How to separate into unimodal or bimodal

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Jórdan Venâncio Leite 2022-3-21

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https://ww2.mathworks.cn/matlabcentral/answers/1676234-how-to-separate-into-unimodal-or-bimodal

评论： Jórdan Venâncio Leite 2022-4-10

采纳的回答： Image Analyst

image66.mat

Hello, I have some histograms. How can I separate them through Matlab code and tell which one is unimodal or bimodal ?

thanks in advance

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Answer 1

Image Analyst 2022-3-22

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编辑：Image Analyst 2022-3-22

Maybe use kstest(), lillietest(), or chi2gof().

Or fit the data to two Gaussians and see if the peak locations are separated by enough distance. See attached demos.

Also see links on the right, such as

https://www.mathworks.com/matlabcentral/answers/474774-kstest-for-unimodal-and-bimodal-models?s_tid=answers_rc1-2_p2_MLT

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Jórdan Venâncio Leite 2022-3-24

在 MATLAB Online 中打开

Yes, however, I still don't know what this part of the code here below does. I know before this is the part where I enter my noisy data. However, after that I got a little confused.

% Convert X and Y into a table, which is the form fitnlm() likes the input data to be in.
tbl = table(X(:), Y(:));
% Define the model as Y = a + b*x + c*exp(-(x-d)^2/e) + d * exp(-(x-f)^2/g)
% Note how this "x" of modelfun is related to big X and big Y.
% x(:, 1) is actually X and x(:, 2) is actually Y - the first and second columns of the table.
modelfun = @(b,x) b(1) + b(2) * x(:, 1) + b(3) * exp(-(x(:, 1) - b(4)).^2/b(5)) + b(6) * exp(-(x(:, 1) - b(7)).^2/b(8));  
beta0 = [6, 0.1, 35, 10, 3, 25, 50, 9]; % Guess values to start with.  Just make your best guess.
% Now the next line is where the actual model computation is done.
mdl = fitnlm(tbl, modelfun, beta0);
% Now the model creation is done and the coefficients have been determined.
% YAY!!!!
% Extract the coefficient values from the the model object.
% The actual coefficients are in the "Estimate" column of the "Coefficients" table that's part of the mode.
coefficients = mdl.Coefficients{:, 'Estimate'}
% Let's do a fit, but let's get more points on the fit, beyond just the widely spaced training points,
% so that we'll get a much smoother curve.
X = linspace(min(X), max(X), 1920); % Let's use 1920 points, which will fit across an HDTV screen about one sample per pixel.
% Create smoothed/regressed data using the model:
yFitted = coefficients(1) + coefficients(2) * X + coefficients(3) * exp(-(X - coefficients(4)).^2 / coefficients(5)) + ...
	coefficients(6) * exp(-(X - coefficients(7)).^2 / coefficients(8));
% Now we're done and we can plot the smooth model as a red line going through the noisy blue markers.
hold on;
plot(X, yFitted, 'r-', 'LineWidth', 2);
grid on;
title('Exponential Regression with fitnlm()', 'FontSize', fontSize);
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
legendHandle = legend('Noisy Y', 'Fitted Y', 'Location', 'northeast');
legendHandle.FontSize = 25;

Jórdan Venâncio Leite 2022-3-28

在 MATLAB Online 中打开

Image Analyst, i can keep using this model here in my case which is a histogram? MODEL: Y = a + b*x + c*exp(-(x-d)^2/e) + d * exp(-(x-f)^2/g). How do I convert the histogram into a table to be used in the line 10 of my code knowing that the variable of this histogram in the workspace is a graph and not values?

clc
clear
close all
load('image66.mat');
img=PerfilCinzasVertical;
N = histogram(img,12);
% Convert the histogram into a table
tbl = table(X(:), Y(:));
% Define the model as Y = a + b*x + c*exp(-(x-d)^2/e) + d * exp(-(x-f)^2/g)
% Note how this "x" of modelfun is related to big X and big Y.
% x(:, 1) is actually X and x(:, 2) is actually Y - the first and second columns of the table.
modelfun = @(b,x) b(1) + b(2) * x(:, 1) + b(3) * exp(-(x(:, 1) - b(4)).^2/b(5)) + b(6) * exp(-(x(:, 1) - b(7)).^2/b(8));  
beta0 = [6, 0.1, 35, 10, 3, 25, 50, 9]; % Guess values to start with.  Just make your best guess.
% Now the next line is where the actual model computation is done.
mdl = fitnlm(tbl, modelfun, beta0);
% Now the model creation is done and the coefficients have been determined.
% YAY!!!!
% Extract the coefficient values from the the model object.
% The actual coefficients are in the "Estimate" column of the "Coefficients" table that's part of the mode.
coefficients = mdl.Coefficients{:, 'Estimate'}
% Let's do a fit, but let's get more points on the fit, beyond just the widely spaced training points,
% so that we'll get a much smoother curve.
X = linspace(min(X), max(X), 1920); % Let's use 1920 points, which will fit across an HDTV screen about one sample per pixel.
% Create smoothed/regressed data using the model:
yFitted = coefficients(1) + coefficients(2) * X + coefficients(3) * exp(-(X - coefficients(4)).^2 / coefficients(5)) + ...
	coefficients(6) * exp(-(X - coefficients(7)).^2 / coefficients(8));
% Now we're done and we can plot the smooth model as a red line going through the noisy blue markers.
hold on;
plot(X, yFitted, 'r-', 'LineWidth', 2);
grid on;
title('Exponential Regression with fitnlm()', 'FontSize', fontSize);
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
legendHandle = legend('Noisy Y', 'Fitted Y', 'Location', 'northeast');
legendHandle.FontSize = 25;
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
% 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')

Jórdan Venâncio Leite 2022-4-8

在 MATLAB Online 中打开

Image Analyst. I'm having doubts about which model to use to represent the gaussian. Can you give me some tips ?

clc;
clear
close all
load('image66.mat');
img=PerfilCinzasVertical;
N = histogram(img,12);
% Get the bin values into their own separate variable.
x = N.Values
% Get the bin counts into their own separate variable.
y = N.BinEdges(1:12)
% Convert the histogram into a table
tbl = table(x(:), y(:));
% Now the next line is where the actual model computation is done.
mdl = fitnlm(tbl, modelfun, beta0);
% Now the model creation is done and the coefficients have been determined.
% YAY!!!!
% Extract the coefficient values from the the model object.
% The actual coefficients are in the "Estimate" column of the "Coefficients" table that's part of the mode.
coefficients = mdl.Coefficients{:, 'Estimate'}
% Let's do a fit, but let's get more points on the fit, beyond just the widely spaced training points,
% so that we'll get a much smoother curve.
X = linspace(min(X), max(X), 1920); % Let's use 1920 points, which will fit across an HDTV screen about one sample per pixel.
% Create smoothed/regressed data using the model:
yFitted = coefficients(1) + coefficients(2) * X + coefficients(3) * exp(-(X - coefficients(4)).^2 / coefficients(5)) + ...
	coefficients(6) * exp(-(X - coefficients(7)).^2 / coefficients(8));
% Now we're done and we can plot the smooth model as a red line going through the noisy blue markers.
hold on;
plot(X, yFitted, 'r-', 'LineWidth', 2);
grid on;
title('Exponential Regression with fitnlm()', 'FontSize', fontSize);
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
legendHandle = legend('Noisy Y', 'Fitted Y', 'Location', 'northeast');
legendHandle.FontSize = 25;
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
% 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')

Image Analyst 2022-4-9

在 MATLAB Online 中打开

image66.mat

Try this:

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 = 20;
s = load('image66.mat')
subplot(2, 1, 1);
img = s.PerfilCinzasVertical;
plot(img, 'b-');
grid on;
title('Original Data', 'FontSize', fontSize);
subplot(2, 1, 2);
histogramObject = histogram(img, 12)
xlabel('Value', 'FontSize', fontSize);
ylabel('Count', 'FontSize', fontSize);
grid on;
% Convert the histogram into a table
X = histogramObject.BinEdges(1:end-1);
Y = histogramObject.BinCounts;
tbl = table(X(:), Y(:))
% Define the model as Y = a + b*x + c*exp(-(x-d)^2/e) + d * exp(-(x-f)^2/g)
% Note how this "x" of modelfun is related to big X and big Y.
% x(:, 1) is actually X and x(:, 2) is actually Y - the first and second columns of the table.
modelfun = @(b,x) b(1) * exp(-(x(:, 1) - b(2)).^2/b(3)) + b(4) * exp(-(x(:, 1) - b(5)).^2/b(6));  
beta0 = [100, 190, 200, 150, 235, 200]; % Guess values to start with.  Just make your best guess.
% Plot guess
xl = xlim; % Get range of x axis.
xGuess = linspace(xl(1), xl(2), 500)';
yGuess = modelfun(beta0, xGuess)
hold on;
plot(xGuess, yGuess, 'r-');
hold off;
% Now the next line is where the actual model computation is done.
mdl = fitnlm(tbl, modelfun, beta0);
% Now the model creation is done and the coefficients have been determined.
% YAY!!!!
% Extract the coefficient values from the the model object.
% The actual coefficients are in the "Estimate" column of the "Coefficients" table that's part of the mode.
coefficients = mdl.Coefficients{:, 'Estimate'}
% Let's do a fit, but let's get more points on the fit, beyond just the widely spaced training points,
% so that we'll get a much smoother curve.
X = linspace(min(X), max(X), 1920); % Let's use 1920 points, which will fit across an HDTV screen about one sample per pixel.
% Create smoothed/regressed data using the model:
yFitted = coefficients(1) * exp(-(X - coefficients(2)).^2 / coefficients(3)) + ...
    coefficients(4) * exp(-(X - coefficients(5)).^2 / coefficients(6));
% Now we're done and we can plot the smooth model as a red line going through the noisy blue markers.
hold on;
plot(X, yFitted, 'r-', 'LineWidth', 2);
grid on;
title('Exponential Regression with fitnlm()', 'FontSize', fontSize);
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
legendHandle = legend('Noisy Y', 'Guess', 'Fitted Y', 'Location', 'northwest');
legendHandle.FontSize = 25;
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
% 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')

Image Analyst 2022-4-9

Strange. So you don't know why you need to know? Is it your homework then, and it's just something the professor asked? Did you discuss some method in class? Or if it's not your homework, why don't we just forget about that and figure out what to do with your original signal. Of course any signal that has even a little bit of noise could be considered the composition of two Gaussians. So let's just assume it is. OK, now what? What do you now need to do with your original signal knowing that its histogram is two Gaussians?

Well sorry I couldn't help more (I'm not an expert statistician) but good luck.

Jórdan Venâncio Leite 2022-4-10

THANKS for your answer IMAGE ANALYST!! See if you can help me with this https://www.mathworks.com/matlabcentral/answers/1693350-how-to-define-if-a-histogram-is-unimodal-or-bimodal. It's almost finished already .

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