MATLAB: Matlab determine a curve

curve

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!

Best Answer

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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