Fix inconsistencies in examples and many more improvements

doc/examples/plot_hough_transform.py

@@ -1,50 +1,47 @@
-'''
+"""
 ===============
 Hough transform
 ===============
 
-The Hough transform in its simplest form is a `method to detect
-straight lines <http://en.wikipedia.org/wiki/Hough_transform>`__.
+The Hough transform in its simplest form is a `method to detect straight lines
+<http://en.wikipedia.org/wiki/Hough_transform>`__.
 
-In the following example, we construct an image with a line
-intersection.  We then use the Hough transform to explore a parameter
-space for straight lines that may run through the image.
+In the following example, we construct an image with a line intersection.  We
+then use the Hough transform to explore a parameter space for straight lines
+that may run through the image.
 
 Algorithm overview
 ------------------
 
-Usually, lines are parameterised as :math:`y = mx + c`, with a
-gradient :math:`m` and y-intercept `c`.  However, this would mean that
-:math:`m` goes to infinity for vertical lines.  Instead, we therefore
-construct a segment perpendicular to the line, leading to the origin.
-The line is represented by the length of that segment, :math:`r`, and
-the angle it makes with the x-axis, :math:`\theta`.
+Usually, lines are parameterised as :math:`y = mx + c`, with a gradient
+:math:`m` and y-intercept `c`. However, this would mean that :math:`m` goes to
+infinity for vertical lines. Instead, we therefore construct a segment
+perpendicular to the line, leading to the origin. The line is represented by the
+length of that segment, :math:`r`, and the angle it makes with the x-axis,
+:math:`\theta`.
 
-The Hough transform constructs a histogram array representing the
-parameter space (i.e., an :math:`M \times N` matrix, for :math:`M`
-different values of the radius and :math:`N` different values of
-:math:`\theta`).  For each parameter combination, :math:`r` and
-:math:`\theta`, we then find the number of non-zero pixels in the
-input image that would fall close to the corresponding line, and
+The Hough transform constructs a histogram array representing the parameter
+space (i.e., an :math:`M \times N` matrix, for :math:`M` different values of the
+radius and :math:`N` different values of :math:`\theta`).  For each parameter
+combination, :math:`r` and :math:`\theta`, we then find the number of non-zero
+pixels in the input image that would fall close to the corresponding line, and
 increment the array at position :math:`(r, \theta)` appropriately.
 
-We can think of each non-zero pixel "voting" for potential line
-candidates.  The local maxima in the resulting histogram indicates the
-parameters of the most probably lines.  In our example, the maxima
-occur at 45 and 135 degrees, corresponding to the normal vector
-angles of each line.
+We can think of each non-zero pixel "voting" for potential line candidates. The
+local maxima in the resulting histogram indicates the parameters of the most
+probably lines. In our example, the maxima occur at 45 and 135 degrees,
+corresponding to the normal vector angles of each line.
 
-Another approach is the Progressive Probabilistic Hough Transform
-[1]_.  It is based on the assumption that using a random subset of
-voting points give a good approximation to the actual result, and that
-lines can be extracted during the voting process by walking along
-connected components.  This returns the beginning and end of each
-line segment, which is useful.
+Another approach is the Progressive Probabilistic Hough Transform [1]_. It is
+based on the assumption that using a random subset of voting points give a good
+approximation to the actual result, and that lines can be extracted during the
+voting process by walking along connected components. This returns the beginning
+and end of each line segment, which is useful.
 
-The function `probabilistic_hough` has three parameters: a general
-threshold that is applied to the Hough accumulator, a minimum line
-length and the line gap that influences line merging.  In the example
-below, we find lines longer than 10 with a gap less than 3 pixels.
+The function `probabilistic_hough` has three parameters: a general threshold
+that is applied to the Hough accumulator, a minimum line length and the line gap
+that influences line merging. In the example below, we find lines longer than 10
+with a gap less than 3 pixels.
 
 References
 ----------
@@ -57,7 +54,7 @@ References
        Detect Lines and Curves in Pictures," Comm. ACM, Vol. 15,
        pp. 11-15 (January, 1972)
 
-'''
+"""
 
 from skimage.transform import (hough_line, hough_line_peaks,
                                probabilistic_hough_line)