How can I get ellipse coefficient from fitEllipse function of OpenCV?

Question

I want to extract the red ball from one picture and get the detected ellipse matrix in picture.

Here is my example:

I threshold the picture, find the contou

Answer 1

Here is some code that worked for me which I based on the other responses on this thread.

def getConicCoeffFromEllipse(e):
    # ellipse(Point(xc, yc),Size(a, b), theta)
    xc = e[0][0]
    yc = e[0][1]
    a = e[1][0]/2
    b = e[1][1]/2
    theta = math.radians(e[2])
    # See https://en.wikipedia.org/wiki/Ellipse
    # Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 is the equation
    A = a*a*math.pow(math.sin(theta),2) + b*b*math.pow(math.cos(theta),2)
    B = 2*(b*b - a*a)*math.sin(theta)*math.cos(theta)
    C = a*a*math.pow(math.cos(theta),2) + b*b*math.pow(math.sin(theta),2)
    D = -2*A*xc - B*yc
    E = -B*xc - 2*C*yc
    F = A*xc*xc + B*xc*yc + C*yc*yc - a*a*b*b
    coef = np.array([A,B,C,D,E,F]) / F
    return coef

def getConicMatrixFromCoeff(c):
    C = np.array([[c[0], c[1]/2, c[3]/2], # [ a, b/2, d/2 ]
                 [c[1]/2, c[2], c[4]/2],  # [b/2,  c, e/2 ]
                 [c[3]/2, c[4]/2, c[5]]])  # [d/2], e/2, f ]
    return C

Answer 2

The function fitEllipse returns a RotatedRect that contains all the parameters of the ellipse.

An ellipse is defined by 5 parameters:

• xc : x coordinate of the center
• yc : y coordinate of the center
• a : major semi-axis
• b : minor semi-axis
• theta : rotation angle

You can obtain these parameters like:

RotatedRect e = fitEllipse(points);

float xc    = e.center.x;
float yc    = e.center.y;
float a     = e.size.width  / 2;    // width >= height
float b     = e.size.height / 2;
float theta = e.angle;              // in degrees

You can draw an ellipse with the function ellipse using the RotatedRect:

ellipse(image, e, Scalar(0,255,0)); 

or, equivalently using the ellipse parameters:

ellipse(res, Point(xc, yc), Size(a, b), theta, 0.0, 360.0, Scalar(0,255,0));

If you need the values of the coefficients of the implicit equation, you can do like (from Wikipedia):

So, you can get the parameters you need from the RotatedRect, and you don't need to change the function fitEllipse. The solve function is used to solve linear systems or least-squares problems. Using the SVD decomposition method the system can be over-defined and/or the matrix src1 can be singular.

For more details on the algorithm, you can see the paper of Fitzgibbon that proposed this fit ellipse method.