Doxygen tutorials: basic structure
This commit is contained in:
Maksim Shabunin
@@ -0,0 +1,209 @@
|
||||
Harris corner detector {#tutorial_harris_detector}
|
||||
======================
|
||||
|
||||
Goal
|
||||
----
|
||||
|
||||
In this tutorial you will learn:
|
||||
|
||||
- What features are and why they are important
|
||||
- Use the function @ref 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 \f$I\f$. We are going to sweep a window \f$w(x,y)\f$ (with displacements \f$u\f$
|
||||
in the x direction and \f$v\f$ in the right direction) \f$I\f$ and will calculate the variation of
|
||||
intensity.
|
||||
|
||||
\f[E(u,v) = \sum _{x,y} w(x,y)[ I(x+u,y+v) - I(x,y)]^{2}\f]
|
||||
|
||||
where:
|
||||
|
||||
- \f$w(x,y)\f$ is the window at position \f$(x,y)\f$
|
||||
- \f$I(x,y)\f$ is the intensity at \f$(x,y)\f$
|
||||
- \f$I(x+u,y+v)\f$ is the intensity at the moved window \f$(x+u,y+v)\f$
|
||||
- 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:
|
||||
|
||||
\f[\sum _{x,y}[ I(x+u,y+v) - I(x,y)]^{2}\f]
|
||||
|
||||
- Using *Taylor expansion*:
|
||||
|
||||
\f[E(u,v) \approx \sum _{x,y}[ I(x,y) + u I_{x} + vI_{y} - I(x,y)]^{2}\f]
|
||||
|
||||
- Expanding the equation and cancelling properly:
|
||||
|
||||
\f[E(u,v) \approx \sum _{x,y} u^{2}I_{x}^{2} + 2uvI_{x}I_{y} + v^{2}I_{y}^{2}\f]
|
||||
|
||||
- Which can be expressed in a matrix form as:
|
||||
|
||||
\f[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}\f]
|
||||
|
||||
- Let's denote:
|
||||
|
||||
\f[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}\f]
|
||||
|
||||
- So, our equation now is:
|
||||
|
||||
\f[E(u,v) \approx \begin{bmatrix}
|
||||
u & v
|
||||
\end{bmatrix}
|
||||
M
|
||||
\begin{bmatrix}
|
||||
u \\
|
||||
v
|
||||
\end{bmatrix}\f]
|
||||
|
||||
- A score is calculated for each window, to determine if it can possibly contain a corner:
|
||||
|
||||
\f[R = det(M) - k(trace(M))^{2}\f]
|
||||
|
||||
where:
|
||||
|
||||
- det(M) = \f$\lambda_{1}\lambda_{2}\f$
|
||||
- trace(M) = \f$\lambda_{1}+\lambda_{2}\f$
|
||||
|
||||
a window with a score \f$R\f$ 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](https://github.com/Itseez/opencv/tree/master/samples/cpp/tutorial_code/TrackingMotion/cornerHarris_Demo.cpp)
|
||||
@code{.cpp}
|
||||
#include "opencv2/highgui.hpp"
|
||||
#include "opencv2/imgproc.hpp"
|
||||
#include <iostream>
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
using namespace cv;
|
||||
using namespace std;
|
||||
|
||||
/// Global variables
|
||||
Mat src, src_gray;
|
||||
int thresh = 200;
|
||||
int max_thresh = 255;
|
||||
|
||||
char* source_window = "Source image";
|
||||
char* corners_window = "Corners detected";
|
||||
|
||||
/// Function header
|
||||
void cornerHarris_demo( int, void* );
|
||||
|
||||
/* @function main */
|
||||
int main( int argc, char** argv )
|
||||
{
|
||||
/// Load source image and convert it to gray
|
||||
src = imread( argv[1], 1 );
|
||||
cvtColor( src, src_gray, COLOR_BGR2GRAY );
|
||||
|
||||
/// Create a window and a trackbar
|
||||
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);
|
||||
}
|
||||
|
||||
/* @function cornerHarris_demo */
|
||||
void cornerHarris_demo( int, void* )
|
||||
{
|
||||
|
||||
Mat dst, dst_norm, dst_norm_scaled;
|
||||
dst = Mat::zeros( src.size(), CV_32FC1 );
|
||||
|
||||
/// Detector parameters
|
||||
int blockSize = 2;
|
||||
int apertureSize = 3;
|
||||
double k = 0.04;
|
||||
|
||||
/// Detecting corners
|
||||
cornerHarris( src_gray, dst, blockSize, apertureSize, k, BORDER_DEFAULT );
|
||||
|
||||
/// Normalizing
|
||||
normalize( dst, dst_norm, 0, 255, NORM_MINMAX, CV_32FC1, Mat() );
|
||||
convertScaleAbs( dst_norm, dst_norm_scaled );
|
||||
|
||||
/// Drawing a circle around corners
|
||||
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 );
|
||||
}
|
||||
}
|
||||
}
|
||||
/// Showing the result
|
||||
namedWindow( corners_window, WINDOW_AUTOSIZE );
|
||||
imshow( corners_window, dst_norm_scaled );
|
||||
}
|
||||
@endcode
|
||||
Explanation
|
||||
-----------
|
||||
|
||||
Result
|
||||
------
|
||||
|
||||
The original image:
|
||||
|
||||
|
||||
|
||||
The detected corners are surrounded by a small black circle
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user