text: """
  ========================================
  Circular and Elliptical Hough Transforms
  ========================================
  
  The Hough transform in its simplest form is a `method to detect
  straight lines <https://en.wikipedia.org/wiki/Hough_transform>`__
  but it can also be used to detect circles or ellipses.
  The algorithm assumes that the edge is detected and it is robust against
  noise or missing points.
  
  Circle detection
  ================
  
  In the following example, the Hough transform is used to detect
  coin positions and match their edges. We provide a range of
  plausible radii. For each radius, two circles are extracted and
  we finally keep the five most prominent candidates.
  The result shows that coin positions are well-detected.
  
  
  Algorithm overview
  ------------------
  
  Given a black circle on a white background, we first guess its
  radius (or a range of radii) to construct a new circle.
  This circle is applied on each black pixel of the original picture
  and the coordinates of this circle are voting in an accumulator.
  From this geometrical construction, the original circle center
  position receives the highest score.
  
  Note that the accumulator size is built to be larger than the
  original picture in order to detect centers outside the frame.
  Its size is extended by two times the larger radius.
  
  """
  import numpy as np
  import matplotlib.pyplot as plt
  
  from skimage import data, color
  from skimage.transform import hough_circle, hough_circle_peaks
  from skimage.feature import canny
  from skimage.draw import circle_perimeter
  from skimage.util import img_as_ubyte
  
  
  # Load picture and detect edges
  image = img_as_ubyte(data.coins()[160:230, 70:270])
  edges = canny(image, sigma=3, low_threshold=10, high_threshold=50)
  
  
  # Detect two radii
  hough_radii = np.arange(20, 35, 2)
  hough_res = hough_circle(edges, hough_radii)
  
  # Select the most prominent 5 circles
  accums, cx, cy, radii = hough_circle_peaks(hough_res, hough_radii,
                                             total_num_peaks=3)
  
  # Draw them
  fig, ax = plt.subplots(ncols=1, nrows=1, figsize=(10, 4))
  image = color.gray2rgb(image)
  for center_y, center_x, radius in zip(cy, cx, radii):
      circy, circx = circle_perimeter(center_y, center_x, radius)
      image[circy, circx] = (220, 20, 20)
  
  ax.imshow(image, cmap=plt.cm.gray)
  plt.show()
  
  
  ######################################################################
  # Ellipse detection
  # =================
  #
  # In this second example, the aim is to detect the edge of a coffee cup.
  # Basically, this is a projection of a circle, i.e. an ellipse. The problem
  # to solve is much more difficult because five parameters have to be
  # determined, instead of three for circles.
  #
  # Algorithm overview
  # -------------------
  #
  # The algorithm takes two different points belonging to the ellipse. It
  # assumes that it is the main axis. A loop on all the other points determines
  # how much an ellipse passes to them. A good match corresponds to high
  # accumulator values.
  #
  # A full description of the algorithm can be found in reference [1]_.
  #
  # References
  # ----------
  # .. [1] Xie, Yonghong, and Qiang Ji. "A new efficient
  #        ellipse detection method." Pattern Recognition, 2002. Proceedings.
  #        16th International Conference on. Vol. 2. IEEE, 2002
  
  import matplotlib.pyplot as plt
  
  from skimage import data, color, img_as_ubyte
  from skimage.feature import canny
  from skimage.transform import hough_ellipse
  from skimage.draw import ellipse_perimeter
  
  # Load picture, convert to grayscale and detect edges
  image_rgb = data.coffee()[0:220, 160:420]
  image_gray = color.rgb2gray(image_rgb)
  edges = canny(image_gray, sigma=2.0,
                low_threshold=0.55, high_threshold=0.8)
  
  # Perform a Hough Transform
  # The accuracy corresponds to the bin size of a major axis.
  # The value is chosen in order to get a single high accumulator.
  # The threshold eliminates low accumulators
  result = hough_ellipse(edges, accuracy=20, threshold=250,
                         min_size=100, max_size=120)
  result.sort(order='accumulator')
  
  # Estimated parameters for the ellipse
  best = list(result[-1])
  yc, xc, a, b = [int(round(x)) for x in best[1:5]]
  orientation = best[5]
  
  # Draw the ellipse on the original image
  cy, cx = ellipse_perimeter(yc, xc, a, b, orientation)
  image_rgb[cy, cx] = (0, 0, 255)
  # Draw the edge (white) and the resulting ellipse (red)
  edges = color.gray2rgb(img_as_ubyte(edges))
  edges[cy, cx] = (250, 0, 0)
  
  fig2, (ax1, ax2) = plt.subplots(ncols=2, nrows=1, figsize=(8, 4),
                                  sharex=True, sharey=True)
  
  ax1.set_title('Original picture')
  ax1.imshow(image_rgb)
  
  ax2.set_title('Edge (white) and result (red)')
  ax2.imshow(edges)
  
  plt.show()
  