Ellipsemodel.estimate: some data points lead to scaling issues about scikit-image HOT 5 CLOSED

from pylab import *
from matplotlib.ticker import (MultipleLocator, FormatStrFormatter, AutoMinorLocator)

import numpy as np

try:
  from skimage.measure import EllipseModel
  scikitloaded = True
except:
  scikitloaded = False
  print("\nscikit not installed!\n")


# scale measuring data for optimized calculations
# move data central around average values
# scale numbers to <2
# return scaled data and scales
def scalePoints(x,y,enableMove=True,enableScale=True):

    if enableMove:
      # calculate average of x and y
      avgx = np.mean(x)
      avgy = np.mean(y)
    else:
      avgx = avgy = 0

    if enableScale:
      # calculating scale factors
      sfx = (np.max(x) - np.min(x))/2
      sfy = (np.max(y) - np.min(y))/2
      # uniform scale factor = max(sfx, sfy)
      # is easier for unscaling
      sfx = sfy = max(sfx, sfy)
      
    else:
      sfx = sfy = 1

    # creating scaled and centroid data points
    # in order to keep calculation results small
    x = (x - avgx)/sfx
    y = (y - avgy)/sfy
    return [x, y, avgx, avgy, sfx, sfy]


# https://stackoverflow.com/questions/39693869/fitting-an-ellipse-to-a-set-of-data-points-in-python
def fitEllipse(x,y, useScale=False):
    if useScale:
      # creating scaled and centroid data points
      # in order to keep calculation results small
      x, y, avgx, avgy, sfx, sfy = scalePoints(x,y)

    points = np.hstack([x, y])

    ell = EllipseModel()
    ell.estimate(points)
    if ell.params is None:
      return ell.params
      
    xc, yc, a, b, phi = ell.params

    if useScale:
      # unscale results
      xc = xc * sfx + avgx
      yc = yc * sfy + avgy
      a = a * sfx
      b = b * sfy
    
    return [xc, yc, a, b, phi]


def get_ellipse_pts(params, npts=100, tmin=0, tmax=2*np.pi):
    """
    Return npts points on the ellipse described by the params = x0, y0, ap,
    bp, phi for values of the parametric variable t between tmin and tmax.

    """

    x0, y0, ap, bp, phi = params
    # A grid of the parametric variable, t.
    t = np.linspace(tmin, tmax, npts)
    x = x0 + ap * np.cos(t) * np.cos(phi) - bp * np.sin(t) * np.sin(phi)
    y = y0 + ap * np.cos(t) * np.sin(phi) + bp * np.sin(t) * np.cos(phi)
    return x, y


titleSample = "pretty linear data"
xSample = np.array([3.0751, 2.9036, 2.7675, 2.6505, 2.5423, 2.4352])
ySample = np.array([3.2164, 3.133, 3.0626, 2.9991, 2.9378, 2.8748])

print("Data Points\nx:\n", xSample, "\ny:\n", ySample, "\n")
# Transpose Coordinates an make it 2 dimensional
xSample = xSample[:, np.newaxis]
ySample = ySample[:, np.newaxis]

fig, ax = plt.subplots()
plot(xSample, ySample, 'bo', label='data points')
xlabel('x')
ylabel('y')
ax.xaxis.set_minor_locator(AutoMinorLocator())
ax.yaxis.set_minor_locator(AutoMinorLocator())

# Prepare Plot
fig.canvas.manager.set_window_title('Fitting of Ellipses with data points')
fig.patch.set_facecolor('white')



if scikitloaded:
    # scale points for fit
    print("\nResult of estimate with scaled points:\n[xc, yc, a, b, phi]")
    para = fitEllipse(xSample,ySample, True)
    print(para)
    xx, yy = get_ellipse_pts(para)
    plot(xx, yy, 'g-' , linewidth = 1, label = "Result of estimate with scaled points")
    xc, yc = para[0:2]
    plot(xc, yc, 'k.')

    # do not scale points for fit
    print("\nResult of estimate without scaling:\n[xc, yc, a, b, phi]")
    para = fitEllipse(xSample,ySample, False)
    print(para)
    if para is not None:
        xx, yy = get_ellipse_pts(para)
        plot(xx, yy, 'r-' , linewidth = 1, label = "Result of estimate without scaling")
        xc, yc = para[0:2]
        plot(xc, yc, 'b.')

    # set general plot parameter
    legend(loc='lower right', labelcolor='linecolor', facecolor="darkgray")
    plt.show()