Centroid of polyarea

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Jaejin Hwang
Jaejin Hwang 2012-1-9
How to get a centroid of polyarea?
Here is my code.
Thanks.
figure, imshow('000445.png')
hold on
xy = [];
n = 0;
but = 1;
while but == 1
[xi,yi,but] = ginput(1);
plot(xi,yi,'r.')
n = n+1;
xy(:,n) = [xi;yi];
end
t = 1:n;
ts = 1: 0.1: n;
xys = spline(t,xy,ts);
plot(xys(1,:),xys(2,:),'r-');
A = polyarea(xys(1,:),xys(2,:));
plot(xys(1,:),xys(2,:),'r-');
title (['Area = ' num2str(A)]);
axis image
hold off

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采纳的回答

Chandra Kurniawan
Hi,
I modified your first code becomes :
I = imread('peppers.png');
[r c o] = size(I);
imshow(I); hold on;
xy = [];
n = 0;
but = 1;
while but == 1
[xi, yi, but] = ginput(1);
plot(xi, yi, 'r.');
n = n + 1;
xy(:, n) = [xi; yi];
end
t = 1 : n;
ts = 1 : 0.1 : n;
xys = spline(t, xy, ts);
plot(xys(1,:), xys(2,:), 'r-');
A = polyarea(xys(1,:), xys(2,:));
plot(xys(1,:), xys(2,:), 'r-');
title (['Area = ' num2str(A)]);
axis image
%hold off
Then, I create my own code.
J = logical(zeros(r, c));
xcoor = floor(xys(1,:));
ycoor = floor(xys(2,:));
for x = 1 : numel(xcoor)
J(ycoor(x),xcoor(x)) = 1;
end
J = imdilate(J,strel('square',20));
J = bwmorph(J,'thin',inf);
J = imfill(J,'holes');
stat = regionprops(J,'Centroid');
plot(stat.Centroid(1),stat.Centroid(2),'go',...
'markerfacecolor','b')
And the result is :
  2 个评论
Sean de Wolski
Sean de Wolski 2012-1-9
You could use poly2mask() instead of the dilation/skeletonization. I do not believe the method you are using would be correct at boundaries. I.e. where the strel is not fully represented on boundary of the image, the thinning operation will be shifted in and not centered since the strel was not centered at the edge.
Though regionprops/works for this, in two dimensions the formula is well defined:
http://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon
Chandra Kurniawan
Chandra Kurniawan 2012-1-9
Hi, Sean
thanks for the suggestion
I will use it in the future.

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更多回答（1 个）

Sean de Wolski
Sean de Wolski 2012-1-9
Once you know area, A, and coordinates: x, y:
As = sum(A)/2;
x_bar = (sum((x(2:end)+x(1:end-1)).*A)*1/6)/As;
y_bar = (sum((y(2:end)+y(1:end-1)).*A)*1/6)/As;
Source
  2 个评论
Jaejin Hwang
Jaejin Hwang 2012-1-9
That's interesting. But If I add it, I couldn't see the centroid point. What did I make mistake? Thanks.
% spline function
I= imread('000445.png');
[r c o] = size(I);
imshow(I);
hold on
xy = [];
n = 0;
but = 1;
while but == 1
[xi,yi,but] = ginput(1);
plot(xi,yi,'r.')
n = n+1;
xy(:,n) = [xi;yi];
end
t = 1:n;
ts = 1: 0.1: n;
xys = spline(t,xy,ts);
plot(xys(1,:),xys(2,:),'r-');
% calculating area
A = polyarea(xys(1,:),xys(2,:));
plot(xys(1,:),xys(2,:),'r-');
title (['Area = ' num2str(A)]);
axis image
% calculating centroid
As = sum(A)/2;
x_bar = (sum((x(2:end)+x(1:end-1)).*A)*1/6)/As;
y_bar = (sum((y(2:end)+y(1:end-1)).*A)*1/6)/As;
plot(x_bar,y_bar,'b*');
THAMMISHETTI NIKESH
THAMMISHETTI NIKESH 2012-11-12
x=[0 10 10 12 12 20 20 12 10 8 8 0 0]; y=[3 3 0 0 3 3 6 6 20 20 6 6 3]; As=polyarea(x,y); X_bar=0; Y_bar=0; h=length(x)-1; for a=1:h X_bar=(1/(6*As))*(x(a)+x(a+1))*(x(a)*y(a+1)-x(a+1)*y(a))+X_bar; Y_bar=(1/(6*As))*(y(a)+y(a+1))*(x(a)*y(a+1)-x(a+1)*y(a))+Y_bar; end
I used the above code, hope it helps you

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