How do I calculate area enclosed by contour lines?

I have

[x, y, z] = peaks; [C, h] = contour(x, y, z, 20);

Kindly suggest an algorithm or necessary functions to find the area enclosed by, and between, contour lines.

Thanks!

Answer 1

[Sara]

[x, y, z] = peaks; 
[C, h] = contour(x, y, z, 20);
ch = get(h,'children');
area = zeros(numel(ch),1);
for i = 1:numel(ch)
    x = get(ch(i),'xdata');
    y = get(ch(i),'ydata');
    [x,y] = poly2cw(x,y);
    area(i) = polyarea(x,y);
end

[Image Analyst]

What is poly2cw()? What toolbox is it in? Do you have a version that works without any toolboxes?

Undefined function 'poly2cw' for input arguments of type 'double'.
Error in test2 (line 8)
    [x, y] = poly2cw(x, y);

[Sara]

It's in the mapping toolbox. It orders the points in a contour in clockwise order, so that the contour is external and an area can be computed (counterclockwise contours are considered internal contours). This is ArcGIS convention and it's followed also by Matlab (not sure who started first). I personally don't have a version working with the basic matlab license and never looked if there is something similar in the file exchange since I have the mapping toolbox.

[XING ZHENG]

Dear Sara,

Now I am using your function in the version 2017b: [C, h] = contour(x, y, z, 20); ch = get(h,'children');

However, I can not get 'h' from this sentence. therefore, there is No result of ch. I think this is the difference between the version 2014b and 2017b.

How can I fix this problem? Thanks

Xing

Answer 2

[A. Shokouhi]

I believe some commands in the code provided by Sara is not available in new versions here a code I wrote down that does the same job.

[x, y, z] = peaks;
[C, h] = contour(x, y, z, 5);

n = 0;
i = 1;
sz = size(h.ContourMatrix,2);
nn(1) = h.ContourMatrix(2,1);
xx = h.ContourMatrix(1,2:nn(1)+1);
yy = h.ContourMatrix(2,2:nn(1)+1);
area(1) = polyarea(xx,yy);

while n+nn(i)+i < sz
    n = n + nn(i);
    i = i + 1;
    nn(i)=h.ContourMatrix(2,n+i);
    xx = h.ContourMatrix(1,n+i+1:n+nn(i)+i);
    yy = h.ContourMatrix(2,n+i+1:n+nn(i)+i);
    area(i) = polyarea(xx,yy);
end

[Vikas Sharma]

I also observe some issue with MATLAB version. Moreover code by A. Shokouhi also produce some zero area(I dont know why?). Below is my tweak to find out area of contour in MATLAB

[C,h] = contour(X,Y,Z,v); % the coontour whose area is required

% contour lines at the data values specified in the monotonically increasing vector v.

clabel(C,h); colorbar; grid on

areas = zeros(1,length(v)); % The number of areas to be calculated

i = 1; k=1; % i is for area loop. k is another couter

for i=1:length(v)

xx = C(1,k+1:k+C(2,k)); % x data of a particular contour line

yy = C(2,k+1:k+C(2,k)); % y data of a particular contour line

areas(i) = polyarea(xx,yy);

k=k+C(2,k)+1; % Take our counter to the next target

end

areas % to see the calculated areas

[Tim Oyeboade]

This is helpful. But please can you tell me the mathematical algorithm behind this method of yours. Its urgent pleas.

[Sesha Sai Anudeep Karnam]

Is this area enclosed by contour lines or area enclosed between contour lines?

[S Ch]

@Sesha Sai Anudeep Karnam Hello, did you have an answer ? I think it gives the area of the colors,

Is it the integral ?