matlab determine a curve

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joo 2012-9-16

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Imagine i have an original plot with superimposed '8' shape curves (the curves are all different but similar to the '8' shape). Does anyone know how to obtain a mean curve having a matrix with the correspondent x,y points from the original plot? I mean, I pretend a medium single curve.

Any code or just ideas would be very very helpful for me. Thank you very very much!

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Walter Roberson 2012-9-17

http://www.mathworks.com/matlabcentral/answers/7924-where-can-i-upload-images-and-files-for-use-on-matlab-answers

Image Analyst 2012-9-18

Can you post your code where you use xlsread to read it in and loop over each curve to find the left-most part and record its row? And your code to use circshift to align them? Can you do any of that to help us help you?

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Answer 1

Image Analyst 2012-9-18

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编辑：Image Analyst 2012-9-18

在 MATLAB Online 中打开

You have a little noise on your y-data, as you can see from this example code. You might need to smooth that out first.

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.
workspace;  % Make sure the workspace panel is showing.
format longg;
format compact;
fontSize = 20;
folder = 'C:\Users\joo\Documents\Temporary';
fullFileName = fullfile(folder, 'livro1.xlsx');
% Check if file exists.
if ~exist(fullFileName, 'file')
  % File doesn't exist -- 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 in the search path folders.', fullFileName);
    uiwait(warndlg(errorMessage));
    return;
  end
end
[num txt raw] = xlsread(fullFileName);
x = num(:, 1);
y = num(:, 2);
% Plot x
subplot(2,2,1);
plot(x, 'b-');
xlabel('Element Number', 'FontSize', fontSize);
ylabel('X', 'FontSize', fontSize);
title('X', 'FontSize', fontSize);
grid on;
% Plot y
subplot(2,2,2);
plot(y, 'b-');
xlabel('Element Number', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
title('Y', 'FontSize', fontSize);
grid on;
% Plot curves
subplot(2,2,3);
plot(num(:, 1), num(:, 2), 'b-');
title('X', 'FontSize', fontSize);
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
grid on;
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
% Calculate distance from (50,360) of every point.
distances = sqrt((x - 50).^2 - (y - 360).^2)
subplot(2,2,4);
plot(distances, 'b-');
title('Distance from (50, 360)', 'FontSize', fontSize);
xlabel('index', 'FontSize', fontSize);
ylabel('Distances', 'FontSize', fontSize);
grid on;
% Find valleys in distances to find out where it turned around.
[valleys, indexesAtMins] = findpeaks(-distances)
% Plot them.
hold on;
plot(indexesAtMins, -valleys, 'r*');

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joo 2012-9-18

and why do you Calculate distance from (50,360) of every point? thank you very much!

Image Analyst 2012-9-18

I just answered that. Run my code and look at the graph and I think you'll see why.

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Answer 2

joo 2012-9-19

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https://ww2.mathworks.cn/matlabcentral/answers/48294-matlab-determine-a-curve#answer_59382

编辑：joo 2012-9-19

image analyst i am sorry to insist but i have been working all these days in this and still i can't understand. i see that in the plot you can vizualize (50,360). but why are these numbers and not for example (55,365)-with this pair the results would be different... i really don't understand where do they come from since i investigated all the results and code and nothing related with (50,360)... i am stucked in this for days. i am so grateful for your help. this is very important for me. thank you so much for your attention.

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Image Analyst 2012-9-20

在 MATLAB Online 中打开

Sure, you can use that point. It doesn't really matter. Of course the distances will be different but that doesn't matter when all you need to do is to determine what element the loop turns around at. You can pick any point that's sort of off the end of the loop end. If you want, simply fit all the points to a line with polyfit() and then use polyval() to find a point exactly along the mean axis of all the curves. You can do that but you'd probably get pretty much the same elements that define where the curve turns around at. All right, here -- I did the whole thing for you.

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.
workspace;  % Make sure the workspace panel is showing.
format longg;
format compact;
fontSize = 20;
folder = 'C:\Users\Mark\Documents\Temporary';
baseFileName = 'livro1.xlsx';
fullFileName = fullfile(folder, baseFileName);
% Check if file exists.
if ~exist(fullFileName, 'file')
  % File doesn't exist -- 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 in the search path folders.', fullFileName);
    uiwait(warndlg(errorMessage));
    return;
  end
end
[num txt raw] = xlsread(fullFileName);
x = num(:, 1);
y = num(:, 2);
% Plot x
subplot(2,2,1);
plot(x, 'b-');
xlabel('Element Number', 'FontSize', fontSize);
ylabel('X', 'FontSize', fontSize);
title('X', 'FontSize', fontSize);
grid on;
% Plot y
subplot(2,2,2);
plot(y, 'b-');
xlabel('Element Number', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
title('Y', 'FontSize', fontSize);
grid on;
% Plot curves
subplot(2,2,3);
plot(num(:, 1), num(:, 2), 'b-');
title('X', 'FontSize', fontSize);
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
grid on;
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
% Calculate distance from (50,360) of every point.
distances = sqrt((x - 450).^2 + (y - 550).^2)
subplot(2,2,4);
plot(distances, 'b-');
title('Distance from (450, 550)', 'FontSize', fontSize);
xlabel('index', 'FontSize', fontSize);
ylabel('Distances', 'FontSize', fontSize);
grid on;
% Find valleys in distances to find out where it turned around.
[peakValues, indexesAtPeaks] = findpeaks(distances)
% Take just the "good" peaks = those that are higher than
goodPeaks = peakValues > 300;
peakValues = peakValues(goodPeaks);
indexesAtPeaks = indexesAtPeaks(goodPeaks);
% Plot them.
hold on;
plot(indexesAtPeaks, peakValues, 'r*');
% We only want to go between the peaks because the
% data before the first peak and after the last peak
% are only partial peaks.
% Average the x and y between the peaks
figure;
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
sumX = zeros(1,100);
sumY = zeros(1,100);
count = 0;
for peak = 1 : length(indexesAtPeaks)-1
    index1 = indexesAtPeaks(peak);
    index2 = indexesAtPeaks(peak+1)-1;
    % Extract the curve between those indexes.
    thisX = x(index1:index2);
    thisY = y(index1:index2);
    % Skip bad (short) ones;
    if length(thisX) < 5
        break;
    end
    % Plot them.
    hold on;
    plot(thisX, thisY, 'r*');
    grid on;
    % These may not all be the same number of elements for every peak.
    % So we need to interpolate before we can average.
  originalIndexes = 1 : length(thisX);
  interpolatedIndexes = linspace(originalIndexes(1), originalIndexes(end), 100);  % Interpolate 100 points in our curves.
    interpX = interp1(originalIndexes, thisX, interpolatedIndexes, 'spline');
    interpY = interp1(originalIndexes, thisY, interpolatedIndexes, 'spline');
  % Plot the interpolated curve.
    plot(interpX, interpY, 'b-');
  % Sum them up
  sumX = sumX + interpX;
  sumY = sumY + interpY;
  count = count + 1; % # times through the loop.
end
meanX = sumX / count;
meanY = sumY / count;
% Plot the mean curve.
plot(meanX, meanY, 'g-', 'LineWidth', 3);

joo 2012-10-5

in your code you filter x,y data responsible for the noise/small peaks. you discover this peaks by x^2 +y^2. how can you justify this? shouldn't the noise data be seen only in x and y data alone? how can i justify this filtering?

i am not at all declining your code... i just need to justify the steps, and this is a doubt of mine... can you clear me this last doubt? thank you very much.

Image Analyst 2012-10-5

I'm calculating the Euclidean distance from some point way off the end of the curve's travel to the points on the curve using the Pythagorean Theorem, which is the sqrt of the sum of the squares. That distance oscillates as the point on the curve gets closer and farther away from the fixed, distant point as the curve point travels.

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matlab determine a curve

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