init - 初始化项目

doc/py_tutorials/py_imgproc/py_houghlines/images/houghlines1.svg

@@ -0,0 +1,234 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   xmlns:osb="http://www.openswatchbook.org/uri/2009/osb"
+   xmlns:dc="http://purl.org/dc/elements/1.1/"
+   xmlns:cc="http://creativecommons.org/ns#"
+   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
+   xmlns:svg="http://www.w3.org/2000/svg"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   width="177.16013"
+   height="162.30061"
+   id="svg2"
+   version="1.1"
+   inkscape:version="0.48.4 r9939"
+   sodipodi:docname="houghline1.svg">
+  <defs
+     id="defs4">
+    <inkscape:path-effect
+       effect="skeletal"
+       id="path-effect8912"
+       is_visible="true"
+       pattern="M 0,0 1,0"
+       copytype="single_stretched"
+       prop_scale="1"
+       scale_y_rel="false"
+       spacing="0"
+       normal_offset="0"
+       tang_offset="0"
+       prop_units="false"
+       vertical_pattern="false"
+       fuse_tolerance="0" />
+    <marker
+       inkscape:stockid="Arrow1Send"
+       orient="auto"
+       refY="0"
+       refX="0"
+       id="Arrow1Send"
+       style="overflow:visible">
+      <path
+         id="path3774"
+         d="M 0,0 5,-5 -12.5,0 5,5 0,0 z"
+         style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt"
+         transform="matrix(-0.2,0,0,-0.2,-1.2,0)"
+         inkscape:connector-curvature="0" />
+    </marker>
+    <inkscape:path-effect
+       effect="skeletal"
+       id="path-effect7919"
+       is_visible="true"
+       pattern="m -1.0101525,-0.75761441 0.99999995,0"
+       copytype="single_stretched"
+       prop_scale="1"
+       scale_y_rel="false"
+       spacing="0"
+       normal_offset="0"
+       tang_offset="0"
+       prop_units="false"
+       vertical_pattern="false"
+       fuse_tolerance="0" />
+    <linearGradient
+       id="linearGradient7535"
+       osb:paint="solid">
+      <stop
+         style="stop-color:#000000;stop-opacity:1;"
+         offset="0"
+         id="stop7537" />
+    </linearGradient>
+    <inkscape:path-effect
+       effect="skeletal"
+       id="path-effect6087"
+       is_visible="true"
+       pattern="m -18.94036,-2.5253814 1,0"
+       copytype="single_stretched"
+       prop_scale="1"
+       scale_y_rel="false"
+       spacing="0"
+       normal_offset="0"
+       tang_offset="0"
+       prop_units="false"
+       vertical_pattern="false"
+       fuse_tolerance="0" />
+    <marker
+       inkscape:stockid="Arrow1Mstart"
+       orient="auto"
+       refY="0"
+       refX="0"
+       id="Arrow1Mstart"
+       style="overflow:visible">
+      <path
+         id="path3765"
+         d="M 0,0 5,-5 -12.5,0 5,5 0,0 z"
+         style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt"
+         transform="matrix(0.4,0,0,0.4,4,0)"
+         inkscape:connector-curvature="0" />
+    </marker>
+    <marker
+       inkscape:stockid="Arrow1Mend"
+       orient="auto"
+       refY="0"
+       refX="0"
+       id="Arrow1Mend"
+       style="overflow:visible">
+      <path
+         id="path3768"
+         d="M 0,0 5,-5 -12.5,0 5,5 0,0 z"
+         style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt"
+         transform="matrix(-0.4,0,0,-0.4,-4,0)"
+         inkscape:connector-curvature="0" />
+    </marker>
+    <marker
+       inkscape:stockid="Arrow1Lend"
+       orient="auto"
+       refY="0"
+       refX="0"
+       id="Arrow1Lend"
+       style="overflow:visible">
+      <path
+         id="path3762"
+         d="M 0,0 5,-5 -12.5,0 5,5 0,0 z"
+         style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt"
+         transform="matrix(-0.8,0,0,-0.8,-10,0)"
+         inkscape:connector-curvature="0" />
+    </marker>
+    <marker
+       inkscape:stockid="Arrow2Lstart"
+       orient="auto"
+       refY="0"
+       refX="0"
+       id="Arrow2Lstart"
+       style="overflow:visible">
+      <path
+         id="path3777"
+         style="fill-rule:evenodd;stroke-width:0.625;stroke-linejoin:round"
+         d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
+         transform="matrix(1.1,0,0,1.1,1.1,0)"
+         inkscape:connector-curvature="0" />
+    </marker>
+  </defs>
+  <sodipodi:namedview
+     id="base"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:pageopacity="0.0"
+     inkscape:pageshadow="2"
+     inkscape:zoom="11.2"
+     inkscape:cx="52.657337"
+     inkscape:cy="137.18191"
+     inkscape:document-units="px"
+     inkscape:current-layer="layer1"
+     showgrid="false"
+     fit-margin-top="10"
+     fit-margin-left="10"
+     fit-margin-right="5"
+     fit-margin-bottom="5"
+     inkscape:window-width="1366"
+     inkscape:window-height="709"
+     inkscape:window-x="0"
+     inkscape:window-y="27"
+     inkscape:window-maximized="1" />
+  <metadata
+     id="metadata7">
+    <rdf:RDF>
+      <cc:Work
+         rdf:about="">
+        <dc:format>image/svg+xml</dc:format>
+        <dc:type
+           rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
+        <dc:title></dc:title>
+      </cc:Work>
+    </rdf:RDF>
+  </metadata>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     transform="translate(-179.63266,-391.69653)">
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.7592535px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-start:url(#Arrow1Mstart);marker-end:url(#Arrow1Mend)"
+       d="m 350.84372,403.40485 -159.50274,0 0,144.64323"
+       id="path2985"
+       inkscape:connector-curvature="0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       d="M 313.14729,416.97623 207.33381,522.78971"
+       id="path5321"
+       inkscape:connector-curvature="0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:3, 1;stroke-dashoffset:0;marker-start:none;marker-end:none"
+       d="M 191.17137,403.33917 259.2304,471.3982"
+       id="path5323"
+       inkscape:connector-curvature="0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       d="m 264.65997,465.46355 -7.95495,-7.95495 -5.93465,5.93465"
+       id="path5701"
+       inkscape:connector-curvature="0" />
+    <text
+       xml:space="preserve"
+       style="font-size:17.18746948px;font-style:normal;font-weight:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans"
+       x="222.84058"
+       y="431.17072"
+       id="text8491"
+       sodipodi:linespacing="125%"
+       transform="scale(0.95341781,1.0488581)"><tspan
+         sodipodi:role="line"
+         id="tspan8493"
+         x="222.84058"
+         y="431.17072">ρ</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:11.58907604px;font-style:normal;font-weight:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans"
+       x="241.60213"
+       y="356.61414"
+       id="text8495"
+       sodipodi:linespacing="125%"
+       transform="scale(0.8575127,1.1661635)"><tspan
+         sodipodi:role="line"
+         id="tspan8497"
+         x="241.60213"
+         y="356.61414">θ</tspan></text>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.46696162;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none;marker-end:url(#Arrow1Send)"
+       d="m 205.18489,403.44491 c -0.0814,1.73816 0.44467,3.57132 -0.24208,5.17013 -0.64958,1.51228 -2.24971,2.34519 -3.3891,3.53293"
+       id="path8910"
+       inkscape:path-effect="#path-effect8912"
+       inkscape:original-d="m 205.18489,403.44491 c -0.0807,1.72338 0.43883,3.58492 -0.24208,5.17013 -0.64405,1.49942 -2.2594,2.35529 -3.3891,3.53293"
+       inkscape:connector-curvature="0"
+       sodipodi:nodetypes="cac" />
+  </g>
+</svg>

doc/py_tutorials/py_imgproc/py_houghlines/py_houghlines.markdown

@@ -0,0 +1,108 @@
+Hough Line Transform {#tutorial_py_houghlines}
+====================
+
+Goal
+----
+
+In this chapter,
+    -   We will understand the concept of the Hough Transform.
+    -   We will see how to use it to detect lines in an image.
+    -   We will see the following functions: **cv.HoughLines()**, **cv.HoughLinesP()**
+
+Theory
+------
+
+The Hough Transform is a popular technique to detect any shape, if you can represent that shape in a
+mathematical form. It can detect the shape even if it is broken or distorted a little bit. We will
+see how it works for a line.
+
+A line can be represented as \f$y = mx+c\f$ or in a parametric form, as
+\f$\rho = x \cos \theta + y \sin \theta\f$ where \f$\rho\f$ is the perpendicular distance from the origin to the
+line, and \f$\theta\f$ is the angle formed by this perpendicular line and the horizontal axis measured in
+counter-clockwise (That direction varies on how you represent the coordinate system. This
+representation is used in OpenCV). Check the image below:
+
+![image](images/houghlines1.svg)
+
+So if the line is passing below the origin, it will have a positive rho and an angle less than 180. If it
+is going above the origin, instead of taking an angle greater than 180, the angle is taken less than 180,
+and rho is taken negative. Any vertical line will have 0 degree and horizontal lines will have 90
+degree.
+
+Now let's see how the Hough Transform works for lines. Any line can be represented in these two terms,
+\f$(\rho, \theta)\f$. So first it creates a 2D array or accumulator (to hold the values of the two parameters)
+and it is set to 0 initially. Let rows denote the \f$\rho\f$ and columns denote the \f$\theta\f$. Size of
+array depends on the accuracy you need. Suppose you want the accuracy of angles to be 1 degree, you will
+need 180 columns. For \f$\rho\f$, the maximum distance possible is the diagonal length of the image. So
+taking one pixel accuracy, the number of rows can be the diagonal length of the image.
+
+Consider a 100x100 image with a horizontal line at the middle. Take the first point of the line. You
+know its (x,y) values. Now in the line equation, put the values \f$\theta = 0,1,2,....,180\f$ and check
+the \f$\rho\f$ you get. For every \f$(\rho, \theta)\f$ pair, you increment value by one in our accumulator
+in its corresponding \f$(\rho, \theta)\f$ cells. So now in accumulator, the cell (50,90) = 1 along with
+some other cells.
+
+Now take the second point on the line. Do the same as above. Increment the values in the cells
+corresponding to `(rho, theta)` you got. This time, the cell (50,90) = 2. What you actually
+do is voting the \f$(\rho, \theta)\f$ values. You continue this process for every point on the line. At
+each point, the cell (50,90) will be incremented or voted up, while other cells may or may not be
+voted up. This way, at the end, the cell (50,90) will have maximum votes. So if you search the
+accumulator for maximum votes, you get the value (50,90) which says, there is a line in this image
+at a distance 50 from the origin and at angle 90 degrees. It is well shown in the below animation (Image
+Courtesy: [Amos Storkey](http://homepages.inf.ed.ac.uk/amos/hough.html) )
+
+![](images/houghlinesdemo.gif)
+
+This is how hough transform works for lines. It is simple, and may be you can implement it using
+Numpy on your own. Below is an image which shows the accumulator. Bright spots at some locations
+denote they are the parameters of possible lines in the image. (Image courtesy: [Wikipedia](http://en.wikipedia.org/wiki/Hough_transform) )
+
+![](images/houghlines2.jpg)
+
+Hough Transform in OpenCV
+=========================
+
+Everything explained above is encapsulated in the OpenCV function, **cv.HoughLines()**. It simply returns an array of :math:(rho,
+theta)\` values. \f$\rho\f$ is measured in pixels and \f$\theta\f$ is measured in radians. First parameter,
+Input image should be a binary image, so apply threshold or use canny edge detection before
+applying hough transform. Second and third parameters are \f$\rho\f$ and \f$\theta\f$ accuracies
+respectively. Fourth argument is the threshold, which means the minimum vote it should get to be
+considered as a line. Remember, number of votes depends upon the number of points on the line. So it
+represents the minimum length of line that should be detected.
+@include hough_line_transform.py
+Check the results below:
+
+![image](images/houghlines3.jpg)
+
+Probabilistic Hough Transform
+-----------------------------
+
+In the hough transform, you can see that even for a line with two arguments, it takes a lot of
+computation. Probabilistic Hough Transform is an optimization of the Hough Transform we saw. It doesn't
+take all the points into consideration. Instead, it takes only a random subset of points which is
+sufficient for line detection. We just have to decrease the threshold. See image below which compares
+Hough Transform and Probabilistic Hough Transform in Hough space. (Image Courtesy :
+[Franck Bettinger's home page](http://phdfb1.free.fr/robot/mscthesis/node14.html) )
+
+![image](images/houghlines4.png)
+
+OpenCV implementation is based on Robust Detection of Lines Using the Progressive Probabilistic
+Hough Transform by Matas, J. and Galambos, C. and Kittler, J.V. @cite Matas00. The function used is
+**cv.HoughLinesP()**. It has two new arguments.
+-   **minLineLength** - Minimum length of line. Line segments shorter than this are rejected.
+-   **maxLineGap** - Maximum allowed gap between line segments to treat them as a single line.
+
+Best thing is that, it directly returns the two endpoints of lines. In previous case, you got only
+the parameters of lines, and you had to find all the points. Here, everything is direct and simple.
+@include probabilistic_hough_line_transform.py
+See the results below:
+
+![image](images/houghlines5.jpg)
+
+Additional Resources
+--------------------
+
+-#  [Hough Transform on Wikipedia](http://en.wikipedia.org/wiki/Hough_transform)
+
+Exercises
+---------