Mean radial profile from a given point

Hi,

I'm quite new using Matlab and I want to write a program to do the following things:

1- from the attached file I have, I want to locate the coordinate center of the irradiation (ideally, with an histogram to avoid a trouble with 1 pixel). Note that it is a circular irradiation in this example but it can be squared too.

2- from that point, I would plot the mean radial profile (over 360°, thanks to the symmetry), and compare to the mean profile plot from X and Y direction (on that way, is it possible to modify the band width when plotting the profile?)

I find some examples here but they didn't help me...

Thanks in advance !

Answer 1

[Hugo Trentesaux]

To find the center, check regionprops Matlab function, it has a lot of features.

To compute the radial profile, you can program a function like this :

function profile = radialAverage(IMG, cx, cy, w)
    % computes the radial average of the image IMG around the cx,cy point
    % w is the vector of radii starting from zero
    [a,b] = size(IMG);
    [X, Y] = meshgrid( (1:a)-cx, (1:b)-cy);
    R = sqrt(X.^2 + Y.^2);
    profile = [];
    for i = w % radius of the circle
        mask = (i-1<R & R<i+1); % smooth 1 px around the radius
        values = (1-abs(R(mask)-i)) .* double(IMG(mask)); % smooth based on distance to ring
        % values = IMG(mask); % without smooth
        profile(end+1) = mean( values(:) );
    end
end

Answer 2

[Sergey Loginov]

Sergey Loginov (2021). Very Fast Radial Profile (https://www.mathworks.com/matlabcentral/fileexchange/101480-very-fast-radial-profile), MATLAB Central File Exchange. Retrieved November 5, 2021.

Answer 3

[yanqi liu]

clc; clear all; close all;
img = imread('https://ww2.mathworks.cn/matlabcentral/answers/uploaded_files/203087/Irradiation.JPG');
bw = imbinarize(rgb2gray(img), 'adaptive','ForegroundPolarity','dark','Sensitivity',0.6);
bw = ~bw;
bw = imfill(bw, 'holes');
bw = imclearborder(bw);
bw = bwareafilt(bw,1);
figure; imshow(bw);

be = bwperim(bw);
[y,x] = find(be);
data = [x(:) y(:)];
[Tics,Average]=radial_profile(data,1);

function [Tics,Average]=radial_profile(data,radial_step)
% use:https://ww2.mathworks.cn/matlabcentral/fileexchange/101480-very-fast-radial-profile
%main axii cpecified:
x=(1:size(data,2))-size(data,2)/2;
y=(1:size(data,1))-size(data,1)/2;
% coordinate grid:
[X,Y]=meshgrid(x,y);
% creating circular layers
Z_integer=round(abs(X+1i*Y)/radial_step)+1;
% % illustrating the principle:
% % figure;imagesc(Z_integer.*data)
figure;imagesc(Z_integer.*data)
% very fast MatLab calculations:
Tics=accumarray(Z_integer(:),abs(X(:)+1i*Y(:)),[],@mean);
Average=accumarray(Z_integer(:),data(:),[],@mean);
end