Fit a cylinder to scattered 3D XYZ point data

Question

As in the title, I want to fit a cylinder to a group of 3D points with Python. This is a nice solution with MATLAB. How can we do it with Python?

Answer 1

Using scipy.optimize.leastsq, we can create an error function in which the difference between the observed cylinder radius and the modelled radius is minimized. The following is an example of fitting a vertical cylinder

import numpy as np
from scipy.optimize import leastsq


def cylinderFitting(xyz,p,th):

    """
    This is a fitting for a vertical cylinder fitting
    Reference:
    http://www.int-arch-photogramm-remote-sens-spatial-inf-sci.net/XXXIX-B5/169/2012/isprsarchives-XXXIX-B5-169-2012.pdf

    xyz is a matrix contain at least 5 rows, and each row stores x y z of a cylindrical surface
    p is initial values of the parameter;
    p[0] = Xc, x coordinate of the cylinder centre
    P[1] = Yc, y coordinate of the cylinder centre
    P[2] = alpha, rotation angle (radian) about the x-axis
    P[3] = beta, rotation angle (radian) about the y-axis
    P[4] = r, radius of the cylinder

    th, threshold for the convergence of the least squares

    """   
    x = xyz[:,0]
    y = xyz[:,1]
    z = xyz[:,2]

    fitfunc = lambda p, x, y, z: (- np.cos(p[3])*(p[0] - x) - z*np.cos(p[2])*np.sin(p[3]) - np.sin(p[2])*np.sin(p[3])*(p[1] - y))**2 + (z*np.sin(p[2]) - np.cos(p[2])*(p[1] - y))**2 #fit function
    errfunc = lambda p, x, y, z: fitfunc(p, x, y, z) - p[4]**2 #error function 

    est_p , success = leastsq(errfunc, p, args=(x, y, z), maxfev=1000)

    return est_p

if __name__=="__main__":

    np.set_printoptions(suppress=True)    
    xyz = np.loadtxt('cylinder11.xyz')
    #print xyz
    print "Initial Parameters: "
    p = np.array([-13.79,-8.45,0,0,0.3])
    print p
    print " "

    print "Performing Cylinder Fitting ... "
    est_p =  cylinderFitting(xyz,p,0.00001)
    print "Fitting Done!"
    print " "


    print "Estimated Parameters: "
    print est_p

Answer 2

There is paper at David Eberly site "Fitting 3D Data with a Cylinder" that describes math basics and shows pseudocode.

You can also refer to C++ code in Geometric Tools Engine at the same site. I think that some auxiliary math functions like matrix inverse etc could be implemented in NymPy.