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C++ opencv Linear algebra(opencv 線性代數) GITHUB: https://github.com/jash-git/CPP-opencv-Linear-algebra 資料來源:https://www.raben.com/content/linear-algebra-opencv http://pklab.net/?id=380 https://blog.csdn.net/guduruyu/article/details/72866144 https://blog.csdn.net/dcrmg/article/details/52404580 矩陣運算-加 減 乘 反矩陣 解聯立方程(連拋物線都可以) 擬合曲線(最小平方 估測) #include #include #include #include #include #include #include #if defined(WIN32) #define TIMEB _timeb #define ftime _ftime typedef __int64 TIME_T; #else #define TIMEB timeb typedef long long TIME_T; #endif using namespace cv; using namespace std; void Pause() { printf("Press Enter key to continue..."); fgetc(stdin); } void addMatrix() { float a[2][2] = {{1, 2}, {3, 4}}; float b[2][2] = {{5, 6}, {7, 8}}; Mat A = Mat(2, 2, CV_32FC1, a); Mat B = Mat(2, 2, CV_32FC1, b); Mat C; C = A + B; cout << "A =" << endl << " " << A << endl << endl; cout << "B =" << endl << " " << B << endl << endl; cout << "A+B =" << endl << " " << C << endl << endl; } void subMatrix() { float a[2][2] = {{1, 2}, {3, 4}}; float b[2][2] = {{5, 6}, {7, 8}}; Mat A = Mat(2, 2, CV_32FC1, a); Mat B = Mat(2, 2, CV_32FC1, b); Mat C; C = A - B; cout << "A =" << endl << " " << A << endl << endl; cout << "B =" << endl << " " << B << endl << endl; cout << "A-B =" << endl << " " << C << endl << endl; } void dotmatrix() { //Opencv中.dot操作才算得上是真正的“点乘”，A.dot(B)操作相当于数学向量运算中的点乘，也叫向量的内积、数量积。 Mat A=Mat::ones(2,3,CV_8UC1); Mat B=Mat::ones(2,3,CV_8UC1); A.at(0,0)=1; A.at(0,1)=2; A.at(0,2)=3; A.at(1,0)=4; A.at(1,1)=5; A.at(1,2)=6; B.at(0,0)=1; B.at(0,1)=2; B.at(0,2)=3; B.at(1,0)=4; B.at(1,1)=5; B.at(1,2)=6; double AB=A.dot(B); cout< | a(pt1.x)^2 + b(pt1.x) + c(1) = pt1.y | // | a(pt2.x)^2 + b(pt2.x) + c(1) = pt2.y | // | a(pt3.x)^2 + b(pt3.x) + c(1) = pt3.y | // coefficients for the system are the 3 points // variables for the system are the parabola coefficient a,b,c // // Finally set the matrix for the linear system solver cv::Mat A = (cv::Mat_(3, 3) << std::pow(pt1.x, 2), pt1.x, 1, std::pow(pt2.x, 2), pt2.x, 1, std::pow(pt3.x, 2), pt3.x, 1); cv::Mat B = (cv::Mat_(3, 1) << pt1.y, pt2.y, pt3.y); // declare a vector for results cv::Mat abc; // solve the linear system cv::solve(A, B, abc); // printout the result cout << "Coefficients:\n " << abc << endl; a = abc.at(0); b = abc.at(1); c = abc.at(2); cout << "Equation:\n y = " << a << "x^2 + " << b << "x + " << c << endl; } //--- //擬合曲線(最小平方法) bool polynomial_curve_fit(std::vector& key_point, int n, cv::Mat& A) { //Number of key points int N = key_point.size(); //构造矩阵X cv::Mat X = cv::Mat::zeros(n + 1, n + 1, CV_64FC1); for (int i = 0; i < n + 1; i++) { for (int j = 0; j < n + 1; j++) { for (int k = 0; k < N; k++) { X.at(i, j) = X.at(i, j) + std::pow(key_point[k].x, i + j); } } } //构造矩阵Y cv::Mat Y = cv::Mat::zeros(n + 1, 1, CV_64FC1); for (int i = 0; i < n + 1; i++) { for (int k = 0; k < N; k++) { Y.at(i, 0) = Y.at(i, 0) + std::pow(key_point[k].x, i) * key_point[k].y; } } A = cv::Mat::zeros(n + 1, 1, CV_64FC1); //求解矩阵A cv::solve(X, Y, A, cv::DECOMP_LU); return true; } void Test_polynomial_curve_fit() { //创建用于绘制的深蓝色背景图像 cv::Mat image = cv::Mat::zeros(480, 640, CV_8UC3); image.setTo(cv::Scalar(100, 0, 0)); //输入拟合点 std::vector points; points.push_back(cv::Point(100., 58.)); points.push_back(cv::Point(150., 70.)); points.push_back(cv::Point(200., 90.)); points.push_back(cv::Point(252., 140.)); points.push_back(cv::Point(300., 220.)); points.push_back(cv::Point(350., 400.)); //将拟合点绘制到空白图上 for (int i = 0; i < points.size(); i++) { cv::circle(image, points[i], 5, cv::Scalar(0, 0, 255), 2, 8, 0); } //绘制折线 cv::polylines(image, points, false, cv::Scalar(0, 255, 0), 1, 8, 0); cv::Mat A; polynomial_curve_fit(points, 3, A); std::cout << "A = " << A << std::endl; std::vector points_fitted; for (int x = 0; x < 400; x++) { double y = A.at(0, 0) + A.at(1, 0) * x + A.at(2, 0)*std::pow(x, 2) + A.at(3, 0)*std::pow(x, 3); points_fitted.push_back(cv::Point(x, y)); } cv::polylines(image, points_fitted, false, cv::Scalar(0, 255, 255), 1, 8, 0); cv::imshow("image", image); } //---擬合曲線(最小平方法) int main() { addMatrix(); cout << endl << "===================" << endl << endl; subMatrix(); cout << endl << "===================" << endl << endl; dotmatrix(); cout << endl << "===================" << endl << endl; matrixMultiplication(); cout << endl << "===================" << endl << endl; solveLinearEquation(); cout << endl << "===================" << endl << endl; solveLinear_parabola();//拋物線(線性方程)求解 cout << endl << "===================" << endl << endl; Test_polynomial_curve_fit();//擬合曲線(最小平方法) cv::waitKey(0); Pause(); return 0; }