init - 初始化项目
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doc/tutorials/imgproc/imgtrans/hough_lines/hough_lines.markdown
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doc/tutorials/imgproc/imgtrans/hough_lines/hough_lines.markdown
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Hough Line Transform {#tutorial_hough_lines}
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====================
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@tableofcontents
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@prev_tutorial{tutorial_canny_detector}
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@next_tutorial{tutorial_hough_circle}
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| | |
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| -: | :- |
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| Original author | Ana Huamán |
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| Compatibility | OpenCV >= 3.0 |
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Goal
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----
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In this tutorial you will learn how to:
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- Use the OpenCV functions **HoughLines()** and **HoughLinesP()** to detect lines in an
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image.
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Theory
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------
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@note The explanation below belongs to the book **Learning OpenCV** by Bradski and Kaehler.
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Hough Line Transform
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--------------------
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-# The Hough Line Transform is a transform used to detect straight lines.
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-# To apply the Transform, first an edge detection pre-processing is desirable.
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### How does it work?
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-# As you know, a line in the image space can be expressed with two variables. For example:
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-# In the **Cartesian coordinate system:** Parameters: \f$(m,b)\f$.
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-# In the **Polar coordinate system:** Parameters: \f$(r,\theta)\f$
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For Hough Transforms, we will express lines in the *Polar system*. Hence, a line equation can be
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written as:
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\f[y = \left ( -\dfrac{\cos \theta}{\sin \theta} \right ) x + \left ( \dfrac{r}{\sin \theta} \right )\f]
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Arranging the terms: \f$r = x \cos \theta + y \sin \theta\f$
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-# In general for each point \f$(x_{0}, y_{0})\f$, we can define the family of lines that goes through
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that point as:
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\f[r_{\theta} = x_{0} \cdot \cos \theta + y_{0} \cdot \sin \theta\f]
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Meaning that each pair \f$(r_{\theta},\theta)\f$ represents each line that passes by
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\f$(x_{0}, y_{0})\f$.
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-# If for a given \f$(x_{0}, y_{0})\f$ we plot the family of lines that goes through it, we get a
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sinusoid. For instance, for \f$x_{0} = 8\f$ and \f$y_{0} = 6\f$ we get the following plot (in a plane
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\f$\theta\f$ - \f$r\f$):
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We consider only points such that \f$r > 0\f$ and \f$0< \theta < 2 \pi\f$.
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-# We can do the same operation above for all the points in an image. If the curves of two
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different points intersect in the plane \f$\theta\f$ - \f$r\f$, that means that both points belong to a
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same line. For instance, following with the example above and drawing the plot for two more
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points: \f$x_{1} = 4\f$, \f$y_{1} = 9\f$ and \f$x_{2} = 12\f$, \f$y_{2} = 3\f$, we get:
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The three plots intersect in one single point \f$(0.925, 9.6)\f$, these coordinates are the
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parameters (\f$\theta, r\f$) or the line in which \f$(x_{0}, y_{0})\f$, \f$(x_{1}, y_{1})\f$ and
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\f$(x_{2}, y_{2})\f$ lay.
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-# What does all the stuff above mean? It means that in general, a line can be *detected* by
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finding the number of intersections between curves.The more curves intersecting means that the
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line represented by that intersection have more points. In general, we can define a *threshold*
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of the minimum number of intersections needed to *detect* a line.
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-# This is what the Hough Line Transform does. It keeps track of the intersection between curves of
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every point in the image. If the number of intersections is above some *threshold*, then it
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declares it as a line with the parameters \f$(\theta, r_{\theta})\f$ of the intersection point.
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### Standard and Probabilistic Hough Line Transform
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OpenCV implements two kind of Hough Line Transforms:
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a. **The Standard Hough Transform**
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- It consists in pretty much what we just explained in the previous section. It gives you as
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result a vector of couples \f$(\theta, r_{\theta})\f$
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- In OpenCV it is implemented with the function **HoughLines()**
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b. **The Probabilistic Hough Line Transform**
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- A more efficient implementation of the Hough Line Transform. It gives as output the extremes
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of the detected lines \f$(x_{0}, y_{0}, x_{1}, y_{1})\f$
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- In OpenCV it is implemented with the function **HoughLinesP()**
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### What does this program do?
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- Loads an image
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- Applies a *Standard Hough Line Transform* and a *Probabilistic Line Transform*.
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- Display the original image and the detected line in three windows.
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Code
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----
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@add_toggle_cpp
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The sample code that we will explain can be downloaded from
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[here](https://raw.githubusercontent.com/opencv/opencv/master/samples/cpp/tutorial_code/ImgTrans/houghlines.cpp).
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A slightly fancier version (which shows both Hough standard and probabilistic
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with trackbars for changing the threshold values) can be found
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[here](https://raw.githubusercontent.com/opencv/opencv/master/samples/cpp/tutorial_code/ImgTrans/HoughLines_Demo.cpp).
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@include samples/cpp/tutorial_code/ImgTrans/houghlines.cpp
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@end_toggle
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@add_toggle_java
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The sample code that we will explain can be downloaded from
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[here](https://raw.githubusercontent.com/opencv/opencv/master/samples/java/tutorial_code/ImgTrans/HoughLine/HoughLines.java).
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@include samples/java/tutorial_code/ImgTrans/HoughLine/HoughLines.java
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@end_toggle
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@add_toggle_python
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The sample code that we will explain can be downloaded from
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[here](https://raw.githubusercontent.com/opencv/opencv/master/samples/python/tutorial_code/ImgTrans/HoughLine/hough_lines.py).
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@include samples/python/tutorial_code/ImgTrans/HoughLine/hough_lines.py
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@end_toggle
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Explanation
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-----------
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#### Load an image:
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@add_toggle_cpp
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@snippet samples/cpp/tutorial_code/ImgTrans/houghlines.cpp load
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@end_toggle
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@add_toggle_java
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@snippet samples/java/tutorial_code/ImgTrans/HoughLine/HoughLines.java load
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@end_toggle
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@add_toggle_python
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@snippet samples/python/tutorial_code/ImgTrans/HoughLine/hough_lines.py load
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@end_toggle
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#### Detect the edges of the image by using a Canny detector:
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@add_toggle_cpp
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@snippet samples/cpp/tutorial_code/ImgTrans/houghlines.cpp edge_detection
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@end_toggle
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@add_toggle_java
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@snippet samples/java/tutorial_code/ImgTrans/HoughLine/HoughLines.java edge_detection
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@end_toggle
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@add_toggle_python
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@snippet samples/python/tutorial_code/ImgTrans/HoughLine/hough_lines.py edge_detection
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@end_toggle
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Now we will apply the Hough Line Transform. We will explain how to use both OpenCV functions
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available for this purpose.
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#### Standard Hough Line Transform:
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First, you apply the Transform:
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@add_toggle_cpp
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@snippet samples/cpp/tutorial_code/ImgTrans/houghlines.cpp hough_lines
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@end_toggle
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@add_toggle_java
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@snippet samples/java/tutorial_code/ImgTrans/HoughLine/HoughLines.java hough_lines
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@end_toggle
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@add_toggle_python
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@snippet samples/python/tutorial_code/ImgTrans/HoughLine/hough_lines.py hough_lines
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@end_toggle
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- with the following arguments:
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- *dst*: Output of the edge detector. It should be a grayscale image (although in fact it
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is a binary one)
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- *lines*: A vector that will store the parameters \f$(r,\theta)\f$ of the detected lines
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- *rho* : The resolution of the parameter \f$r\f$ in pixels. We use **1** pixel.
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- *theta*: The resolution of the parameter \f$\theta\f$ in radians. We use **1 degree**
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(CV_PI/180)
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- *threshold*: The minimum number of intersections to "*detect*" a line
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- *srn* and *stn*: Default parameters to zero. Check OpenCV reference for more info.
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And then you display the result by drawing the lines.
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@add_toggle_cpp
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@snippet samples/cpp/tutorial_code/ImgTrans/houghlines.cpp draw_lines
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@end_toggle
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@add_toggle_java
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@snippet samples/java/tutorial_code/ImgTrans/HoughLine/HoughLines.java draw_lines
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@end_toggle
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@add_toggle_python
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@snippet samples/python/tutorial_code/ImgTrans/HoughLine/hough_lines.py draw_lines
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@end_toggle
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#### Probabilistic Hough Line Transform
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First you apply the transform:
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@add_toggle_cpp
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@snippet samples/cpp/tutorial_code/ImgTrans/houghlines.cpp hough_lines_p
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@end_toggle
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@add_toggle_java
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@snippet samples/java/tutorial_code/ImgTrans/HoughLine/HoughLines.java hough_lines_p
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@end_toggle
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@add_toggle_python
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@snippet samples/python/tutorial_code/ImgTrans/HoughLine/hough_lines.py hough_lines_p
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@end_toggle
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- with the arguments:
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- *dst*: Output of the edge detector. It should be a grayscale image (although in fact it
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is a binary one)
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- *lines*: A vector that will store the parameters
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\f$(x_{start}, y_{start}, x_{end}, y_{end})\f$ of the detected lines
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- *rho* : The resolution of the parameter \f$r\f$ in pixels. We use **1** pixel.
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- *theta*: The resolution of the parameter \f$\theta\f$ in radians. We use **1 degree**
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(CV_PI/180)
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- *threshold*: The minimum number of intersections to "*detect*" a line
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- *minLineLength*: The minimum number of points that can form a line. Lines with less than
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this number of points are disregarded.
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- *maxLineGap*: The maximum gap between two points to be considered in the same line.
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And then you display the result by drawing the lines.
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@add_toggle_cpp
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@snippet samples/cpp/tutorial_code/ImgTrans/houghlines.cpp draw_lines_p
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@end_toggle
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@add_toggle_java
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@snippet samples/java/tutorial_code/ImgTrans/HoughLine/HoughLines.java draw_lines_p
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@end_toggle
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@add_toggle_python
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@snippet samples/python/tutorial_code/ImgTrans/HoughLine/hough_lines.py draw_lines_p
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@end_toggle
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#### Display the original image and the detected lines:
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@add_toggle_cpp
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@snippet samples/cpp/tutorial_code/ImgTrans/houghlines.cpp imshow
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@end_toggle
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@add_toggle_java
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@snippet samples/java/tutorial_code/ImgTrans/HoughLine/HoughLines.java imshow
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@end_toggle
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@add_toggle_python
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@snippet samples/python/tutorial_code/ImgTrans/HoughLine/hough_lines.py imshow
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@end_toggle
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#### Wait until the user exits the program
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@add_toggle_cpp
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@snippet samples/cpp/tutorial_code/ImgTrans/houghlines.cpp exit
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@end_toggle
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@add_toggle_java
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@snippet samples/java/tutorial_code/ImgTrans/HoughLine/HoughLines.java exit
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@end_toggle
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@add_toggle_python
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@snippet samples/python/tutorial_code/ImgTrans/HoughLine/hough_lines.py exit
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@end_toggle
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Result
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------
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@note
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The results below are obtained using the slightly fancier version we mentioned in the *Code*
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section. It still implements the same stuff as above, only adding the Trackbar for the
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Threshold.
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Using an input image such as a [sudoku image](https://raw.githubusercontent.com/opencv/opencv/master/samples/data/sudoku.png).
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We get the following result by using the Standard Hough Line Transform:
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And by using the Probabilistic Hough Line Transform:
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You may observe that the number of lines detected vary while you change the *threshold*. The
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explanation is sort of evident: If you establish a higher threshold, fewer lines will be detected
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(since you will need more points to declare a line detected).
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