How to find the arc length of a trajectory?

Asked by Julián Mauricio Ruiz Echeverri

Julián Mauricio Ruiz Echeverri (view profile)

on 14 Oct 2019
Latest activity Edited by Stephan

Stephan (view profile)

on 16 Oct 2019
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 = 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

darova (view profile)

on 15 Oct 2019
Can't you measure the diameter? Looks like circle

Stephan (view profile)

on 15 Oct 2019
Edited by Stephan

Stephan (view profile)

on 16 Oct 2019

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:
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);
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
% 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 ;-)