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Tutorial work
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Pieter Holtzhausen
@@ -5,26 +5,28 @@ The Hough transform in its simplest form is a method to detect straight lines.
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http://en.wikipedia.org/wiki/Hough_transform
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For a first example we construct an example of intersecting lines.
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As a first example we construct a line intersection.
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In [1]: import numpy as np
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.. ipython::
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In [2]: from scikits.image.transform import hough, probabilistic_hough
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In [1]: import numpy as np
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In [3]: import matplotlib.pyplot as plt
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In [2]: from scikits.image.transform import hough, probabilistic_hough
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In [4]: from matplotlib.lines import Line2D
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In [3]: import matplotlib.pyplot as plt
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In [5]: image = np.zeros((100, 100))
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In [4]: from matplotlib.lines import Line2D
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In [6]: for i in range(25, 75):
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...: image[100 - i, i] = 255
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...: image[i, i] = 255
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...:
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In [5]: image = np.zeros((100, 100))
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In [7]: plt.imshow(image)
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In [6]: for i in range(25, 75):
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...: image[100 - i, i] = 255
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...: image[i, i] = 255
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...:
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In [8]: plt.show()
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In [7]: plt.imshow(image)
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In [8]: plt.show()
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The Hough transform converts the image into a parameter space that represents
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@@ -34,81 +36,93 @@ origin and by the angle theta of this vector.
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Every non-zero pixel of the image votes for potential line candidates, and the
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local maxima represents the parameters of probable lines.
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In [9]: h, theta, d = hough(image)
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.. ipython::
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In [10]: plt.figure()
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In [9]: h, theta, d = hough(image)
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In [10]: plt.title("hough transform")
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In [10]: plt.figure()
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In [10]: plt.xlabel("degrees")
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In [10]: plt.title("hough transform")
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In [10]: plt.ylabel("distance")
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In [10]: plt.xlabel("degrees")
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In [11]: plt.imshow(h)
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In [10]: plt.ylabel("distance")
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In [11]: plt.imshow(h)
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In [12]: plt.show()
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In [12]: plt.show()
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As can be seen, the maxima occur at 45 and 135 degrees, corresponding to the
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normal vector angles of each line.
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Another method is to use probabilistic_hough, an implementation
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Another method is to use the function probabilistic_hough, an implementation
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based on the Progressive Probabilistic Hough Transform [1]. It states that a
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random subset of voting points give good enough results, and that lines can
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be extracted during the voting process by walking along connected components.
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This returns the beginning and end of line segments, which are useful.
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The function has three parameters: a general threshold that is applied to
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the hough accumulator, a minimum line length and the line gap that influences
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the Hough accumulator, a minimum line length and the line gap that influences
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line merging.
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In [13]: lines = probabilistic_hough(image, threshold=10, line_length=10, line_gap=1)
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.. ipython::
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In [14]: plt.figure()
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In [13]: lines = probabilistic_hough(image, threshold=10, line_length=10, line_gap=1)
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In [15]: for line in lines:
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....: p0, p1 = line
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....: plt.plot((p0[0], p1[0]), (p0[1], p1[1]))
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....:
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In [14]: plt.figure()
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In [15]: for line in lines:
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....: p0, p1 = line
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....: plt.plot((p0[0], p1[0]), (p0[1], p1[1]))
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....:
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In [16]: plt.show()
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In [16]: plt.show()
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The Hough transform are often used on edge detected images.
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In [17]: from scikits.image.io import imread
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.. ipython::
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In [18]: from scikits.image import data_dir
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In [17]: from scikits.image.io import imread
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In [19]: from scikits.image.filter import canny
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In [18]: from scikits.image import data_dir
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In [20]: image = imread(data_dir + "/camera.png")
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In [19]: from scikits.image.filter import canny
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In [21]: edges = canny(image, 2, 1, 25)
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In [20]: image = imread(data_dir + "/camera.png")
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In [22]: plt.imshow(edges)
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In [21]: edges = canny(image, 2, 1, 25)
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In [22]: plt.imshow(edges)
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In [23]: plt.show()
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In [23]: plt.show()
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Apply the Probabilistic Hough Transform and find lines longer than 10 with a
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gap less than 3 pixels.
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In [24]: plt.figure()
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.. ipython::
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In [25]: plt.imshow(np.zeros(edges.shape))
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In [24]: plt.figure()
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In [26]: lines = probabilistic_hough(edges, threshold=1, line_length=10, line_gap=3)
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In [25]: plt.imshow(np.zeros(edges.shape))
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In [27]: for line in lines:
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....: p0, p1 = line
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....: plt.plot((p0[0], p1[0]), (p0[1], p1[1]))
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....:
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In [26]: lines = probabilistic_hough(edges, threshold=1, line_length=10, line_gap=3)
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In [28]: plt.show()
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In [27]: for line in lines:
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....: p0, p1 = line
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....: plt.plot((p0[0], p1[0]), (p0[1], p1[1]))
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....:
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In [28]: plt.show()
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References
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----------
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.. [1] C. Galamhos, J. Matas and J. Kittler,"Progressive probabilistic Hough
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.. [1] C. Galamhos, J. Matas and J. Kittler,"Progressive probabilistic Hough
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transform for line detection", in IEEE Computer Society Conference on
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Computer Vision and Pattern Recognition, 1999.
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.. [2] Duda, R. O. and P. E. Hart, "Use of the Hough Transformation to Detect
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[2] Duda, R. O. and P. E. Hart, "Use of the Hough Transformation to Detect
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Lines and Curves in Pictures," Comm. ACM, Vol. 15, pp. 11–15 (January,
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1972)
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