实现Harris Corner Detector,输出结果以及中间过程。

实验过程

实现了一个HarrisCornerDetector函数,函数原型如下:

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void HarrisCornerDetector(Mat& src, Mat& R, int aperture_size, double k);

整体实现过程按照HarrisCornerDetector的运算过程来。

先将彩色图片转为单通道的灰度图,便于计算。

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cvtColor(src, src_gray, cv::COLOR_BGR2GRAY);

然后计算X和Y方向的导数,本质上是用一个算子做一下卷积,我这里使用了Sobel算子,会根据aperture_size生成对应的模板来计算近似的导数。

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Sobel(src_gray, Ix, CV_32FC1, 1, 0, aperture_size);
Sobel(src_gray, Iy, CV_32FC1, 0, 1, aperture_size);

然后就对整张导数的图来计算IxIx, IxIy, IyIy:

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for (int i = 0; i < size.height; ++i) {
for (int j = 0; j < size.width; ++j) {
IxIx.at<float>(i,j) = Ix.at<float>(i, j) * Ix.at<float>(i, j);
IxIy.at<float>(i,j) = Ix.at<float>(i, j) * Iy.at<float>(i, j);
IyIy.at<float>(i,j) = Iy.at<float>(i, j) * Iy.at<float>(i, j);
}
}

如此就得到了这个矩阵的值:

\[ \begin{vmatrix} I_xI_x & I_xI_y \\ I_xI_y & I_yI_y \end{vmatrix} \]

然后就是用W[x,y] 来求和

\[ \sum W(x,y) \begin{vmatrix} I_xI_x & I_xI_y \\ I_xI_y & I_yI_y \end{vmatrix} \] W(x,y)可以取高斯滤波函数。

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Size block(3,3);
GaussianBlur(IxIx, IxIx, block, 0);
GaussianBlur(IxIy, IxIy, block, 0);
GaussiaBlur(IyIy, IyIy, block, 0);

然后就可以求得到的矩阵的特征值。

因为是2x2的矩阵,特征方程就是λ^2-(a+d)λ+ad-bc=0, 直接使用求根公式来求特征值,用韦达定理可以得到R的值。 \[ R = det(H) - k \times trace(H) ^2 \\ \]

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for (int i = 0; i < size.height; ++i) {
for (int j = 0; j < size.width; ++j) {
float a = IxIx.at<float>(i, j);
float b = IxIy.at<float>(i, j);
float c = b;
float d = IyIy.at<float>(i, j);
// 2-D mat a b c d
// λ^2-(a+d)λ+ad-bc=0
// λ1 + λ2 = a+d
// λ1 * λ2 = ad-bc
R.at<float>(i,j) = (a*d - b*c) - k*(a + d)*(a + d);
largeEigen.at<float>(i, j) = ((a + d) + sqrt((a + d)*(a + d) - 4 * (a*d - b*c))) / 2;
smallEigen.at<float>(i, j) = ((a + d) - sqrt((a + d)*(a + d) - 4 * (a*d - b*c))) / 2;
}
}

然后就可以根据R矩阵的值来画出检测出是角的点。

画的时候为避免多个点聚集,使用了Non Maximum Suppression, 只取一定范围内R值最大的点作为角的特征点。

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for (int i = 0; i < size.height; ++i) {
for (int j = 0; j < size.width; ++j) {
if ((int)R.at<uchar>(i, j) > threshold) {
// Non Maximum Suppression
if (R.at<uchar>(i, j) == maxValue(R, NMS_size, i, j)) {
circle(src, Point(j, i), 5, Scalar(0, 0, 255.0), 2, 8, 0);
}
}
}
}

最后展示结果并存储结果

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imshow("LargeEigen", largeEigen);
imshow("SmallEigen", smallEigen);
imshow("R", R);
imshow("result", src);

waitKey(0);

imwrite("LargeEigen.png", largeEigen);
imwrite("SmallEigen.png", smallEigen);
imwrite("R.png", R);
imwrite("result.png", src);

实验结果

略。

心得体会

实验中实现了 Harris Corner Detector,充分体会了这样的角点检测的运算过程。在实现的过程中,深刻理解了Harris的这种检测的原理,推导了计算的公式,加深了理解。实验的结果也符合预期。

在代码的编写过程中也进一步熟悉了OpenCV的使用,可以熟练地使用OpenCV进行图片的处理和卷积运算,提高了使用的熟练度。

附:源代码

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#include <opencv2/opencv.hpp>
#include <iostream>
#include <string>
#include <cmath>
using namespace std;
using namespace cv;

void HarrisCornerDetector(Mat& src, Mat& R, int aperture_size, double k);

int main(int argc, const char** argv) {
char* filename = new char[100];
//system("dir");
int apertureSize = 3;
double k = 0.04;

if (argc != 4) {
cout << "Illegal Input." << endl;
cout << "HarrisDetector.exe $path $k $aperture_size." << endl;
//cout << "using default settings." << endl;
//filename = "sample.png";
filename = "Sydney_Opera_House_Sails_edit02_adj.jpg";
}
else {
// parse commandline args
sscanf_s(argv[1], "%s", filename, 99);
sscanf_s(argv[2], "%lf", &k);
sscanf_s(argv[3], "%d", &apertureSize);
}

Mat src = imread(filename);
if (!src.data) {
cout << "imread failed" << endl;
return 0;
}
Mat dst;

cout << "path: " << filename << endl;
cout << "k: " << k << endl;
cout << "aperture_size: " << apertureSize << endl;

HarrisCornerDetector(src, dst, apertureSize, k);

return 0;
}

int maxValue(Mat& img, int size, int y, int x)
{
uchar maxval = 0;
for (int i = y-size; i<y + size; ++i)
{
if (i < 0 || i >= img.rows)continue;
for (int j = x-size; j< x + size; ++j)
{
if (j<0 || j >= img.cols)continue;
if (img.at<uchar>(i,j) > maxval)
{
maxval = img.at<uchar>(i, j);
}
}
}
//cout << "maxval" << (int)maxval << endl;
return maxval;
}

void HarrisCornerDetector(Mat& src, Mat& R, int aperture_size, double k)
{
Mat src_gray;
// convert to gray
cvtColor(src, src_gray, cv::COLOR_BGR2GRAY);
// normalize src
normalize(src_gray, src_gray, 0, 255, NORM_MINMAX);
convertScaleAbs(src_gray, src_gray);

R.create(src_gray.size(), CV_32FC1);
Mat Ix, Iy;

//sobel operation get Ix, Iy
Sobel(src_gray, Ix, CV_32FC1, 1, 0, aperture_size);
Sobel(src_gray, Iy, CV_32FC1, 0, 1, aperture_size);
//cout << Ix.size() << " " << Ix.channels() << " " << Ix.depth() << endl;

// prepare Mat to store info
Mat IxIx(src_gray.size(), CV_32FC1);
Mat IxIy(src_gray.size(), CV_32FC1);
Mat IyIy(src_gray.size(), CV_32FC1);
Mat largeEigen(src_gray.size(), CV_32FC1);
Mat smallEigen(src_gray.size(), CV_32FC1);
//Mat heat(src_gray.size(), CV_8SC3);

Size size = src_gray.size();
for (int i = 0; i < size.height; ++i) {
for (int j = 0; j < size.width; ++j) {
IxIx.at<float>(i,j) = Ix.at<float>(i, j) * Ix.at<float>(i, j);
IxIy.at<float>(i,j) = Ix.at<float>(i, j) * Iy.at<float>(i, j);
IyIy.at<float>(i,j) = Iy.at<float>(i, j) * Iy.at<float>(i, j);
}
}

// W[x,y] * I
// W[x,y] is Gaussian Filter
Size block(3,3);
GaussianBlur(IxIx, IxIx, block, 0);
GaussianBlur(IxIy, IxIy, block, 0);
GaussianBlur(IyIy, IyIy, block, 0);

for (int i = 0; i < size.height; ++i) {
for (int j = 0; j < size.width; ++j) {
float a = IxIx.at<float>(i, j);
float b = IxIy.at<float>(i, j);
float c = b;
float d = IyIy.at<float>(i, j);
// 2-D mat a b c d
// λ^2-(a+d)λ+ad-bc=0
// λ1 + λ2 = a+d
// λ1 * λ2 = ad-bc
R.at<float>(i,j) = (a*d - b*c) - k*(a + d)*(a + d);
largeEigen.at<float>(i, j) = ((a + d) + sqrt((a + d)*(a + d) - 4 * (a*d - b*c))) / 2;
smallEigen.at<float>(i, j) = ((a + d) - sqrt((a + d)*(a + d) - 4 * (a*d - b*c))) / 2;
}
}
cout << endl;
normalize(R, R, 0, 255, NORM_MINMAX, CV_32FC1, Mat());
convertScaleAbs(R, R);
int threshold = 50;
int NMS_size = 15;
// Draw circles with NMS
for (int i = 0; i < size.height; ++i) {
for (int j = 0; j < size.width; ++j) {
if ((int)R.at<uchar>(i, j) > threshold) {
// Non Maximum Suppression
if (R.at<uchar>(i, j) == maxValue(R, NMS_size, i, j)) {
circle(src, Point(j, i), 5, Scalar(0, 0, 255.0), 2, 8, 0);
}
}
}
}

// Show the result
imshow("LargeEigen", largeEigen);
imshow("SmallEigen", smallEigen);
//imshow("heat", heat);
imshow("R", R);
imshow("result", src);

waitKey(0);

imwrite("LargeEigen.png", largeEigen);
imwrite("SmallEigen.png", smallEigen);
imwrite("R.png", R);
imwrite("result.png", src);
destroyAllWindows();
}