Major And Minor Axis
Using the same technique from a prev post we can find the major and minor axis and their ratio.
From Circular to Elliptical Effective Radius
We can find $R_e$ manually by measuring out from the the center of the source until we get reach $I_e$
To find the ellipse that has the same area as the circle above with the same axis ratio as the major and minor axis above we solve for a and b in the following equations:
Where $Q$ is the axis ratio found in our eigen decompostion of the image covariance matrix.
With that solved we get the following ellipse
If we perform this for the image in all four bands we get the following. I lowered the alpha int the images so the ellipses would be easier to see.