Ellipse Fit
라이선스 없음
Usage:
[semimajor_axis, semiminor_axis, x0, y0, phi] = ellipse_fit(x, y)
Input:
x - a vector of x measurements
y - a vector of y measurements
Output:
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
the x-axis
Algorithm used:
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:
http://mathworld.wolfram.com/Ellipse.html
인용 양식
Tal Hendel (2024). Ellipse Fit (https://www.mathworks.com/matlabcentral/fileexchange/22423-ellipse-fit), MATLAB Central File Exchange. 검색됨 .
MATLAB 릴리스 호환 정보
플랫폼 호환성
Windows macOS Linux카테고리
- Image Processing and Computer Vision > Image Processing Toolbox > Image Segmentation and Analysis > Region and Image Properties >
태그
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!