warndlg(errorMessage));
    return;
  end
end
rgbImage = imread(fullFileName);
% Get the dimensions of the image.  numberOfColorBands should be = 3.
[rows columns numberOfColorBands] = size(rgbImage);
% Display the original color image.
subplot(2, 2, 1);
imshow(rgbImage, []);
axis on;
title('Original Color Image', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
smallSubImage = imcrop(rgbImage, [192 82 60 52]);
subplot(2, 2, 2);
imshow(smallSubImage, []);
axis on;
title('Template Image to Search For', 'FontSize', fontSize);
% Search the red channel for a match.
correlationOutput = normxcorr2(smallSubImage(:,:,1), rgbImage(:,:,1));
subplot(2, 2, 3);
imshow(correlationOutput, []);
title('Correlation Output', 'FontSize', fontSize);
[maxCorrValue, maxIndex] = max(abs(correlationOutput(:)));
[ypeak, xpeak] = ind2sub(size(correlationOutput),maxIndex(1));
corr_offset = [(xpeak-size(smallSubImage,2)) (ypeak-size(smallSubImage,1))];
subplot(2, 2, 4);
imshow(rgbImage);
hold on;
rectangle('position',[corr_offset(1) corr_offset(2) 50 50],...
          'edgecolor','g','linewidth',2);
title('Template Image Found in Original Image', 'FontSize', fontSize);

MATLAB: How to relatively compare the height of objects in inamge

Try this:

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 25;
%===============================================================================
% Get the name of the first image the user wants to use.
baseFileName = 'IMG_20171202_181031[2364].jpg';
folder = fileparts(which(baseFileName)); % Determine where demo folder is (works with all versions).
fullFileName = fullfile(folder, baseFileName);
% Check if file exists.
if ~exist(fullFileName, 'file')
  % The file doesn't exist -- didn't find it there in that folder.
  % Check the entire search path (other folders) for the file by stripping off the folder.
  fullFileNameOnSearchPath = baseFileName; % No path this time.
  if ~exist(fullFileNameOnSearchPath, 'file')
    % Still didn't find it.  Alert user.
    errorMessage = sprintf('Error: %s does not exist in the search path folders.', fullFileName);
    uiwait(warndlg(errorMessage));
    return;
  end
end
%=======================================================================================

% Read in demo image.
rgbImage = imread(fullFileName);
% Get the dimensions of the image.
[rows, columns, numberOfColorChannels] = size(rgbImage);
% Display the original image.
subplot(2, 2, 1);
imshow(rgbImage, []);
axis on;
caption = sprintf('Original Color Image, %s', baseFileName);
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0.05 1 0.95]);
% Get rid of tool bar and pulldown menus that are along top of figure.
% set(gcf, 'Toolbar', 'none', 'Menu', 'none');
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off')
drawnow;
hp = impixelinfo(); % Set up status line to see values when you mouse over the image.
[rows, columns, numberOfColorChannels] = size(rgbImage)
if numberOfColorChannels > 1
  % It's not really gray scale like we expected - it's color.
  % Use weighted sum of ALL channels to create a gray scale image.
  grayImage = rgb2gray(rgbImage);
  % ALTERNATE METHOD: Convert it to gray scale by taking only the green channel,
  % which in a typical snapshot will be the least noisy channel.
  % grayImage = grayImage(:, :, 2); % Take green channel.
end
% Display the image.
subplot(2, 2, 2);
imshow(grayImage, []);
axis on;
caption = sprintf('Gray Image');
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
hp = impixelinfo();
drawnow;
% Display the histogram of the image.
subplot(2, 2, 3);
histogram(grayImage, 256);
caption = sprintf('Gray Image');
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
grid on;
drawnow;
%=======================================================================================
mask = grayImage < 75;
% Fill the mask to get rid of holes.
mask = imfill(mask, 'holes');
% Extract the largest 4 blobs only.
mask = bwareafilt(mask, 4);
% Display the masked image.
subplot(2, 2, 4);
imshow(mask, []);
axis on;
caption = sprintf('Mask Image');
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
hp = impixelinfo();
drawnow;
% Get the bounding box of all cups
props = regionprops(mask, 'BoundingBox');
bb = [props.BoundingBox]
allHeights = bb(4:4:end)
% Find the tallest:
[tallestHeight, indexOfTallest] = max(allHeights)
% Make message
message = sprintf('The tallest cup is cup #%d with a height of %d', indexOfTallest,tallestHeight);
helpdlg(message);
% Bound it with the box:
subplot(2, 2, 1);
hold on;
rectangle('Position', props(indexOfTallest).BoundingBox, 'EdgeColor', 'r', 'LineWidth', 2);

Best Answer

Related Solutions

MATLAB: Correlation between the two images;

MATLAB: How to relatively compare the height of objects in inamge

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