How to find the arc length of a trajectory?

Hello , Regards!

I want to find the arc length of every length . I am trying to find the position of every point with bwmorph(img,'endpoints') but Matlab doesn't give me in order the position of every point how I need it. I tried to find the Euclidean distance between points and then the angle between them (to find the arc length L = angle * radius) but the problem is that I can't accommodate the coordinates in the correct order of each start and end of each length stretch of Arc

I have this:

img = imread('img.bmp');
img = rgb2gray(I);
g=bwmorph(img,'thin','inf');%thining
 figure,imshow(g)
B1 = bwmorph(g,'endpoints');%endpoints
figure,imshow(B1);
[ye xe] = find(B1);%Position end points

[darova]

Can't you measure the diameter? Looks like circle

Answer 1

[Stephan]

Maybe it helps if you know the center coordinates and the radius of your circle -after that you can calculate the angles and use them to calculate the arc-lengths:

% your original code
img = imread('image.bmp');
img = rgb2gray(img);
g=bwmorph(img,'thin','inf');%thining

% Find the center and radius of the circle
g1=imdilate(g,strel('square',20));
g1=bwmorph(g1,'thin','inf');
g1=imfill(g1,round((size(g1)./2)),4);
[center, radius] = imfindcircles(g1,[180 220],'ObjectPolarity','bright','Method','TwoStage','Sensitivity',0.95);

% Proceeding with your code
B1 = bwmorph(g,'endpoints');%endpoints
[ye, xe] = find(B1);%Position end points

% Sort the values to plot the lines later in the right order 
Pe = [];
Pe_temp = [xe, ye, xe-center(1), center(2)-ye];
Pe = [Pe; sortrows(Pe_temp(Pe_temp(:,3)>0 & Pe_temp(:,4)>0,:),[4 -3])];
Pe = [Pe; sortrows(Pe_temp(Pe_temp(:,3)<0 & Pe_temp(:,4)>0,:),[-3 -4])];
Pe = [Pe; sortrows(Pe_temp(Pe_temp(:,3)<0 & Pe_temp(:,4)<0,:),[-4 3])];
Pe = [Pe; sortrows(Pe_temp(Pe_temp(:,3)>0 & Pe_temp(:,4)<0,:),[3 -4])];
Pe(2:numel(xe)+1,:) = Pe;
Pe(1,:) = Pe(end,:);

% Calculate Arc-Lengths
vec = [Pe(:,3), Pe(:,4)];
angles = zeros(1,numel(xe)/2);
n = 1;
for k = 1:2:numel(xe)-1
    angles(n) = acosd(dot(vec(k,:)./norm(vec(k,:)),vec(k+1,:)./norm(vec(k+1,:))));
    n = n + 1;
end

% Tada: The result
arc_lengths = radius*pi*angles./180;

% Plot results
figure
Lines = gobjects(1,numel(xe));
imshow(g)
hold on
for k = 1:size(Pe,1)-1
    Lines(k) = drawline('Position', [Pe(k,1), Pe(k,2); center],'label',string(k));  
end
scatter(xe,ye,'or')
scatter(center(1),center(2),'xg')
hold off

% Clean up
clearvars -except arc_lengths angles

The results appear to be correct to me - but you should check them by yourself. Dont miss to accept useful answers ;-)