From d32a134b0f1fbe890c3211b26c007c4f16110357 Mon Sep 17 00:00:00 2001 From: Ana Huaman Date: Wed, 29 Jun 2011 00:20:05 +0000 Subject: [PATCH] Added Hough Lines Tutorial in reST --- doc/conf.py | 5 +- ...Canny_Detector_Tutorial_Original_Image.jpg | Bin 0 -> 39974 bytes .../images/Canny_Detector_Tutorial_Result.jpg | Bin 0 -> 32049 bytes .../imgtrans/hough_circle/hough_circle.rst | 78 +++++ .../images/Hough_Circle_Tutorial_Result.jpg | Bin 0 -> 46941 bytes .../imgtrans/hough_lines/hough_lines.rst | 289 ++++++++++++++++++ .../Hough_Lines_Tutorial_Original_Image.jpg | Bin 0 -> 34843 bytes .../images/Hough_Lines_Tutorial_Result.jpg | Bin 0 -> 63151 bytes .../images/Hough_Lines_Tutorial_Theory_0.jpg | Bin 0 -> 13994 bytes .../images/Hough_Lines_Tutorial_Theory_1.jpg | Bin 0 -> 17452 bytes .../images/Hough_Lines_Tutorial_Theory_2.jpg | Bin 0 -> 23090 bytes ...place_Operator_Tutorial_Original_Image.jpg | Bin 0 -> 72839 bytes .../Laplace_Operator_Tutorial_Result.jpg | Bin 0 -> 78543 bytes ...lace_Operator_Tutorial_Theory_Previous.jpg | Bin 0 -> 31109 bytes ...e_Operator_Tutorial_Theory_ddIntensity.jpg | Bin 0 -> 15533 bytes ...ves_Tutorial_Theory_Intensity_Function.jpg | Bin 0 -> 12741 bytes ...es_Tutorial_Theory_dIntensity_Function.jpg | Bin 0 -> 15194 bytes ...s_Tutorial_Theory_ddIntensity_Function.jpg | Bin 0 -> 15533 bytes doc/tutorials/imgproc/pyramids/pyramids.rst | 4 +- .../imgtrans/Hough_Circle_Tutorial_Cover.jpg | Bin 0 -> 46941 bytes .../imgtrans/Hough_Lines_Tutorial_Cover.jpg | Bin 0 -> 63151 bytes .../table_of_content_imgproc.rst | 36 +++ 22 files changed, 409 insertions(+), 3 deletions(-) create mode 100644 doc/tutorials/imgproc/imgtrans/canny_detector/images/Canny_Detector_Tutorial_Original_Image.jpg create mode 100644 doc/tutorials/imgproc/imgtrans/canny_detector/images/Canny_Detector_Tutorial_Result.jpg create mode 100644 doc/tutorials/imgproc/imgtrans/hough_circle/hough_circle.rst create mode 100644 doc/tutorials/imgproc/imgtrans/hough_circle/images/Hough_Circle_Tutorial_Result.jpg create mode 100644 doc/tutorials/imgproc/imgtrans/hough_lines/hough_lines.rst create mode 100644 doc/tutorials/imgproc/imgtrans/hough_lines/images/Hough_Lines_Tutorial_Original_Image.jpg create mode 100644 doc/tutorials/imgproc/imgtrans/hough_lines/images/Hough_Lines_Tutorial_Result.jpg create mode 100644 doc/tutorials/imgproc/imgtrans/hough_lines/images/Hough_Lines_Tutorial_Theory_0.jpg create mode 100644 doc/tutorials/imgproc/imgtrans/hough_lines/images/Hough_Lines_Tutorial_Theory_1.jpg create mode 100644 doc/tutorials/imgproc/imgtrans/hough_lines/images/Hough_Lines_Tutorial_Theory_2.jpg create mode 100644 doc/tutorials/imgproc/imgtrans/laplace_operator/images/Laplace_Operator_Tutorial_Original_Image.jpg create mode 100644 doc/tutorials/imgproc/imgtrans/laplace_operator/images/Laplace_Operator_Tutorial_Result.jpg create mode 100644 doc/tutorials/imgproc/imgtrans/laplace_operator/images/Laplace_Operator_Tutorial_Theory_Previous.jpg create mode 100644 doc/tutorials/imgproc/imgtrans/laplace_operator/images/Laplace_Operator_Tutorial_Theory_ddIntensity.jpg create mode 100644 doc/tutorials/imgproc/imgtrans/sobel_derivatives/images/Sobel_Derivatives_Tutorial_Theory_Intensity_Function.jpg create mode 100644 doc/tutorials/imgproc/imgtrans/sobel_derivatives/images/Sobel_Derivatives_Tutorial_Theory_dIntensity_Function.jpg create mode 100644 doc/tutorials/imgproc/imgtrans/sobel_derivatives/images/Sobel_Derivatives_Tutorial_Theory_ddIntensity_Function.jpg create mode 100644 doc/tutorials/imgproc/table_of_content_imgproc/images/imgtrans/Hough_Circle_Tutorial_Cover.jpg create mode 100644 doc/tutorials/imgproc/table_of_content_imgproc/images/imgtrans/Hough_Lines_Tutorial_Cover.jpg diff --git a/doc/conf.py b/doc/conf.py index cf0134b2fc..474ce14965 100644 --- a/doc/conf.py +++ b/doc/conf.py @@ -313,7 +313,10 @@ extlinks = {'cvt_color': ('http://opencv.willowgarage.com/documentation/cpp/imgp 'laplacian': ('http://opencv.willowgarage.com/documentation/cpp/image_filtering.html#cv-laplacian%s', None), 'canny': ('http://opencv.willowgarage.com/documentation/cpp/imgproc_feature_detection.html?#Canny%s', None), 'copy_to': ('http://opencv.willowgarage.com/documentation/cpp/core_basic_structures.html?#Mat::copyTo%s', None), - 'opencv_group' : ('http://tech.groups.yahoo.com/group/OpenCV/%s', None) + 'opencv_group' : ('http://tech.groups.yahoo.com/group/OpenCV/%s', None), + 'hough_lines' : ('http://opencv.willowgarage.com/documentation/cpp/imgproc_feature_detection.html?#cv-houghlines%s', None), + 'hough_lines_p' : ('http://opencv.willowgarage.com/documentation/cpp/imgproc_feature_detection.html?#cv-houghlinesp%s', None), + 'hough_circles' : ('http://opencv.willowgarage.com/documentation/cpp/imgproc_feature_detection.html?#cv-houghcircles%s', None) } diff --git 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a/doc/tutorials/imgproc/imgtrans/hough_circle/hough_circle.rst b/doc/tutorials/imgproc/imgtrans/hough_circle/hough_circle.rst new file mode 100644 index 0000000000..feb3bf1cf4 --- /dev/null +++ b/doc/tutorials/imgproc/imgtrans/hough_circle/hough_circle.rst @@ -0,0 +1,78 @@ +.. _hough_circle: + +Hough Circle Transform +*********************** + +Goal +===== +In this tutorial you will learn how to: + +* Use the OpenCV functions :hough_circles:`HoughCircles <>` to detect circles in an image. + +Code +====== + +#. **What does this program do?** + + * Loads an image and blur it to reduce the noise + * Applies the *Hough Circle Transform* to the blurred image . + * Display the detected circle in a window. + +#. The sample code that we will explain can be downloaded from `here `_. A slightly fancier version (which shows both Hough standard and probabilistic with trackbars for changing the threshold values) can be found `here `_ + +.. code-block:: cpp + + #include "opencv2/highgui/highgui.hpp" + #include "opencv2/imgproc/imgproc.hpp" + #include + #include + + using namespace cv; + + /** @function main */ + int main(int argc, char** argv) + { + Mat src, src_gray; + + /// Read the image + src = imread( argv[1], 1 ); + + if( !src.data ) + { return -1; } + + /// Convert it to gray + cvtColor( src, src_gray, CV_BGR2GRAY ); + + /// Reduce the noise so we avoid false circle detection + GaussianBlur( src_gray, src_gray, Size(9, 9), 2, 2 ); + + vector circles; + + /// Apply the Hough Transform to find the circles + HoughCircles( src_gray, circles, CV_HOUGH_GRADIENT, 1, src_gray.rows/8, 200, 100, 0, 0 ); + + /// Draw the circles detected + for( size_t i = 0; i < circles.size(); i++ ) + { + Point center(cvRound(circles[i][0]), cvRound(circles[i][1])); + int radius = cvRound(circles[i][2]); + // circle center + circle( src, center, 3, Scalar(0,255,0), -1, 8, 0 ); + // circle outline + circle( src, center, radius, Scalar(0,0,255), 3, 8, 0 ); + } + + /// Show your results + namedWindow( "Hough Circle Transform Demo", CV_WINDOW_AUTOSIZE ); + imshow( "Hough Circle Transform Demo", src ); + + waitKey(0); + return 0; + } + +Result +======= + +.. image:: images/Hough_Circle_Tutorial_Result.jpg + :alt: Result of detecting circles with Hough Transform + :align: center diff --git a/doc/tutorials/imgproc/imgtrans/hough_circle/images/Hough_Circle_Tutorial_Result.jpg b/doc/tutorials/imgproc/imgtrans/hough_circle/images/Hough_Circle_Tutorial_Result.jpg new file mode 100644 index 0000000000000000000000000000000000000000..2a599fc6ca6cda07ee8d2382a732e0c785e3739e GIT binary patch literal 46941 zcmd?QWmFu&)-F7_ySvK_?iSn!9~hhvT!-KUm*52V;4;8q0fG}CSnvc78iEE77F<5g zdGA`^`}h97)xGxW?y_gEe#&<3dR~0~4Il)osH*^wkdOdsFBjl>1)vB(LqSDFML~NJ 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Bradski and Kaehler. + +Hough Line Transform +--------------------- +#. The Hough Line Transform is a transform used to detect straight lines. +#. To apply the Transform, first an edge detection pre-processing is desirable. + +How does it work? +^^^^^^^^^^^^^^^^^^ + +#. As you know, a line in the image space can be expressed with two variables. For example: + + a. In the **Cartesian coordinate system:** Parameters: :math:`(m,b)`. + b. In the **Polar coordinate system:** Parameters: :math:`(r,\theta)` + + .. image:: images/Hough_Lines_Tutorial_Theory_0.jpg + :alt: Line variables + :height: 200pt + :align: center + + For Hough Transforms, we will express lines in the *Polar system*. Hence, a line equation can be written as: + + .. math:: + + y = \left ( -\dfrac{\cos \theta}{\sin \theta} \right ) x + \left ( \dfrac{r}{\sin \theta} \right ) + + Arranging the terms: :math:`r = x \cos \theta + y \sin \theta` + +#. In general for each point :math:`(x_{0}, y_{0})`, we can define the family of lines that goes through that point as: + + .. math:: + + r_{\theta} = x_{0} \cdot \cos \theta + y_{0} \cdot \sin \theta + + Meaning that each pair :math:`(r_{\theta},\theta)` represents each line that passes by :math:`(x_{0}, y_{0})`. + +#. 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`): + + .. image:: images/Hough_Lines_Tutorial_Theory_1.jpg + :alt: Polar plot of a the family of lines of a point + :height: 200pt + :align: center + + We consider only points such that :math:`r > 0` and :math:`0< \theta < 2 \pi`. + +#. 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: + + .. image:: images/Hough_Lines_Tutorial_Theory_2.jpg + :alt: Polar plot of the family of lines for three points + :height: 200pt + :align: center + 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. + +#. 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. + +#. This is what the Hough Line Transform does. It keeps track of the intersection between curves of every point in the image. If the number of intersections is above some *threshold*, then it declares it as a line with the parameters :math:`(\theta, r_{\theta})` of the intersection point. + +Standard and Probabilistic Hough Line Transform +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +OpenCV implements two kind of Hough Line Transforms: + +a. **The Standard Hough Transform** + + * It consists in pretty much what we just explained in the previous section. It gives you as result a vector of couples :math:`(\theta, r_{\theta})` + + * In OpenCV it is implemented with the function :hough_lines:`HoughLines <>` + +b. **The Probabilistic Hough Line Transform** + + * A more efficient implementation of the Hough Line Transform. It gives as output the extremes of the detected lines :math:`(x_{0}, y_{0}, x_{1}, y_{1})` + + * In OpenCV it is implemented with the function :hough_lines_p:`HoughLinesP <>` + +Code +====== + +#. **What does this program do?** + + * Loads an image + * Applies either a *Standard Hough Line Transform* or a *Probabilistic Line Transform*. + * Display the original image and the detected line in two windows. + +#. The sample code that we will explain can be downloaded from `here `_. A slightly fancier version (which shows both Hough standard and probabilistic with trackbars for changing the threshold values) can be found `here `_ + +.. code-block:: cpp + + #include "opencv2/highgui/highgui.hpp" + #include "opencv2/imgproc/imgproc.hpp" + + #include + + using namespace cv; + using namespace std; + + void help() + { + cout << "\nThis program demonstrates line finding with the Hough transform.\n" + "Usage:\n" + "./houghlines , Default is pic1.png\n" << endl; + } + + int main(int argc, char** argv) + { + const char* filename = argc >= 2 ? argv[1] : "pic1.png"; + + Mat src = imread(filename, 0); + if(src.empty()) + { + help(); + cout << "can not open " << filename << endl; + return -1; + } + + Mat dst, cdst; + Canny(src, dst, 50, 200, 3); + cvtColor(dst, cdst, CV_GRAY2BGR); + + #if 0 + vector lines; + HoughLines(dst, lines, 1, CV_PI/180, 100, 0, 0 ); + + for( size_t i = 0; i < lines.size(); i++ ) + { + float rho = lines[i][0], theta = lines[i][1]; + Point pt1, pt2; + double a = cos(theta), b = sin(theta); + double x0 = a*rho, y0 = b*rho; + pt1.x = cvRound(x0 + 1000*(-b)); + pt1.y = cvRound(y0 + 1000*(a)); + pt2.x = cvRound(x0 - 1000*(-b)); + pt2.y = cvRound(y0 - 1000*(a)); + line( cdst, pt1, pt2, Scalar(0,0,255), 3, CV_AA); + } + #else + vector lines; + HoughLinesP(dst, lines, 1, CV_PI/180, 50, 50, 10 ); + for( size_t i = 0; i < lines.size(); i++ ) + { + Vec4i l = lines[i]; + line( cdst, Point(l[0], l[1]), Point(l[2], l[3]), Scalar(0,0,255), 3, CV_AA); + } + #endif + imshow("source", src); + imshow("detected lines", cdst); + + waitKey(); + + return 0; + } + +Explanation +============= + +#. Load an image + + .. code-block:: cpp + + Mat src = imread(filename, 0); + if(src.empty()) + { + help(); + cout << "can not open " << filename << endl; + return -1; + } + +#. Detect the edges of the image by using a Canny detector + + .. code-block:: cpp + + Canny(src, dst, 50, 200, 3); + + Now we will apply the Hough Line Transform. We will explain how to use both OpenCV functions available for this purpose: + +#. **Standard Hough Line Transform** + + a. First, you apply the Transform: + + .. code-block:: cpp + + vector lines; + HoughLines(dst, lines, 1, CV_PI/180, 100, 0, 0 ); + + with the following arguments: + + * *dst*: Output of the edge detector. It should be a grayscale image (although in fact it is a binary one) + * *lines*: A vector that will store the parameters :math:`(r,\theta)` of the detected lines + * *rho* : The resolution of the parameter :math:`r` in pixels. We use **1** pixel. + * *theta*: The resolution of the parameter :math:`\theta` in radians. We use **1 degree** (CV_PI/180) + * *threshold*: The minimum number of intersections to "*detect*" a line + * *srn* and *stn*: Default parameters to zero. Check OpenCV reference for more info. + + b. And then you display the result by drawing the lines. + + .. code-block:: cpp + + for( size_t i = 0; i < lines.size(); i++ ) + { + float rho = lines[i][0], theta = lines[i][1]; + Point pt1, pt2; + double a = cos(theta), b = sin(theta); + double x0 = a*rho, y0 = b*rho; + pt1.x = cvRound(x0 + 1000*(-b)); + pt1.y = cvRound(y0 + 1000*(a)); + pt2.x = cvRound(x0 - 1000*(-b)); + pt2.y = cvRound(y0 - 1000*(a)); + line( cdst, pt1, pt2, Scalar(0,0,255), 3, CV_AA); + } + +#. **Probabilistic Hough Line Transform** + + a. First you apply the transform: + + .. code-block:: cpp + + vector lines; + HoughLinesP(dst, lines, 1, CV_PI/180, 50, 50, 10 ); + + with the arguments: + + * *dst*: Output of the edge detector. It should be a grayscale image (although in fact it is a binary one) + * *lines*: A vector that will store the parameters :math:`(x_{start}, y_{start}, x_{end}, y_{end})` of the detected lines + * *rho* : The resolution of the parameter :math:`r` in pixels. We use **1** pixel. + * *theta*: The resolution of the parameter :math:`\theta` in radians. We use **1 degree** (CV_PI/180) + * *threshold*: The minimum number of intersections to "*detect*" a line + * *minLinLength*: The minimum number of points that can form a line. Lines with less than this number of points are disregarded. + * *maxLineGap*: The maximum gap between two points to be considered in the same line. + + b. And then you display the result by drawing the lines. + + .. code-block:: cpp + + for( size_t i = 0; i < lines.size(); i++ ) + { + Vec4i l = lines[i]; + line( cdst, Point(l[0], l[1]), Point(l[2], l[3]), Scalar(0,0,255), 3, CV_AA); + } + + +#. Display the original image and the detected lines: + + .. code-block:: cpp + + imshow("source", src); + imshow("detected lines", cdst); + +#. Wait until the user exits the program + + .. code-block:: cpp + + waitKey(); + + +Result +======= + +.. note:: + + The results below are obtained using the slightly fancier version we mentioned in the *Code* section. It still implements the same stuff as above, only adding the Trackbar for the Threshold. + +Using an input image such as: + +.. image:: images/Hough_Lines_Tutorial_Original_Image.jpg + :alt: Result of detecting lines with Hough Transform + :align: center + +We get the following result by using the Probabilistic Hough Line Transform: + +.. image:: images/Hough_Lines_Tutorial_Result.jpg + :alt: Result of detecting lines with Hough Transform + :align: center + +You may observe that the number of lines detected vary while you change the *threshold*. 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