Some reST syntax correction. Now the PDF documentation builds correctly under Windows using MIKTEX. Some update on the tutorial structure. Some CSS syntax correction. Windows Install Tutorial v0.4.
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@@ -27,12 +27,12 @@ Steps
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.. math::
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K = \dfrac{1}{159}\begin{bmatrix}
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2 & 4 & 5 & 4 & 2 \\
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4 & 9 & 12 & 9 & 4 \\
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5 & 12 & 15 & 12 & 5 \\
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4 & 9 & 12 & 9 & 4 \\
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2 & 4 & 5 & 4 & 2
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\end{bmatrix}
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2 & 4 & 5 & 4 & 2 \\
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4 & 9 & 12 & 9 & 4 \\
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5 & 12 & 15 & 12 & 5 \\
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4 & 9 & 12 & 9 & 4 \\
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2 & 4 & 5 & 4 & 2
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\end{bmatrix}
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#. Find the intensity gradient of the image. For this, we follow a procedure analogous to Sobel:
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@@ -206,7 +206,8 @@ Explanation
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#. Create a window to display the results
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.. code-block:: cpp
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namedWindow( window_name, CV_WINDOW_AUTOSIZE );
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namedWindow( window_name, CV_WINDOW_AUTOSIZE );
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#. Create a Trackbar for the user to enter the lower threshold for our Canny detector:
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@@ -1,4 +1,4 @@
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.. _copyMakeBorder:
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.. _copyMakeBorderTutorial:
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Adding borders to your images
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******************************
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@@ -132,6 +132,7 @@ Code
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return 0;
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}
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Explanation
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=============
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@@ -30,9 +30,9 @@ How does it work?
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b. In the **Polar coordinate system:** Parameters: :math:`(r,\theta)`
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.. image:: images/Hough_Lines_Tutorial_Theory_0.jpg
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:alt: Line variables
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:height: 200pt
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:align: center
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:alt: Line variables
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:height: 200pt
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:align: center
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For Hough Transforms, we will express lines in the *Polar system*. Hence, a line equation can be written as:
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@@ -53,18 +53,19 @@ How does it work?
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#. If for a given :math:`(x_{0}, y_{0})` we plot the family of lines that goes through it, we get a sinusoid. For instance, for :math:`x_{0} = 8` and :math:`y_{0} = 6` we get the following plot (in a plane :math:`\theta` - :math:`r`):
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.. image:: images/Hough_Lines_Tutorial_Theory_1.jpg
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:alt: Polar plot of a the family of lines of a point
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:height: 200pt
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:align: center
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:alt: Polar plot of a the family of lines of a point
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:height: 200pt
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:align: center
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We consider only points such that :math:`r > 0` and :math:`0< \theta < 2 \pi`.
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#. We can do the same operation above for all the points in an image. If the curves of two different points intersect in the plane :math:`\theta` - :math:`r`, that means that both points belong to a same line. For instance, following with the example above and drawing the plot for two more points: :math:`x_{1} = 9`, :math:`y_{1} = 4` and :math:`x_{2} = 12`, :math:`y_{2} = 3`, we get:
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.. image:: images/Hough_Lines_Tutorial_Theory_2.jpg
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:alt: Polar plot of the family of lines for three points
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:height: 200pt
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:align: center
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:alt: Polar plot of the family of lines for three points
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:height: 200pt
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:align: center
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The three plots intersect in one single point :math:`(0.925, 9.6)`, these coordinates are the parameters (:math:`\theta, r`) or the line in which :math:`(x_{0}, y_{0})`, :math:`(x_{1}, y_{1})` and :math:`(x_{2}, y_{2})` lay.
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#. What does all the stuff above mean? It means that in general, a line can be *detected* by finding the number of intersections between curves.The more curves intersecting means that the line represented by that intersection have more points. In general, we can define a *threshold* of the minimum number of intersections needed to *detect* a line.
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@@ -276,14 +277,14 @@ Result
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Using an input image such as:
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.. image:: images/Hough_Lines_Tutorial_Original_Image.jpg
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:alt: Result of detecting lines with Hough Transform
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:align: center
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:alt: Result of detecting lines with Hough Transform
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:align: center
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We get the following result by using the Probabilistic Hough Line Transform:
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.. image:: images/Hough_Lines_Tutorial_Result.jpg
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:alt: Result of detecting lines with Hough Transform
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:align: center
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:alt: Result of detecting lines with Hough Transform
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:align: center
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You may observe that the number of lines detected vary while you change the *threshold*. The explanation is sort of evident: If you establish a higher threshold, fewer lines will be detected (since you will need more points to declare a line detected).
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@@ -231,6 +231,7 @@ Explanation
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Sobel( src_gray, grad_x, ddepth, 1, 0, 3, scale, delta, BORDER_DEFAULT );
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/// Gradient Y
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Sobel( src_gray, grad_y, ddepth, 0, 1, 3, scale, delta, BORDER_DEFAULT );
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The function takes the following arguments:
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* *src_gray*: In our example, the input image. Here it is *CV_8U*
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