How can I get the angle between centroid of a binary object and a point on it's boundary?

How to calculate angle between centroid of a binary object and a point on it's boundary?

For example as in attached figure I want the angle between 'a' and centrioid is near to "0 degree" and for 'b' it will be near to "45 degree (maybe 42 or 40)"

[KALYAN ACHARJYA]

Hint: Here

Answer 1

[KSSV]

Get the centorid of the image by using mean. So I assume you know all the points A,B,C,D and O. You have (x,y) in hand. If you want angle w.r.t x-axes..simply find slope and get tan inverse of it.

th = atan((y2-y1)/(x2-x1)) ;

If you want angle between two lines...say OA and OB, ude dot product.

cos(th) = oa.ob/(|oa|*|ob|) ;