You don't need the (x,y) coordinates. You can work from the binary image directly. Getting the (x,y) coordinates just complicates things.
First get a better photo without those horrendous background illumination problems. For example, use a flatbed scanner. Then threshold and call imfill to get a solid blob. Then you can use regionprops to measure things about the shape. For example area mask = imfill(mask, 'holes');
mask = bwareafilt(mask, 1);
props = regionprops(mask, 'Area', 'Perimeter')
thePerimeter = props.Perimeter
For a different way to compute area you can use bwarea which gives area depending on the local shape of the boundary of the blob, as opposed to regionprops which gives area as a simple pixel count.
It's a generic, general purpose demo of how to threshold an image to find blobs, and then measure things about the blobs, and extract certain blobs based on their areas or diameters.
To measure moments of inertia, see attached demo.
