Source Image

segmap

src-image

Major And Minor Axis

Using the same technique from a prev post we can find the major and minor axis and their ratio.

maj-min-axis

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 $I_e$

circ-re

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

ell-re

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.

ell-all