how can curve fitting

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fereshte 2014-5-17

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编辑： fereshte 2014-6-29

hi...i have some scatter points in x-y coordinate.how can curve fitting without using of cftool?i want do it by gussian fitt but in gussian code there are x and y.i domt know how obtain them!

% f = fit(x,y,'gauss8'); % plot(f,x,y); % coeff=fit(x,y,ft);

G is sample matrix with 106*47 in size and meanValue is mean of columns in matrix.result matrix is 1*47 that it is scatter points.

meanValue = mean(G)

thank you

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Image Analyst 2014-5-17

A screenshot of your data, or attaching your data file, would help us envision what you're talking about.

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Star Strider 2014-5-17

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在 MATLAB Online 中打开

Here’s my version of Gauss1 using fminsearch:

% % Single Gaussian Regression
% % Generate x- and y- data:
% x = linspace(0,10);                     % Generate x-data
% Normal distribution — b(1) = mean,  b(2) = std
N = @(b,x)  exp(-((x-b(1)).^2)./(2*b(2)^2)) ./ (b(2)*sqrt(2*pi));
% b = [5; 1];
% d1 = N(b,x);                            % Generate smooth y-data
% d2 = d1 + 0.05*(rand(size(d1))-.5);     % Add noise
% % —————  Assign your variables to x and y here —————
x = your independent variable
y = your dependent variable
% % Use ‘fminsearch’ to do regression:
y = d2;
OLS = @(b) sum((N(b,x) - y).^2);        % Ordinary Least Squares cost function
opts4 = optimset('MaxFunEvals',50000, 'MaxIter',10000);
B = fminsearch(OLS, rand(2,1))
Nfit = N(B,x);                          % Calculate estimated fit

The variables you need to have in your workspace are x and y (or assign them to x and y) to use this without modifying the code. The single ‘%’ commented lines are there for illustration. (Uncomment them if you want to see how it works. Remove them if you don’t need them.)

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Star Strider 2014-5-17

在 MATLAB Online 中打开

I downloaded and fit the data in ‘meanValue.fig’. I changed my code to a 2-Gaussian model, and got what I consider a decent fit.

You will have to assign your x and y variables to the ones I call x and y in my code, just after my comment:

% % ————— Assign your variables to x and y here —————

after that, it should run without problems.

Initial choice of parameters, especially b(2) and b(5) in N2, is important in situations like these, since it’s possible for both Gaussian functions to fit to same peak, ignoring the other one.

I got for the fitted parameter set:

fitting to your data with this code:

% % Double Gaussian Regression
N = @(b,x)  b(1).*exp(-((x-b(2)).^2)./(2*b(3)^2)) ./ (b(3)*sqrt(2*pi));
N2 = @(b,x) b(1).*exp(-((x-b(2)).^2)./(2*b(3)^2)) ./ (b(3)*sqrt(2*pi)) + b(4).*exp(-((x-b(5)).^2)./(2*b(6)^2)) ./ (b(6)*sqrt(2*pi));
% % —————  Assign your variables to x and y here —————
x = ...;
y = ...;
% % Use ‘fminsearch’ to do regression:
OLS = @(b) sum((N2(b,x) - y).^2);        % Ordinary Least Squares cost function
opts4 = optimset('MaxFunEvals',50000, 'MaxIter',10000);
B = fminsearch(OLS, [50 25 5 50 40 5]')
N2fit = N2(B,x);                          % Calculate estimated fit
Nfit(1,:) = N(B(1:3),x);
Nfit(2,:) = N(B(4:6),x);
figure(1)
plot(x, y, '+b')
hold on
plot(x, N2fit, '-r', 'LineWidth',1.5)
plot(x, Nfit(1,:), '-g')
plot(x, Nfit(2,:), '-g')
hold off
grid
text(5, 55, sprintf('Centre #1 = %.2f, \\sigma #1 = %.2f\nCentre #2 = %.2f, \\sigma #2 = %.2f', B(2:3), B(5:6)), 'FontName','Consolas', 'FontSize',7)

producing this plot:

Star Strider 2014-5-18

在 MATLAB Online 中打开

I omitted the lines that read your image because I thought you had access to those data without them. If you want to use that and other images (nothing wrong with that), insert these lines before the comment line:

ssf = openfig('meanValue.fig')
hf2 = get(gca, 'Children');
hf3xc = get(hf2, 'XData');
hf3yc = get(hf2, 'YData');
% % Double Gaussian Regression

then:

% % —————  Assign your variables to x and y here —————
x = hf3xc;
y = hf3yc;

If you want to use other figures as sources of data, simply insert their names in the openfig line. It should run without problems, although you might need to change the values for b(2) and b(5) as I mentioned previously, to initially approximate the centres of the peaks of your data.

I’ll re-post the entirety of my code if necessary, but these are the only changes you need to make it work. The code should work for all sets of x and y data that you want to give it. Unless you use your ‘.fig’ files as input (in which situation you only need to change their names in the openfig statement), you simply have to use the code in my previous comment, plug in the names of your variables in place of hf3xc and hf3yc in my code, and adjust two of the initial parameter estimates. The program should then successfully estimate all the parameters.

Image Analyst 2014-6-29

Please put that "Answer" right here. No need to put a comment here and then say that Star has to look somewhere else down the page for it, especially since it's not really an "Answer" to your original post but a comment to Star.

fereshte 2014-6-29

编辑：fereshte 2014-6-29

dear Star Strider

i use youre code for my dataset. but it dont work for all images. i change B line in this code respect to locs_Rwave for some images that dont get me true response.but its very difficult.can you help me to get the code that run perfectlly for all images with out any change in B line?

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