MATLAB: Fit specific function on scatter plot Matlab

curve fittingStatistics and Machine Learning Toolbox

So i have a scatterplot scatter(x,y) and I would like to find a best fit for a function of the type F(x)=e^(-(Bèta)*x) with x matching x and F(x) matching/approximating the corresponding y.

I would like to find the best fit and get the value of Bèta returned.

How do i do this?

Best Answer

If y = exp(-beta*x) then log(y) = -beta*x and beta = -log(y)/x . Your best fit in log space would then be approximately

beta = mean( -log(y) ./ x )

In linear space,

beta = lsqcurvefit(@(beta,x) exp(-beta*x), 3, x, y);

However, when I constructed artificial data by defining beta and using

   c = 1;
   y = exp(-beta*x + randn(size(x)) * c );

and then fit against that to recover beta, then I found that a closer beta to the one I defined could be calculated as

other_beta = lsqcurvefit(@(beta,x) beta*x, 3, x, -log(y));

As c gets reduced to (say) 1/10 then the two fittings become more similar.

With a noise model like

c = 1/15;
y = exp(-beta*x) + (2 * rand(size(x)) - 1) * c;

then the original beta version becomes a notably better fit. So which one to use would probably depend upon the model of noise / error that you have.

Related Solutions

MATLAB: Adding Noise to the Image

Try this:

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;
%===============================================================================
% Read in a standard MATLAB gray scale demo image.
folder = fileparts(which('cameraman.tif')); % Determine where demo folder is (works with all versions).
baseFileName = 'cameraman.tif';
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);
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  % File doesn't exist -- didn't find it there.  Check the search path for it.
  fullFileNameOnSearchPath = baseFileName; % No path this time.
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% Get the dimensions of the image.  
% numberOfColorBands should be = 1.
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  % It's not really gray scale like we expected - it's color.
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% Display the original gray scale image.
subplot(1, 2, 1);
imshow(grayImage, []);
title('Original Grayscale Image', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
% Give a name to the title bar.
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% Initialize an output image.
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subplot(1, 2, 2);
imshow(noisyImage, []);
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axis on;

MATLAB: Fit a polynimial function on a image curve

How about this:

% Demo to find fitted curve.
% By Image Analyst
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 22;
%--------------------------------------------------------------------------------------------------------


%    READ IN IMAGE
folder = pwd;
baseFileName = 'image.jpeg';
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);
% Check if file exists.
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	% The file doesn't exist -- didn't find it there in that folder.
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		uiwait(warndlg(errorMessage));
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end
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% Get the dimensions of the image.
% numberOfColorChannels should be = 1 for a gray scale image, and 3 for an RGB color image.
[rows, columns, numberOfColorChannels] = size(grayImage);
if numberOfColorChannels > 1
	% It's not really gray scale like we expected - it's color.
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%--------------------------------------------------------------------------------------------------------
%    SEGMENTATION OF IMAGE
% Get a binary image
binaryImage = imbinarize(grayImage);
subplot(3, 1, 1);
imshow(binaryImage, []);
impixelinfo;
title('Binary Image', 'FontSize', fontSize, 'Interpreter', 'None');
hFig = gcf;
hFig.WindowState = 'maximized'; % May not work in earlier versions of MATLAB.
drawnow;
%--------------------------------------------------------------------------------------------------------
% REMOVE BOTTOM ARC
for col = 1 : columns
	thisCol = binaryImage(:, col);
	% Remove largest blob.
	biggestBlob = bwareafilt(thisCol, 1);
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	binaryImage(:, col) = thisCol;
end
% Display it.

subplot(3, 1, 2);
imshow(binaryImage)
grid on;
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% Get (x,y) of what's left
[y, x] = find(binaryImage);
% Add a tiny bit of noise because sometimes there are multiple y for the same x.
x = x + 0.001 * rand(1, length(x));
% Sort them
[x, sortOrder] = sort(x, 'ascend');
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% Filter with movmean
ySmoothed = movmean(y, 5);
% Display it.
subplot(3, 1, 3);
imshow(binaryImage)
grid on;
title('With Fitted Curve in Red', 'FontSize', fontSize, 'Interpreter', 'None');
hold on
plot(x, ySmoothed, 'r-', 'LineWidth', 3);

Best Answer

Related Solutions

MATLAB: Adding Noise to the Image

MATLAB: Fit a polynimial function on a image curve

Related Question