Removed Sphinx documentation files
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Maksim Shabunin
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.. _harris_detector:
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Harris corner detector
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**********************
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Goal
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=====
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In this tutorial you will learn:
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.. container:: enumeratevisibleitemswithsquare
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* What features are and why they are important
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* Use the function :corner_harris:`cornerHarris <>` to detect corners using the Harris-Stephens method.
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Theory
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======
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What is a feature?
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-------------------
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.. container:: enumeratevisibleitemswithsquare
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* In computer vision, usually we need to find matching points between different frames of an environment. Why? If we know how two images relate to each other, we can use *both* images to extract information of them.
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* When we say **matching points** we are referring, in a general sense, to *characteristics* in the scene that we can recognize easily. We call these characteristics **features**.
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* **So, what characteristics should a feature have?**
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* It must be *uniquely recognizable*
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Types of Image Features
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------------------------
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To mention a few:
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.. container:: enumeratevisibleitemswithsquare
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* Edges
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* **Corners** (also known as interest points)
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* Blobs (also known as regions of interest )
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In this tutorial we will study the *corner* features, specifically.
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Why is a corner so special?
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----------------------------
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.. container:: enumeratevisibleitemswithsquare
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* Because, since it is the intersection of two edges, it represents a point in which the directions of these two edges *change*. Hence, the gradient of the image (in both directions) have a high variation, which can be used to detect it.
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How does it work?
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-----------------
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.. container:: enumeratevisibleitemswithsquare
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* Let's look for corners. Since corners represents a variation in the gradient in the image, we will look for this "variation".
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* Consider a grayscale image :math:`I`. We are going to sweep a window :math:`w(x,y)` (with displacements :math:`u` in the x direction and :math:`v` in the right direction) :math:`I` and will calculate the variation of intensity.
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.. math::
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E(u,v) = \sum _{x,y} w(x,y)[ I(x+u,y+v) - I(x,y)]^{2}
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where:
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* :math:`w(x,y)` is the window at position :math:`(x,y)`
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* :math:`I(x,y)` is the intensity at :math:`(x,y)`
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* :math:`I(x+u,y+v)` is the intensity at the moved window :math:`(x+u,y+v)`
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* Since we are looking for windows with corners, we are looking for windows with a large variation in intensity. Hence, we have to maximize the equation above, specifically the term:
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.. math::
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\sum _{x,y}[ I(x+u,y+v) - I(x,y)]^{2}
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* Using *Taylor expansion*:
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.. math::
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E(u,v) \approx \sum _{x,y}[ I(x,y) + u I_{x} + vI_{y} - I(x,y)]^{2}
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* Expanding the equation and cancelling properly:
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.. math::
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E(u,v) \approx \sum _{x,y} u^{2}I_{x}^{2} + 2uvI_{x}I_{y} + v^{2}I_{y}^{2}
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* Which can be expressed in a matrix form as:
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.. math::
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E(u,v) \approx \begin{bmatrix}
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u & v
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\end{bmatrix}
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\left (
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\displaystyle \sum_{x,y}
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w(x,y)
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\begin{bmatrix}
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I_x^{2} & I_{x}I_{y} \\
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I_xI_{y} & I_{y}^{2}
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\end{bmatrix}
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\right )
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\begin{bmatrix}
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u \\
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v
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\end{bmatrix}
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* Let's denote:
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.. math::
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M = \displaystyle \sum_{x,y}
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w(x,y)
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\begin{bmatrix}
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I_x^{2} & I_{x}I_{y} \\
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I_xI_{y} & I_{y}^{2}
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\end{bmatrix}
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* So, our equation now is:
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.. math::
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E(u,v) \approx \begin{bmatrix}
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u & v
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\end{bmatrix}
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M
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\begin{bmatrix}
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u \\
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v
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\end{bmatrix}
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* A score is calculated for each window, to determine if it can possibly contain a corner:
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.. math::
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R = det(M) - k(trace(M))^{2}
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where:
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* det(M) = :math:`\lambda_{1}\lambda_{2}`
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* trace(M) = :math:`\lambda_{1}+\lambda_{2}`
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a window with a score :math:`R` greater than a certain value is considered a "corner"
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Code
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====
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This tutorial code's is shown lines below. You can also download it from `here <https://github.com/Itseez/opencv/tree/master/samples/cpp/tutorial_code/TrackingMotion/cornerHarris_Demo.cpp>`_
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.. code-block:: cpp
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#include "opencv2/highgui.hpp"
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#include "opencv2/imgproc.hpp"
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#include <iostream>
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#include <stdio.h>
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#include <stdlib.h>
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using namespace cv;
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using namespace std;
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/// Global variables
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Mat src, src_gray;
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int thresh = 200;
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int max_thresh = 255;
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char* source_window = "Source image";
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char* corners_window = "Corners detected";
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/// Function header
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void cornerHarris_demo( int, void* );
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/* @function main */
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int main( int argc, char** argv )
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{
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/// Load source image and convert it to gray
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src = imread( argv[1], 1 );
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cvtColor( src, src_gray, COLOR_BGR2GRAY );
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/// Create a window and a trackbar
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namedWindow( source_window, WINDOW_AUTOSIZE );
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createTrackbar( "Threshold: ", source_window, &thresh, max_thresh, cornerHarris_demo );
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imshow( source_window, src );
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cornerHarris_demo( 0, 0 );
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waitKey(0);
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return(0);
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}
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/* @function cornerHarris_demo */
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void cornerHarris_demo( int, void* )
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{
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Mat dst, dst_norm, dst_norm_scaled;
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dst = Mat::zeros( src.size(), CV_32FC1 );
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/// Detector parameters
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int blockSize = 2;
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int apertureSize = 3;
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double k = 0.04;
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/// Detecting corners
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cornerHarris( src_gray, dst, blockSize, apertureSize, k, BORDER_DEFAULT );
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/// Normalizing
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normalize( dst, dst_norm, 0, 255, NORM_MINMAX, CV_32FC1, Mat() );
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convertScaleAbs( dst_norm, dst_norm_scaled );
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/// Drawing a circle around corners
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for( int j = 0; j < dst_norm.rows ; j++ )
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{ for( int i = 0; i < dst_norm.cols; i++ )
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{
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if( (int) dst_norm.at<float>(j,i) > thresh )
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{
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circle( dst_norm_scaled, Point( i, j ), 5, Scalar(0), 2, 8, 0 );
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}
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}
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}
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/// Showing the result
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namedWindow( corners_window, WINDOW_AUTOSIZE );
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imshow( corners_window, dst_norm_scaled );
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}
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Explanation
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============
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Result
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======
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The original image:
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.. image:: images/Harris_Detector_Original_Image.jpg
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:align: center
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The detected corners are surrounded by a small black circle
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.. image:: images/Harris_Detector_Result.jpg
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:align: center
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