OpenCV  3.2.0
Open Source Computer Vision
Harris corner detector

.2.0+dfsg_doc_tutorials_features2d_trackingmotion_harris_detector_harris_detector

Goal

In this tutorial you will learn:

  • What features are and why they are important
  • Use the function cv::cornerHarris to detect corners using the Harris-Stephens method.

Theory

What is a feature?

  • 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.
  • 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.
  • So, what characteristics should a feature have?
    • It must be uniquely recognizable

Types of Image Features

To mention a few:

  • Edges
  • Corners (also known as interest points)
  • Blobs (also known as regions of interest )

In this tutorial we will study the corner features, specifically.

Why is a corner so special?

  • 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.

How does it work?

  • Let's look for corners. Since corners represents a variation in the gradient in the image, we will look for this "variation".
  • Consider a grayscale image \(I\). We are going to sweep a window \(w(x,y)\) (with displacements \(u\) in the x direction and \(v\) in the right direction) \(I\) and will calculate the variation of intensity.

    \[E(u,v) = \sum _{x,y} w(x,y)[ I(x+u,y+v) - I(x,y)]^{2}\]

    where:

    • \(w(x,y)\) is the window at position \((x,y)\)
    • \(I(x,y)\) is the intensity at \((x,y)\)
    • \(I(x+u,y+v)\) is the intensity at the moved window \((x+u,y+v)\)
  • 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:

    \[\sum _{x,y}[ I(x+u,y+v) - I(x,y)]^{2}\]

  • Using Taylor expansion:

    \[E(u,v) \approx \sum _{x,y}[ I(x,y) + u I_{x} + vI_{y} - I(x,y)]^{2}\]

  • Expanding the equation and cancelling properly:

    \[E(u,v) \approx \sum _{x,y} u^{2}I_{x}^{2} + 2uvI_{x}I_{y} + v^{2}I_{y}^{2}\]

  • Which can be expressed in a matrix form as:

    \[E(u,v) \approx \begin{bmatrix} u & v \end{bmatrix} \left ( \displaystyle \sum_{x,y} w(x,y) \begin{bmatrix} I_x^{2} & I_{x}I_{y} \\ I_xI_{y} & I_{y}^{2} \end{bmatrix} \right ) \begin{bmatrix} u \\ v \end{bmatrix}\]

  • Let's denote:

    \[M = \displaystyle \sum_{x,y} w(x,y) \begin{bmatrix} I_x^{2} & I_{x}I_{y} \\ I_xI_{y} & I_{y}^{2} \end{bmatrix}\]

  • So, our equation now is:

    \[E(u,v) \approx \begin{bmatrix} u & v \end{bmatrix} M \begin{bmatrix} u \\ v \end{bmatrix}\]

  • A score is calculated for each window, to determine if it can possibly contain a corner:

    \[R = det(M) - k(trace(M))^{2}\]

    where:

    • det(M) = \(\lambda_{1}\lambda_{2}\)
    • trace(M) = \(\lambda_{1}+\lambda_{2}\)

    a window with a score \(R\) greater than a certain value is considered a "corner"

Code

This tutorial code's is shown lines below. You can also download it from here

#include <iostream>
using namespace cv;
using namespace std;
Mat src, src_gray;
int thresh = 200;
int max_thresh = 255;
const char* source_window = "Source image";
const char* corners_window = "Corners detected";
void cornerHarris_demo( int, void* );
int main( int, char** argv )
{
src = imread( argv[1], IMREAD_COLOR );
cvtColor( src, src_gray, COLOR_BGR2GRAY );
namedWindow( source_window, WINDOW_AUTOSIZE );
createTrackbar( "Threshold: ", source_window, &thresh, max_thresh, cornerHarris_demo );
imshow( source_window, src );
cornerHarris_demo( 0, 0 );
waitKey(0);
return(0);
}
void cornerHarris_demo( int, void* )
{
Mat dst, dst_norm, dst_norm_scaled;
dst = Mat::zeros( src.size(), CV_32FC1 );
int blockSize = 2;
int apertureSize = 3;
double k = 0.04;
cornerHarris( src_gray, dst, blockSize, apertureSize, k, BORDER_DEFAULT );
normalize( dst, dst_norm, 0, 255, NORM_MINMAX, CV_32FC1, Mat() );
convertScaleAbs( dst_norm, dst_norm_scaled );
for( int j = 0; j < dst_norm.rows ; j++ )
{ for( int i = 0; i < dst_norm.cols; i++ )
{
if( (int) dst_norm.at<float>(j,i) > thresh )
{
circle( dst_norm_scaled, Point( i, j ), 5, Scalar(0), 2, 8, 0 );
}
}
}
namedWindow( corners_window, WINDOW_AUTOSIZE );
imshow( corners_window, dst_norm_scaled );
}

Explanation

Result

The original image:

The detected corners are surrounded by a small black circle

cv::Mat::rows
int rows
the number of rows and columns or (-1, -1) when the matrix has more than 2 dimensions
Definition: mat.hpp:1959
imgproc.hpp
cv::IMREAD_COLOR
@ IMREAD_COLOR
If set, always convert image to the 3 channel BGR color image.
Definition: imgcodecs.hpp:67
cv::NORM_MINMAX
@ NORM_MINMAX
flag
Definition: base.hpp:196
cv::Mat::zeros
static MatExpr zeros(int rows, int cols, int type)
Returns a zero array of the specified size and type.
cv::cvtColor
void cvtColor(InputArray src, OutputArray dst, int code, int dstCn=0)
Converts an image from one color space to another.
cv::Mat::at
_Tp & at(int i0=0)
Returns a reference to the specified array element.
cv::waitKey
int waitKey(int delay=0)
Waits for a pressed key.
cv::BORDER_DEFAULT
@ BORDER_DEFAULT
same as BORDER_REFLECT_101
Definition: base.hpp:262
highgui.hpp
cv::namedWindow
void namedWindow(const String &winname, int flags=WINDOW_AUTOSIZE)
Creates a window.
cv::convertScaleAbs
void convertScaleAbs(InputArray src, OutputArray dst, double alpha=1, double beta=0)
Scales, calculates absolute values, and converts the result to 8-bit.
cv::imread
Mat imread(const String &filename, int flags=IMREAD_COLOR)
Loads an image from a file.
cv::COLOR_BGR2GRAY
@ COLOR_BGR2GRAY
convert between RGB/BGR and grayscale, color conversions
Definition: imgproc.hpp:538
cv::Mat::cols
int cols
Definition: mat.hpp:1959
cv::Mat::size
MatSize size
Definition: mat.hpp:1978
imgcodecs.hpp
cv::imshow
void imshow(const String &winname, InputArray mat)
Displays an image in the specified window.
cv::Scalar
Scalar_< double > Scalar
Definition: types.hpp:606
cv::Point
Point2i Point
Definition: types.hpp:183
cv::Mat
n-dimensional dense array class
Definition: mat.hpp:741
i
for i
Definition: modelConvert.m:63
cv::createTrackbar
int createTrackbar(const String &trackbarname, const String &winname, int *value, int count, TrackbarCallback onChange=0, void *userdata=0)
Creates a trackbar and attaches it to the specified window.
cv
Definition: affine.hpp:52
cv::WINDOW_AUTOSIZE
@ WINDOW_AUTOSIZE
the user cannot resize the window, the size is constrainted by the image displayed.
Definition: highgui.hpp:184
cv::normalize
static Vec< _Tp, cn > normalize(const Vec< _Tp, cn > &v)
CV_32FC1
#define CV_32FC1
Definition: interface.h:112
cv::cornerHarris
void cornerHarris(InputArray src, OutputArray dst, int blockSize, int ksize, double k, int borderType=BORDER_DEFAULT)
Harris corner detector.
cv::circle
void circle(InputOutputArray img, Point center, int radius, const Scalar &color, int thickness=1, int lineType=LINE_8, int shift=0)
Draws a circle.