How to determine area of intersection in ellipse?

Hi guys i used the fit_ellipse code by Gal to fit an ellipse to my scatter plot.

https://www.mathworks.com/matlabcentral/fileexchange/3215-fit-ellipse

I have 2 ellipses that intersect with one another as shown and have several parameters obtained from the script for both ellipses

             a: 0.8740
             b: 0.4865
           phi: 0.4669
            X0: -1.4569
            Y0: -1.7190
         X0_in: -2.0746
         Y0_in: -0.8793
     long_axis: 1.7480
    short_axis: 0.9731
        status: ''

and

             a: 0.9021
             b: 0.3466
           phi: 0.4354
            X0: -0.6578
            Y0: -1.6598
         X0_in: -1.2965
         Y0_in: -1.2275
     long_axis: 1.8041
    short_axis: 0.6933
        status: ''
where X0, Y0 are centre of origin of non tilted and X0_in,Y0_in are centres of the tilted ellipse, phi is rotation

Would really like to know how to determine the area of intersection of the 2 ellipses to determine the extent of overlap. Should i use an ellipse code or can i use differentiation? Thank you!

Answer 1

[Image Analyst]

Try Google: https://www.google.com/#q=ellipse+intersection+area&* Lots of leads there. Maybe there is an analytical/mathematical solution.

Otherwise, you can do it numerically pretty simply using poly2mask if you have the perimeter coordinates or using sum and ampersand if you have binary images with the ellipses in them..