Calculate percentage of similarities in two polygons

Hello friends.

Is there any framework in Matlab that can calculate the percentage of similarities between two polygons?

If not, how can i implement one?

Googling i found out a formula to calculate the similarities of two polygons R and P2 using this formula:

But i don't know how to calculate the union and intersection polygons.

Any help please? :)

Thanks in advance!

Answer 1

[Kelly Kearney]

If you have the Mapping Toolbox and want a more exact answer:

% Some example polygons

theta = linspace(0, 2*pi, 100);
x1 = cos(theta) - 0.5;
y1 = -sin(theta);  
x2 = x1 + 1;
y2 = y1;

% Calculate

[xint, yint] = polybool('&', x1, y1, x2, y2);
[xun,  yun]  = polybool('|', x1, y1, x2, y2);
a1 = polyarea(xun, yun);
a2 = polyarea(xint, yint);
sim = 1 - (a1- a2)./a1;

[Amaral]

It worked very well. It gives accurate results which is exactly what i'm looking for. Thanks :)

Answer 2

[Image Analyst]

If that definition works for you, then that's fine. One could think of others, but whatever works for what you need it to, is fine. I think the easiest way to solve the formula is to convert the polygons to images with poly2mask().

rows = 1920; % Whatever is needed to contain your points.
columns = 1600;
image1 = poly2mask(x1,y1, rows, columns);
image2 = poly2mask(x2,y2, rows, columns);
unionImage = image1 & image2;
intersectionImage = xor(image1, image2)
similarity - 1 - (sum(unionImage(:) - intersectionImage(:)) / sum(unionImage(:));

If your x and y are too small, then multiply them by some scaling factor beforehand, like 100 or 1000 or whatever so that your image is big and not too pixelated.

[Amaral]

Thanks for the answer. :) I'll try it out :)

[Amaral]

Your approach worked. But had to do some adjustments because i think the way you calculated the union and intersection is wrong. This way it gives the results i want, at least i think so according to the results in the tests :P

unionImage = image1 | image2;

intersectionImage = image1 & image2;

similarity = (1 - (sum(unionImage(:) - intersectionImage(:)) / sum(unionImage(:)))) * 100