Hi, I have curve fitted an histogram using the gaussian function. Now I would like to know how to extract a series of cell diameters from the gaussian fit.

Histogram with curve fit (x = cell diamters y = frequency)

[David Hill]

What do you mean by cell diameters?

[Akshay Kumar Pakala]

In my histogram the x values are cell diamters

[Akshay Kumar Pakala]

please let me know if you want me to add more comments to the code.

Also, I would like to know, how to create random 3d points based on my gaussian fit?

Answer 1

[yanqi liu]

sir，please check the follow code to get some information

for more information,you can read the book 《计算机视觉与深度学习实战》，Thank you！

clc; clear all; close all;
BW = imread('https://www.mathworks.com/matlabcentral/answers/uploaded_files/783383/image.png');
[nr,nc,layers] = size(BW);

%% converting the image to 2d so the image can be labledd %%
if layers>1
    BW = BW(:,:,1);
end

% end of lablling %%%%%%%%%%%%%%%%%
binaryimage = BW < 128;
bw = logical(binaryimage);
imwrite(bw, 'imagetoapp.jpg');
%% lablelling the image %%%%%%
[labeledimage, numberofblobs] = bwlabel(binaryimage,8);
props = regionprops(labeledimage, 'Equivdiameter');
x = numel(props);
y = zeros(x,1);
for i = 1:1:length(props)
    y(i,1) = struct2array(props(i,1));
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% LAbled image to rgb
colouredimage = label2rgb(labeledimage,'jet', [0,0,0.5]);
coloredLabelsImage = label2rgb (labeledimage, 'jet', 'k', 'shuffle');
imshowpair(labeledimage,colouredimage,'montage')
hold on

%% generating histogram and curve fitting it using gaussian function%%%%%%%%%
figure()
y1 = histogram(y,45);
values = y1.Values;
a=y1.BinEdges;
for i = 1 : length(a)-1
    b(i) = mean(a(i:i+1));
end
[barheights, position] = hist(y,45);
positiontranspose = position';
valuestranspose = values';
gauss = 'd +  a*exp(-(1/2)*((x-b)/c)^2)'

gauss = 'd +  a*exp(-(1/2)*((x-b)/c)^2)'

startpoints = [40 20 10 0.5];
myfit = fit(positiontranspose,valuestranspose,gauss,'start',startpoints);
hold on
plot(myfit)
z(:,1) = myfit(x);
zt=myfit(b);
%%  plot properties
xlabel('cell diamters')
ylabel('frequency')
hold on; plot(b, zt, 'r*')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%

[Akshay Kumar Pakala]

Thank you yanqui liu.

[Akshay Kumar Pakala]

Hey yanqui liu

I would like to know, if i could generate random points in 3d space based on my gaussian distribution of diameters (from the code mentioned above)?

[yanqi liu]

yes,sir,i think 3d can be as a three element vector, aslo apply this process method.

[Akshay Kumar Pakala]

Hey Yanqui Liu

I did not understand what you meant by that. Can you please explain?

Thank you

[yanqi liu]

such as two，make x----y

three，can as [x(1) x(2)]----y

Answer 2

[yanqi liu]

sir, may be upload the data mat file or the figure file to analysis

[Akshay Kumar Pakala]

please let me know if you want me to add more comments to the code.

Also, I would like to know, how to create random 3d points based on my gaussian fit?

Answer 3

[Akshay Kumar Pakala]

clc
clear all
BW = imread('binary.PNG');

[nr,nc,layers] = size(BW);

%% converting the image to 2d so the image can be labledd %%
if layers>1
    BW = BW(:,:,1);
end

% end of lablling %%%%%%%%%%%%%%%%%

binaryimage = BW < 128;
bw = logical(binaryimage);
imwrite(bw, 'imagetoapp.jpg');
%% lablelling the image %%%%%%

[labeledimage, numberofblobs] = bwlabel(binaryimage,8);
props = regionprops(labeledimage, 'Equivdiameter');
x = numel(props);
y = zeros(x,1);
for i = 1:1:length(props)
    y(i,1) = struct2array(props(i,1));
end




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% LAbled image to rgb

colouredimage = label2rgb(labeledimage,'jet', [0,0,0.5]);
coloredLabelsImage = label2rgb (labeledimage, 'jet', 'k', 'shuffle');
imshowpair(labeledimage,colouredimage,'montage')

hold on

%% generating histogram and curve fitting it using gaussian function%%%%%%%%%
figure()
y1 = histogram(y,45);
values = y1.Values;
[barheights, position] = hist(y,45);
positiontranspose = position';
valuestranspose = values';

gauss = 'd +  a*exp(-(1/2)*((x-b)/c)^2)'

startpoints = [40 20 10 0.5];
myfit = fit(positiontranspose,valuestranspose,gauss,'start',startpoints);

hold on
plot(myfit)

z(:,1) = myfit(x);

%%  plot properties

xlabel('cell diamters')
ylabel('frequency')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%