[semimajor_axis, semiminor_axis, x0, y0, phi] = ellipse_fit(x, y)
x - a vector of x measurements
y - a vector of y measurements
semimajor_axis - Magnitude of ellipse longer axis
semiminor_axis - Magnitude of ellipse shorter axis
x0 - x coordinate of ellipse center
y0- y coordinate of ellipse center
phi - Angle of rotation in radians with respect to
Given the quadratic form of an ellipse:
a*x^2 + 2*b*x*y + c*y^2 + 2*d*x + 2*f*y + g = 0 (1)
we need to find the best (in the Least Square sense) parameters a,b,c,d,f,g.
To transform this into the usual way in which such estimation problems are presented,
divide both sides of equation (1) by a and then move x^2 to the other side. This gives us:
2*b'*x*y + c'*y^2 + 2*d'*x + 2*f'*y + g' = -x^2 (2)
where the primed parametes are the original ones divided by a. Now the usual estimation technique is used where the problem is presented as:
M * p = b, where M = [2*x*y y^2 2*x 2*y ones(size(x))],
p = [b c d e f g], and b = -x^2. We seek the vector p, given by:
p = pseudoinverse(M) * b.
From here on I used formulas (19) - (24) in Wolfram Mathworld:
Tal Hendel (2021). Ellipse Fit (https://www.mathworks.com/matlabcentral/fileexchange/22423-ellipse-fit), MATLAB Central File Exchange. Retrieved .
Inspired by: Circle fit
Find the treasures in MATLAB Central and discover how the community can help you!Start Hunting!