霍夫变换

霍夫变换是图像处理中识别几何形状的一种方法, 主要用来检测直线和圆形。

1 平面坐标和极坐标

1) 平面坐标的点 <=> 极坐标(平面化)的曲线

所谓极坐标平面化是指, 将ρ-θ的关系像x-y那样在平面内展开。

公式推导: x-y坐标中的点(x0, y0), 代入极坐标ρ-θ中得

$\quad \begin{align*}\rho = x_{0}\: cos\theta + y_{0}\: sin\theta = \sqrt{x_{0}^{2}+y_{0}^{2}}\:\left (\frac{x_{0}}{\sqrt{x_{0}^{2}+y_{0}^{2}}}\: cos\theta + \frac{y_{0}}{\sqrt{x_{0}^{2}+y_{0}^{2}}}\:sin\theta\right )
= \sqrt{x_{0}^{2}+y_{0}^{2}} \; sin(\varphi_{0} +\theta ) \end{align*} $

其中, $sin\varphi_{0} = \frac{x_{0}}{\sqrt{x_{0}^{2}+y_{0}^{2}}}$

由上述公式可以明显的看出ρ与θ之间的函数关系。

#include "opencv2/imgcodecs.hpp"
#include "opencv2/highgui/highgui.hpp"
#include "opencv2/imgproc/imgproc.hpp"
#include <iostream>

using namespace std;
using namespace cv;

namespace
{
// windows and trackbars name
const std::string windowName = "Hough Circle Detection Demo";
const std::string cannyThresholdTrackbarName = "Canny threshold";
const std::string accumulatorThresholdTrackbarName = "Accumulator Threshold";
const std::string usage = "Usage : tutorial_HoughCircle_Demo <path_to_input_image>\n";

// initial and max values of the parameters of interests.
const int cannyThresholdInitialValue = 200;
const int accumulatorThresholdInitialValue = 50;
const int maxAccumulatorThreshold = 200;
const int maxCannyThreshold = 255;

void HoughDetection(const Mat& src_gray, const Mat& src_display, int cannyThreshold, int accumulatorThreshold)
{
// will hold the results of the detection
std::vector<Vec3f> circles;
// runs the actual detection
HoughCircles( src_gray, circles, HOUGH_GRADIENT, 1, src_gray.rows/8, cannyThreshold, accumulatorThreshold, 0, 0 );

// clone the colour, input image for displaying purposes
Mat display = src_display.clone();
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( display, center, 3, Scalar(0,255,0), -1, 8, 0 );
// circle outline
circle( display, center, radius, Scalar(0,0,255), 3, 8, 0 );
}

// shows the results
imshow( windowName, display);
}
}

int main(int argc, char** argv)
{
Mat src, src_gray;

if (argc < 2)
{
std::cerr<<"No input image specified\n";
std::cout<<usage;
return -1;
}

// Read the image
src = imread( argv[1], 1 );

if( src.empty() )
{
std::cerr<<"Invalid input image\n";
std::cout<<usage;
return -1;
}

// Convert it to gray
cvtColor( src, src_gray, COLOR_BGR2GRAY );

// Reduce the noise so we avoid false circle detection
GaussianBlur( src_gray, src_gray, Size(9, 9), 2, 2 );

//declare and initialize both parameters that are subjects to change
int cannyThreshold = cannyThresholdInitialValue;
int accumulatorThreshold = accumulatorThresholdInitialValue;

// create the main window, and attach the trackbars
namedWindow( windowName, WINDOW_AUTOSIZE );
createTrackbar(cannyThresholdTrackbarName, windowName, &cannyThreshold,maxCannyThreshold);
createTrackbar(accumulatorThresholdTrackbarName, windowName, &accumulatorThreshold, maxAccumulatorThreshold);

// infinite loop to display
// and refresh the content of the output image
// until the user presses q or Q
int key = 0;
while(key != 'q' && key != 'Q')
{
// those paramaters cannot be =0
// so we must check here
cannyThreshold = std::max(cannyThreshold, 1);
accumulatorThreshold = std::max(accumulatorThreshold, 1);

//runs the detection, and update the display
HoughDetection(src_gray, src, cannyThreshold, accumulatorThreshold);

// get user key
key = waitKey(10);
}

return 0;
}

View Code
以上例程均摘自 Opencv 3.1.0 tutorial