前面通过几个篇幅阐述了Ceres的基本应用，本篇基于之前的样例展示一个稍加复杂的样例。在给出使用样例之前，我们先来谈谈捆绑优化(Bundle Adjustment)和单目视觉中的尺度问题。
1.捆绑优化
捆绑优化的概念追溯久远，要从其原始出处说起，还真不是一两话能说清楚，涉及视觉领域相当专业的概念。也许大多数视觉领域的研究者都理解捆绑优化是什么，用得也如火纯青，但真要通俗易懂的说出来就不知道有几人啦，相关书籍和博文也很少有对捆绑优化的通俗阐述。这里，我根据自己的理解，避开视觉中的概念，从更广义的角度来说说自己对捆绑优化的理解。
假设有优化模型A(a)=0，这里A代表线性或非线性或两者混合的方程组，a代表被优化的变量组成的向量。常规而言，只要方程的数量足够，迭代优化即可得到最优值。然而，有时候方程数量再多，得到的解也可能不正确或者说不够精确，至于其原由这里不展开，从哲学的角度来说，大意就是你一直站在角度A看问题，不够全面，自然得到结果a也不全面(即不精确)，如果能同时站在其它角度B、C、D来看问题，你看到的a是否会更正确了？答案很明显。但是当你站在B、C、D的角度来看问题时，包含的变量通常就不只是a了，我们假设站在B的角度会增加变量b、站在C的角度会增加变量c、站在D的角度会增加变量d。于是优化模型变为：
A(a)=0;B(a,b)=0;C(a,c)=0;D(a,d)=0
以上是比较理想的情况，也有可能是如下情况：
A(a)=0;B(a,b)=0;C(a, b,c)=0; D(a,b,c,d)=0。
或
A(a)=0;B(a,b)=0;C(b,c)=0;D(c,b)=0。
具体形式，取决于实际模型。但至少需要存在一个中间角度将a和后续变量关联起来，才有意义。
于是问题转化为求解最优abcd。这里将abcd捆绑优化，也正好呼应了捆绑优化这一概念。
我们来分析之前和本篇的使用样例：
OptimizeRt：这是之前的样例，基于一次观察(即一个角度)计算Rt，这还不能算捆绑优化。
OptimizeKDRt：这是之前的样例，基于多次观察(即多个角度)计算KD和所有Rt，KD出现在所有观察，每个Rt对应一组观察，这就是典型的捆绑优化。
OptimizeKDTP：这是本篇的样例，基于多次观察(即多个角度)计算KD、所有Rt及所有Point3D，KD出现在所有观察，每个Rt对应一组观察，每个Point3D对应至少N组(N大于等于2)观察，这也是典型的捆绑优化。
2.单目视觉中的尺度
单目视觉中，当我们要基于多次观察计算每次观察的Rt和每次观察中某些(这里不说所有是因为一个三维点通常需要被多次观察才能很好地确定，对于没有被多次观察到的则将其排除)三维点时，必须首先得到一些确定的Rt或一些确定的三维点才能使模型收敛到正确的结果。通常有两种方案：
(1)给定位姿：给定一次观察的Rt和另一次观察的t(或t模值)、或给定一次观察的Rt和两次观察的之间的相对t(或t模值)。
(2)给定三维点：给定三个至少能出现在N次(N大于等于2)观察中的Point3D。
以上要求的是最少数量，数量越多越好。关于原理分析，可参见视觉Slam那些古老的论文。
3.使用样例
提供捆绑优化K、D、R、t、XYZ的使用样例，命名为OptimizeKDTP，这是在OptimizeKDRt的基础上增加了对世界坐标的优化。对此使用样例作如下说明：
(1)提供参数设置以决定是否固定K或D或R或t或P，以模拟视觉开发中的各种应用场景(如定位、标定、重建等)。
(2)当要优化世界坐标时，提供参数设置以决定选用位姿真值还是三维点真值来估计尺度。
以下是详细代码，依赖于C++14、OpenCV4.x、Ceres和Spdlog。
1 #include <opencv2/opencv.hpp> 2 #include <opencv2/viz.hpp> 3 #include <spdlog/spdlog.h> 4 #include <ceres/ceres.h> 5 using namespace std; 6 using namespace cv; 7 8 class MotionSim 9 { 10 public: 11 static void TestMe(int argc, char** argv) 12 { 13 MotionSim motionSim(false); 14 motionSim.camFovX = 45; 15 motionSim.camFovY = 30; 16 motionSim.camRand = 10; 17 motionSim.enableVerbose = false; 18 motionSim.runMotion(false, false, 7); 19 motionSim.visMotion(); 20 } 21 22 public: 23 struct MotionView 24 { 25 Mat_<double> r = Mat_<double>(3, 1); 26 Mat_<double> t = Mat_<double>(3, 1); 27 Mat_<double> q = Mat_<double>(4, 1); 28 Mat_<double> rt = Mat_<double>(6, 1); 29 Mat_<double> radian = Mat_<double>(3, 1); 30 Mat_<double> degree = Mat_<double>(3, 1); 31 Mat_<double> R = Mat_<double>(3, 3); 32 Mat_<double> T = Mat_<double>(3, 4); 33 Mat_<double> K; 34 Mat_<double> D; 35 Mat_<Vec3d> point3D; 36 Mat_<Vec2d> point2D; 37 Mat_<int> point3DIds; 38 string print(string savePath = "") 39 { 40 string str; 41 str += fmt::format("r: {} ", cvarr2str(r.t())); 42 str += fmt::format("t: {} ", cvarr2str(t.t())); 43 str += fmt::format("q: {} ", cvarr2str(q.t())); 44 str += fmt::format("rt: {} ", cvarr2str(rt.t())); 45 str += fmt::format("radian: {} ", cvarr2str(radian.t())); 46 str += fmt::format("degree: {} ", cvarr2str(degree.t())); 47 str += fmt::format("R: {} ", cvarr2str(R)); 48 str += fmt::format("T: {} ", cvarr2str(T)); 49 str += fmt::format("K: {} ", cvarr2str(K)); 50 str += fmt::format("D: {} ", cvarr2str(D.t())); 51 if (savePath.empty() == false) { FILE* out = fopen(savePath.c_str(), "w"); fprintf(out, str.c_str()); fclose(out); } 52 return str; 53 } 54 }; 55 static string cvarr2str(InputArray v) 56 { 57 Ptr<Formatted> fmtd = cv::format(v, Formatter::FMT_DEFAULT); 58 string dst; fmtd->reset(); 59 for (const char* str = fmtd->next(); str; str = fmtd->next()) dst += string(str); 60 return dst; 61 } 62 static void euler2matrix(double e[3], double R[9], bool forward = true, int argc = 0, char** argv = 0) 63 { 64 if (argc > 0) 65 { 66 int N = 999; 67 for (int k = 0; k < N; ++k)//OpenCV not better than DIY 68 { 69 //1.GenerateData 70 Matx31d radian0 = radian0.randu(-3.14159265358979323846, 3.14159265358979323846); 71 Matx33d R; euler2matrix(radian0.val, R.val, true); 72 const double deg2rad = 3.14159265358979323846 * 0.0055555555555555556; 73 const double rad2deg = 180 * 0.3183098861837906715; 74 75 //2.CalcByOpenCV 76 Matx31d radian1 = cv::RQDecomp3x3(R, Matx33d(), Matx33d()) * deg2rad; 77 78 //3.CalcByDIY 79 Matx31d radian2; euler2matrix(R.val, radian2.val, false); 80 81 //4.AnalyzeError 82 double infRadian0Radian1 = norm(radian0, radian1, NORM_INF); 83 double infRadian1Radian2 = norm(radian1, radian2, NORM_INF); 84 85 //5.PrintError 86 cout << endl << "LoopCount: " << k << endl; 87 if (infRadian0Radian1 > 0 || infRadian1Radian2 > 0) 88 { 89 cout << endl << "5.1PrintError" << endl; 90 cout << endl << "infRadian0Radian1: " << infRadian0Radian1 << endl; 91 cout << endl << "infRadian1Radian2: " << infRadian1Radian2 << endl; 92 if (0) 93 { 94 cout << endl << "5.2PrintDiff" << endl; 95 cout << endl << "radian0-degree0:" << endl << radian0.t() << endl << radian0.t() * rad2deg << endl; 96 cout << endl << "radian1-degree1:" << endl << radian1.t() << endl << radian1.t() * rad2deg << endl; 97 cout << endl << "radian2-degree2:" << endl << radian2.t() << endl << radian2.t() * rad2deg << endl; 98 cout << endl << "5.3PrintOthers" << endl; 99 cout << endl << "R:" << endl << R << endl; 100 } 101 cout << endl << "Press any key to continue" << endl; std::getchar(); 102 } 103 } 104 return; 105 } 106 if (forward)//check with 3D Rotation Converter 107 { 108 double sinR = std::sin(e[0]); 109 double sinP = std::sin(e[1]); 110 double sinY = std::sin(e[2]); 111 double cosR = std::cos(e[0]); 112 double cosP = std::cos(e[1]); 113 double cosY = std::cos(e[2]); 114 115 //RPY indicates: first Yaw aroundZ, second Pitch aroundY, third Roll aroundX 116 R[0] = cosY * cosP; R[1] = cosY * sinP * sinR - sinY * cosR; R[2] = cosY * sinP * cosR + sinY * sinR; 117 R[3] = sinY * cosP; R[4] = sinY * sinP * sinR + cosY * cosR; R[5] = sinY * sinP * cosR - cosY * sinR; 118 R[6] = -sinP; R[7] = cosP * sinR; R[8] = cosP * cosR; 119 } 120 else 121 { 122 double vs1 = std::abs(R[6] - 1.); 123 double vs_1 = std::abs(R[6] + 1.); 124 if (vs1 > 1E-9 && vs_1 > 1E-9) 125 { 126 e[2] = std::atan2(R[3], R[0]); //Yaw aroundZ 127 e[1] = std::asin(-R[6]);//Pitch aroundY 128 e[0] = std::atan2(R[7], R[8]); //Roll aroundX 129 } 130 else if (vs_1 <= 1E-9) 131 { 132 e[2] = 0; //Yaw aroundZ 133 e[1] = 3.14159265358979323846 * 0.5;//Pitch aroundY 134 e[0] = e[2] + atan2(R[1], R[2]); //Roll aroundX 135 } 136 else 137 { 138 e[2] = 0; //Yaw aroundZ 139 e[1] = -3.14159265358979323846 * 0.5;//Pitch aroundY 140 e[0] = -e[2] + atan2(-R[1], -R[2]); //Roll aroundX 141 } 142 } 143 }; 144 static void quat2matrix(double q[4], double R[9], bool forward = true) 145 { 146 if (forward)//refer to qglviwer 147 { 148 double L1 = std::sqrt(q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]); 149 if (std::abs(L1 - 1) > 1E-9) { std::printf("Not uint quaternion: NormQ=%.9f ", L1); abort(); } 150 151 double xx = 2.0 * q[1] * q[1]; 152 double yy = 2.0 * q[2] * q[2]; 153 double zz = 2.0 * q[3] * q[3]; 154 155 double xy = 2.0 * q[1] * q[2]; 156 double xz = 2.0 * q[1] * q[3]; 157 double wx = 2.0 * q[1] * q[0]; 158 159 double yz = 2.0 * q[2] * q[3]; 160 double wy = 2.0 * q[2] * q[0]; 161 162 double wz = 2.0 * q[3] * q[0]; 163 164 R[0] = 1.0 - yy - zz; 165 R[4] = 1.0 - xx - zz; 166 R[8] = 1.0 - xx - yy; 167 168 R[1] = xy - wz; 169 R[3] = xy + wz; 170 171 R[2] = xz + wy; 172 R[6] = xz - wy; 173 174 R[5] = yz - wx; 175 R[7] = yz + wx; 176 } 177 else 178 { 179 double onePlusTrace = 1.0 + R[0] + R[4] + R[8];// Compute one plus the trace of the matrix 180 if (onePlusTrace > 1E-9) 181 { 182 double s = sqrt(onePlusTrace) * 2.0; 183 double is = 1 / s; 184 q[0] = 0.25 * s; 185 q[1] = (R[7] - R[5]) * is; 186 q[2] = (R[2] - R[6]) * is; 187 q[3] = (R[3] - R[1]) * is; 188 } 189 else 190 { 191 std::printf("1+trace(R)=%.9f is too small and (R11,R22,R33)=(%.9f,%.9f,%.9f) ", onePlusTrace, R[0], R[4], R[8]); 192 if ((R[0] > R[4]) && (R[0] > R[8]))//max(R00, R11, R22)=R00 193 { 194 double s = sqrt(1.0 + R[0] - R[4] - R[8]) * 2.0; 195 double is = 1 / s; 196 q[0] = (R[5] - R[7]) * is; 197 q[1] = 0.25 * s; 198 q[2] = (R[1] + R[3]) * is; 199 q[3] = (R[2] + R[6]) * is; 200 } 201 else if (R[4] > R[8])//max(R00, R11, R22)=R11 202 { 203 double s = sqrt(1.0 - R[0] + R[4] - R[8]) * 2.0; 204 double is = 1 / s; 205 q[0] = (R[2] - R[6]) * is; 206 q[1] = (R[1] + R[3]) * is; 207 q[2] = 0.25 * s; 208 q[3] = (R[5] + R[7]) * is; 209 } 210 else//max(R00, R11, R22)=R22 211 { 212 double s = sqrt(1.0 - R[0] - R[4] + R[8]) * 2.0; 213 double is = 1 / s; 214 q[0] = (R[1] - R[3]) * is; 215 q[1] = (R[2] + R[6]) * is; 216 q[2] = (R[5] + R[7]) * is; 217 q[3] = 0.25 * s; 218 } 219 } 220 double L1 = std::sqrt(q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]); 221 if (L1 < 1e-9) { std::printf("Wrong rotation matrix: NormQ=%.9f ", L1); abort(); } 222 else { L1 = 1 / L1; q[0] *= L1; q[1] *= L1; q[2] *= L1; q[3] *= L1; } 223 } 224 } 225 static void vec2quat(double r[3], double q[4], bool forward = true) 226 { 227 if (forward)//refer to qglviwer 228 { 229 double theta = std::sqrt(r[0] * r[0] + r[1] * r[1] + r[2] * r[2]); 230 if (std::abs(theta) < 1E-9) 231 { 232 q[0] = 1; q[1] = q[2] = q[3] = 0; 233 std::printf("Rotation approximates zero: Theta=%.9f ", theta); 234 }; 235 236 q[0] = std::cos(theta * 0.5); 237 double ss = std::sin(theta * 0.5) / theta; 238 q[1] = r[0] * ss; 239 q[2] = r[1] * ss; 240 q[3] = r[2] * ss; 241 } 242 else 243 { 244 double L1 = std::sqrt(q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]); 245 if (std::abs(L1 - 1) > 1E-9) { std::printf("Not uint quaternion: NormQ=%.9f ", L1); abort(); } 246 247 double theta = 2 * acos(q[0]); 248 if (theta > 3.14159265358979323846) theta = 2 * 3.14159265358979323846 - theta; 249 double thetaEx = theta / std::sin(theta * 0.5); 250 r[0] = q[1] * thetaEx; 251 r[1] = q[2] * thetaEx; 252 r[2] = q[3] * thetaEx; 253 } 254 } 255 static void vec2matrix(double r[3], double R[9], bool forward = true, int argc = 0, char** argv = 0) 256 { 257 if (argc > 0) 258 { 259 int N = 999; 260 for (int k = 0; k < N; ++k) //refer to the subsequent article for more details 261 { 262 //1.GenerateData 263 Matx31d r0 = r0.randu(-999, 999); 264 Matx33d R0; cv::Rodrigues(r0, R0); 265 266 //2.CalcByOpenCV 267 Matx33d R1; 268 Matx31d r1; 269 cv::Rodrigues(r0, R1); 270 cv::Rodrigues(R0, r1); 271 272 //3.CalcByDIY 273 Matx33d R2; 274 Matx31d r2; 275 vec2matrix(r0.val, R2.val, true); 276 vec2matrix(r2.val, R0.val, false); 277 278 //4.AnalyzeError 279 double infR1R2 = norm(R1, R2, NORM_INF); 280 double infr1r2 = norm(r1, r2, NORM_INF); 281 282 //5.PrintError 283 cout << endl << "LoopCount: " << k << endl; 284 if (infR1R2 > 1E-12 || infr1r2 > 1E-12) 285 { 286 cout << endl << "5.1PrintError" << endl; 287 cout << endl << "infR1R2: " << infR1R2 << endl; 288 cout << endl << "infr1r2: " << infr1r2 << endl; 289 if (0) 290 { 291 cout << endl << "5.2PrintDiff" << endl; 292 cout << endl << "R1: " << endl << R1 << endl; 293 cout << endl << "R2: " << endl << R2 << endl; 294 cout << endl; 295 cout << endl << "r1: " << endl << r1.t() << endl; 296 cout << endl << "r2: " << endl << r2.t() << endl; 297 cout << endl << "5.3PrintOthers" << endl; 298 } 299 cout << endl << "Press any key to continue" << endl; std::getchar(); 300 } 301 } 302 return; 303 } 304 305 if (forward) 306 { 307 double theta = std::sqrt(r[0] * r[0] + r[1] * r[1] + r[2] * r[2]); 308 if (theta < 1E-9) 309 { 310 R[0] = R[4] = R[8] = 1.0; 311 R[1] = R[2] = R[3] = R[5] = R[6] = R[7] = 0.0; 312 std::printf("Rotation approximates zero: Theta=%.9f ", theta); 313 return; 314 } 315 double cs = cos(theta); 316 double sn = sin(theta); 317 double itheta = 1. / theta; 318 double cs1 = 1 - cs; 319 double nx = r[0] * itheta; 320 double ny = r[1] * itheta; 321 double nz = r[2] * itheta; 322 323 double nxnx = nx * nx, nyny = ny * ny, nznz = nz * nz; 324 double nxny = nx * ny, nxnz = nx * nz, nynz = ny * nz; 325 double nxsn = nx * sn, nysn = ny * sn, nzsn = nz * sn; 326 327 R[0] = nxnx * cs1 + cs; 328 R[3] = nxny * cs1 + nzsn; 329 R[6] = nxnz * cs1 - nysn; 330 331 R[1] = nxny * cs1 - nzsn; 332 R[4] = nyny * cs1 + cs; 333 R[7] = nynz * cs1 + nxsn; 334 335 R[2] = nxnz * cs1 + nysn; 336 R[5] = nynz * cs1 - nxsn; 337 R[8] = nznz * cs1 + cs; 338 339 if (0) 340 { 341 Mat_<double> dRdu({ 9, 4 }, { 342 2 * nx * cs1, 0, 0, (nxnx - 1) * sn, 343 ny * cs1, nx * cs1, -sn, nxny * sn - nz * cs, 344 nz * cs1, sn, nx * cs1, nxnz * sn + ny * cs, 345 ny * cs1, nx * cs1, sn, nxny * sn + nz * cs, 346 0, 2 * ny * cs1, 0, (nyny - 1) * sn, 347 -sn, nz * cs1, ny * cs1, nynz * sn - nx * cs, 348 nz * cs1, -sn, nx * cs1, nxnz * sn - ny * cs, 349 sn, nz * cs1, ny * cs1, nynz * sn + nx * cs, 350 0, 0, 2 * nz * cs1, (nznz - 1) * sn }); 351 352 Mat_<double> dudv({ 4, 4 }, { 353 itheta, 0, 0, -nx * itheta, 354 0, itheta, 0, -ny * itheta, 355 0, 0, itheta, -nz * itheta, 356 0, 0, 0, 1 }); 357 358 Mat_<double> dvdr({ 4, 3 }, { 359 1, 0, 0, 360 0, 1, 0, 361 0, 0, 1, 362 nx, ny, nz }); 363 364 Mat_<double> Jacobian = dRdu * dudv * dvdr;//rows=9 cols=3 365 } 366 } 367 else 368 { 369 double sx = R[7] - R[5]; 370 double sy = R[2] - R[6]; 371 double sz = R[3] - R[1]; 372 double sn = sqrt(sx * sx + sy * sy + sz * sz) * 0.5; 373 double cs = (R[0] + R[4] + R[8] - 1) * 0.5; 374 double theta = acos(cs); 375 double ss = 2 * sn; 376 double iss = 1. / ss; 377 double tss = theta * iss; 378 r[0] = tss * sx; 379 r[1] = tss * sy; 380 r[2] = tss * sz; 381 382 if (0) 383 { 384 Mat_<double> drdu({ 3, 4 }, { 385 tss, 0, 0, (sn - theta * cs) * iss * iss * sx * 2, 386 0, tss, 0, (sn - theta * cs) * iss * iss * sy * 2, 387 0, 0, tss, (sn - theta * cs) * iss * iss * sz * 2 }); 388 389 Mat_<double> dudR({ 4, 9 }, { 390 0, 0, 0, 0, 0, -1, 0, 1, 0, 391 0, 0, 1, 0, 0, 0, -1, 0, 0, 392 0, -1, 0, 1, 0, 0, 0, 0, 0, 393 -iss, 0, 0, 0, -iss, 0, 0, 0, -iss }); 394 395 Mat_<double> Jacobian = drdu * dudR;//rows=3 cols=9 396 } 397 } 398 } 399 400 private: 401 const int nHorPoint3D = 100; 402 const int nVerPoint3D = 100; 403 const double varPoint3DXY = 10.; 404 const double minPoint3DZ = 1.; 405 const double maxPoint3DZ = 99.; 406 const double minCamZ = 101.; 407 const double maxCamZ = 150.; 408 const double varCamDegree = 10.; 409 Mat_<Vec3d> allPoint3D = Mat_<Vec3d>(nVerPoint3D * nHorPoint3D, 1); 410 Mat_<double> allPoint3DZ = Mat_<double>(nVerPoint3D * nHorPoint3D, 1); 411 Mat_<double> K; 412 Mat_<double> D; 413 const double deg2rad = 3.14159265358979323846 * 0.0055555555555555556; 414 const double rad2deg = 180 * 0.3183098861837906715; 415 416 public: 417 int camRows = 480; 418 int camCols = 640; 419 int camFovY = 90; 420 int camFovX = 90; 421 int camRand = 10;//append random[0,camRand] to camera intrinsics 422 int nCamDist = 5;//refer to opencv for value domain 423 int nMinMotion = 32; // no less than X motion views 424 int nMaxMotion = INT_MAX; // no more than X motion views 425 int nPoint2DThenExit = 32;//exit when less than X pixies 426 int rotMode = 1 + 2 + 4;//0=noRot 1=xAxis 2=yAxis 4=zAxis 427 bool noTrans = false;//translate or not while motion 428 bool world2D = false;//planar world or not 429 bool rndSeek = true;//use random seek or not 430 bool enableVerbose = false;//check motions one by one or not 431 vector<MotionView> motionViews;//World Information: RightX, FrontY, DownZ 432 MotionSim(bool run = true, bool world2D0 = false, bool noTrans0 = false, int rotMode0 = 7) { if (run) runMotion(world2D0, noTrans0, rotMode0); } 433 434 public: 435 void runMotion(bool world2D0 = false, bool noTrans0 = false, int rotMode0 = 7) 436 { 437 world2D = world2D0; 438 noTrans = noTrans0; 439 rotMode = rotMode0; 440 motionViews.clear(); 441 if (rndSeek) cv::setRNGSeed(clock()); 442 while (motionViews.size() < nMinMotion) 443 { 444 //1.GetAllPoint3D 445 if (world2D) allPoint3DZ = 0.; 446 else cv::randu(allPoint3DZ, -maxPoint3DZ, -minPoint3DZ);//DownZ 447 for (int i = 0, k = 0; i < nVerPoint3D; ++i) 448 for (int j = 0; j < nHorPoint3D; ++j, ++k) 449 allPoint3D(k) = Vec3d((j + cv::randu<double>()) * varPoint3DXY, (i + cv::randu<double>()) * varPoint3DXY, allPoint3DZ(i, j)); 450 451 //2.GetCamParams 452 double camFx = camCols / 2. / std::tan(camFovX / 2. * deg2rad) + cv::randu<double>() * camRand; 453 double camFy = camRows / 2. / std::tan(camFovY / 2. * deg2rad) + cv::randu<double>() * camRand; 454 double camCx = camCols / 2. + cv::randu<double>() * camRand; 455 double camCy = camRows / 2. + cv::randu<double>() * camRand; 456 K.create(3, 3); K << camFx, 0, camCx, 0, camFy, camCy, 0, 0, 1; 457 D.create(nCamDist, 1); cv::randu(D, -1.0, 1.0); 458 459 //3.GetAllMotionView 460 motionViews.clear(); 461 for (int64 k = 0; ; ++k) 462 { 463 //3.1 JoinCamParams 464 MotionView view; 465 view.K = K.clone(); 466 view.D = D.clone(); 467 468 //3.2 GetCamTrans 469 if (k == 0) view.t(0) = view.t(1) = 0; 470 else 471 { 472 view.t(0) = motionViews[k - 1].t(0) + cv::randu<double>() * varPoint3DXY; 473 view.t(1) = motionViews[k - 1].t(1) + cv::randu<double>() * varPoint3DXY; 474 } 475 view.t(2) = minCamZ + cv::randu<double>() * (maxCamZ - minCamZ); 476 view.t(2) = -view.t(2);//DownZ 477 if (noTrans && k != 0) { view.t(0) = motionViews[0].t(0); view.t(1) = motionViews[0].t(1); view.t(2) = motionViews[0].t(2); } 478 479 //3.3 GetCamRot: degree-->radian-->matrix-->vector&quaternion 480 view.degree = 0.; 481 if (rotMode & 1) view.degree(0) = cv::randu<double>() * varCamDegree; 482 if (rotMode & 2) view.degree(1) = cv::randu<double>() * varCamDegree; 483 if (rotMode & 4) view.degree(2) = cv::randu<double>() * varCamDegree; 484 view.radian = view.degree * deg2rad; 485 euler2matrix(view.radian.ptr<double>(), view.R.ptr<double>()); 486 cv::Rodrigues(view.R, view.r); 487 quat2matrix(view.q.ptr<double>(), view.R.ptr<double>(), false); 488 cv::hconcat(view.R, view.t, view.T); 489 cv::vconcat(view.r, view.t, view.rt); 490 491 //3.4 GetPoint3DAndPoint2D 492 Mat_<Vec2d> allPoint2D; 493 cv::projectPoints(allPoint3D, -view.r, -view.R.t() * view.t, view.K, view.D, allPoint2D); 494 for (int k = 0; k < allPoint2D.total(); ++k) 495 if (allPoint2D(k)[0] > 0 && allPoint2D(k)[0] < camCols && allPoint2D(k)[1] > 0 && allPoint2D(k)[1] < camRows) 496 { 497 view.point2D.push_back(allPoint2D(k)); 498 view.point3D.push_back(allPoint3D(k)); 499 view.point3DIds.push_back(k); 500 } 501 502 //3.5 PrintDetails 503 motionViews.push_back(view); 504 if (enableVerbose) 505 { 506 cout << endl << view.print(); 507 cout << fmt::format("view={} features={} ", k, view.point2D.rows); 508 double minV = 0, maxV = 0;//Distortion makes some minV next to maxV 509 int minId = 0, maxId = 0; 510 cv::minMaxIdx(allPoint2D.reshape(1, int(allPoint2D.total()) * allPoint2D.channels()), &minV, &maxV, &minId, &maxId); 511 cout << fmt::format("minInfo:({}, {})", minId, minV) << allPoint3D(minId / 2) << allPoint2D(minId / 2) << endl; 512 cout << fmt::format("maxInfo:({}, {})", maxId, maxV) << allPoint3D(maxId / 2) << allPoint2D(maxId / 2) << endl; 513 cout << "Press any key to continue" << endl; std::getchar(); 514 } 515 if (view.point2D.rows < nPoint2DThenExit || motionViews.size() > nMaxMotion) break; 516 } 517 } 518 } 519 void visMotion() 520 { 521 //1.CreateWidgets 522 Size2d validSize(nHorPoint3D * varPoint3DXY, nVerPoint3D * varPoint3DXY); 523 Mat_<cv::Affine3d> camPoses(int(motionViews.size()), 1); for (int k = 0; k < camPoses.rows; ++k) camPoses(k) = cv::Affine3d(motionViews[k].T); 524 viz::WText worldInfo(fmt::format("nMotionView: {} K: {} D: {}", motionViews.size(), cvarr2str(K), cvarr2str(D)), Point(10, 240), 10); 525 viz::WCoordinateSystem worldCSys(1000); 526 viz::WPlane worldGround(Point3d(validSize.width / 2, validSize.height / 2, 0), Vec3d(0, 0, 1), Vec3d(0, 1, 0), validSize); 527 viz::WCloud worldPoints(allPoint3D, Mat_<Vec3b>(allPoint3D.size(), Vec3b(0, 255, 0))); 528 viz::WTrajectory camTraj1(camPoses, viz::WTrajectory::FRAMES, 8); 529 viz::WTrajectorySpheres camTraj2(camPoses, 100, 2); 530 viz::WTrajectoryFrustums camTraj3(camPoses, Matx33d(K), 4., viz::Color::yellow()); 531 worldCSys.setRenderingProperty(viz::OPACITY, 0.1); 532 worldGround.setRenderingProperty(viz::OPACITY, 0.1); 533 camTraj2.setRenderingProperty(viz::OPACITY, 0.6); 534 535 //2.ShowWidgets 536 static viz::Viz3d viz3d(__FUNCTION__); 537 viz3d.showWidget("worldInfo", worldInfo); 538 viz3d.showWidget("worldCSys", worldCSys); 539 viz3d.showWidget("worldGround", worldGround); 540 viz3d.showWidget("worldPoints", worldPoints); 541 viz3d.showWidget("camTraj1", camTraj1); 542 viz3d.showWidget("camTraj2", camTraj2); 543 viz3d.showWidget("camTraj3", camTraj3); 544 545 //3.UpdateWidghts 546 static const vector<MotionView>& views = motionViews; 547 viz3d.registerKeyboardCallback([](const viz::KeyboardEvent& keyboarEvent, void* pVizBorad)->void 548 { 549 if (keyboarEvent.action != viz::KeyboardEvent::KEY_DOWN) return; 550 static int pos = 0; 551 if (keyboarEvent.code == ' ') 552 { 553 size_t num = views.size(); 554 size_t ind = pos % num; 555 double xmin3D = DBL_MAX, ymin3D = DBL_MAX, xmin2D = DBL_MAX, ymin2D = DBL_MAX; 556 double xmax3D = -DBL_MAX, ymax3D = -DBL_MAX, xmax2D = -DBL_MAX, ymax2D = -DBL_MAX; 557 for (size_t k = 0; k < views[ind].point3D.rows; ++k) 558 { 559 Vec3d pt3 = views[ind].point3D(int(k)); 560 Vec2d pt2 = views[ind].point2D(int(k)); 561 if (pt3[0] < xmin3D) xmin3D = pt3[0]; 562 if (pt3[0] > xmax3D) xmax3D = pt3[0]; 563 if (pt3[1] < ymin3D) ymin3D = pt3[1]; 564 if (pt3[1] > ymax3D) ymax3D = pt3[1]; 565 if (pt2[0] < xmin2D) xmin2D = pt2[0]; 566 if (pt2[0] > xmax2D) xmax2D = pt2[0]; 567 if (pt2[1] < ymin2D) ymin2D = pt2[1]; 568 if (pt2[1] > ymax2D) ymax2D = pt2[1]; 569 } 570 if (pos != 0) 571 { 572 for (int k = 0; k < views[ind == 0 ? num - 1 : ind - 1].point3D.rows; ++k) viz3d.removeWidget("active" + std::to_string(k)); 573 viz3d.removeWidget("viewInfo"); 574 viz3d.removeWidget("camSolid"); 575 } 576 for (int k = 0; k < views[ind].point3D.rows; ++k) viz3d.showWidget("active" + std::to_string(k), viz::WSphere(views[ind].point3D(k), 5, 10)); 577 viz3d.showWidget("viewInfo", viz::WText(fmt::format("CurrentMotion: {} ValidPoints: {} Min3DXY_Min2DXY: {}, {}, {}, {} Max3DXY_Max2DXY: {}, {}, {}, {} Rot_Trans_Euler: {} ", 578 ind, views[ind].point3D.rows, xmin3D, ymin3D, xmin2D, ymin2D, xmax3D, ymax3D, xmax2D, ymax2D, 579 cvarr2str(views[ind].r.t()) + cvarr2str(views[ind].t.t()) + cvarr2str(views[ind].degree.t())), Point(10, 10), 10)); 580 viz3d.showWidget("camSolid", viz::WCameraPosition(Matx33d(views[ind].K), 10, viz::Color::yellow()), cv::Affine3d(views[ind].T)); 581 ++pos; 582 } 583 }, 0); 584 viz3d.spin(); 585 } 586 }; 587 588 class OptimizeKDTP 589 { 590 public: 591 using MotionView = MotionSim::MotionView; 592 static void TestMe(int argc = 0, char** argv = 0) 593 { 594 int N = 99; 595 for (int k = 0; k < N; ++k) 596 { 597 //0.GenerateData 598 bool world2D = k % 2; 599 int rotMode = k % 7 + 1; 600 MotionSim motionSim(false); 601 motionSim.camFovX = 90; 602 motionSim.camFovY = 90; 603 motionSim.camRand = 10; 604 motionSim.nMinMotion = 16;//2 605 motionSim.nMaxMotion = 32;//4 606 motionSim.rndSeek = false; 607 static const int nDist = 5; 608 motionSim.nCamDist = nDist; 609 motionSim.runMotion(world2D, false, rotMode); 610 //motionSim.visMotion(); 611 Mat_<double> rs0; for (size_t k = 0; k < motionSim.motionViews.size(); ++k) rs0.push_back(-motionSim.motionViews[k].r); 612 Mat_<double> ts0; for (size_t k = 0; k < motionSim.motionViews.size(); ++k) ts0.push_back(-motionSim.motionViews[k].R.t() * motionSim.motionViews[k].t); 613 Mat_<double> K0({ 4, 1 }, { motionSim.motionViews[0].K(0, 0), motionSim.motionViews[0].K(1, 1), motionSim.motionViews[0].K(0, 2), motionSim.motionViews[0].K(1, 2) }); 614 Mat_<double> D0 = motionSim.motionViews[0].D.clone(); 615 double errRatio = 0.9; 616 double errRatioTrans = 0.99; 617 const int keyViewId = 0; 618 const int nMinMatch = 8; 619 Mat_<Vec3d> point3D0; 620 vector<vector<std::pair<int, int>>> idsPosePoint2DForAll3D; 621 vector<bool> rtsHitted(motionSim.motionViews.size(), false); 622 { 623 //1.Get approapriate world points and its all observations 624 for (int k = 0; k < motionSim.motionViews[keyViewId].point3DIds.rows; ++k) 625 { 626 int which3D = motionSim.motionViews[keyViewId].point3DIds(k); 627 vector<std::pair<int, int>> idsPosePoint2DForCur3D; 628 for (int i = 0; i < motionSim.motionViews.size(); ++i)//WhichPose==WhichView 629 for (int j = 0; j < motionSim.motionViews[i].point3DIds.rows; ++j)//WhichPoint3D=WhichPoint2D 630 if (which3D == motionSim.motionViews[i].point3DIds(j)) idsPosePoint2DForCur3D.push_back(std::pair<int, int>(i, j)); 631 if (idsPosePoint2DForCur3D.size() > nMinMatch) 632 { 633 point3D0.push_back(motionSim.motionViews[keyViewId].point3D(k)); 634 idsPosePoint2DForAll3D.push_back(idsPosePoint2DForCur3D); 635 } 636 } 637 //2.Check which views are used and check above world points whether echo its all observations 638 Scalar sumDBG = 0; 639 for (int k = 0; k < point3D0.rows; ++k) 640 for (int i = 0; i < idsPosePoint2DForAll3D[k].size(); ++i) 641 { 642 int whichView = idsPosePoint2DForAll3D[k][i].first; 643 int whichPoint2D = idsPosePoint2DForAll3D[k][i].second; 644 sumDBG += cv::sum(motionSim.motionViews[whichView].point3D(whichPoint2D) - point3D0(k)); 645 Mat_<Vec2d> pt; cv::projectPoints(point3D0(k), rs0.rowRange(whichView * 3, whichView * 3 + 3), ts0.rowRange(whichView * 3, whichView * 3 + 3), Matx33d(K0(0), 0, K0(2), 0, K0(1), K0(3), 0, 0, 1), D0, pt); 646 sumDBG += cv::sum(motionSim.motionViews[whichView].point2D(whichPoint2D) - pt(0)); 647 rtsHitted[whichView] = true; 648 } 649 if (sumDBG[0] + sumDBG[1] + sumDBG[2] + sumDBG[3] != 0) spdlog::error("Error input: {}", sumDBG[0] + sumDBG[1] + sumDBG[2] + sumDBG[3]); 650 } 651 652 //1.CalcByCeresWithAutoDeriv 653 bool fixK = false; 654 bool fixD = false; 655 bool fixRot = false; 656 bool fixTrans = false; 657 bool fixPoint3D = false; 658 int scaleFrom = 1;//1=fromPose 2=fromPoint3D 659 Mat_<double> Rs1, ts1; 660 for (int k = 0; k < rs0.rows; k += 3) 661 { 662 double errRot = errRatio; 663 double errTrans = errRatioTrans; 664 if (fixRot || rtsHitted[k / 3] == false) errRot = 1.; 665 if (fixTrans || rtsHitted[k / 3] == false) errTrans = 1.; 666 if (fixPoint3D == false && scaleFrom == 1) 667 { 668 if (k / 3 == keyViewId) errRot = 1.;//Fix at least one rotation frame for scale 669 if (k / 3 == keyViewId || k / 3 == keyViewId + 1) errTrans = 1.;//Fix at least two translation frames for scale 670 } 671 Mat_<double> _R; cv::Rodrigues(rs0.rowRange(k, k + 3) * errRot, _R); 672 Rs1.push_back(_R); 673 ts1.push_back(ts0.rowRange(k, k + 3) * errTrans); 674 } 675 Mat_<double> K1 = K0 * (fixK ? 1. : errRatio); 676 Mat_<double> D1 = D0 * (fixD ? 1. : errRatio); 677 Mat_<Vec3d> point3D1 = point3D0 * (fixPoint3D ? 1. : errRatio); 678 if (fixPoint3D == false && scaleFrom == 2) for (int k = 0; k < 3; ++k) point3D1(k) = point3D0(k);//Fix at least three world points for scale 679 ceres::Problem problem1; 680 for (int k = 0; k < point3D1.rows; ++k) 681 for (int i = 0; i < idsPosePoint2DForAll3D[k].size(); ++i) 682 { 683 int whichView = idsPosePoint2DForAll3D[k][i].first; 684 int whichPoint2D = idsPosePoint2DForAll3D[k][i].second; 685 problem1.AddResidualBlock(new ceres::AutoDiffCostFunction<ProjectionModelKDTP, 2, 3, 9, 3, 4, nDist>( 686 new ProjectionModelKDTP(motionSim.motionViews[whichView].point2D.row(whichPoint2D), motionSim.nCamDist)), 687 NULL, point3D1(k).val, Rs1.ptr<double>(whichView * 3), ts1.ptr<double>(whichView * 3), K1.ptr<double>(), D1.ptr<double>()); 688 689 problem1.SetParameterization(Rs1.ptr<double>(whichView * 3), new LocalParamRWithGeneralJ);//it is to be set more than one time 690 if (fixK) problem1.SetParameterBlockConstant(K1.ptr<double>()); 691 if (fixD) problem1.SetParameterBlockConstant(D1.ptr<double>()); 692 if (fixRot) problem1.SetParameterBlockConstant(Rs1.ptr<double>(whichView * 3)); 693 if (fixTrans) problem1.SetParameterBlockConstant(ts1.ptr<double>(whichView * 3)); 694 if (fixPoint3D) problem1.SetParameterBlockConstant(point3D1(k).val); 695 if (fixPoint3D == false && scaleFrom == 1) 696 { 697 if (whichView == keyViewId) problem1.SetParameterBlockConstant(Rs1.ptr<double>(whichView * 3));//Fix at least one rotation and two translations for scale 698 if (whichView == keyViewId || whichView == keyViewId + 1) problem1.SetParameterBlockConstant(ts1.ptr<double>(whichView * 3)); 699 } 700 if (fixPoint3D == false && scaleFrom == 2 && k < 3) problem1.SetParameterBlockConstant(point3D1(k).val);//Fix at least three world points for scale 701 } 702 ceres::Solver::Options options; 703 ceres::Solver::Summary summary; 704 ceres::Solve(options, &problem1, &summary); 705 Mat_<double> rs1; for (int k = 0; k < Rs1.rows; k += 3) { Mat_<double> _r; cv::Rodrigues(Rs1.rowRange(k, k + 3), _r); rs1.push_back(_r); } 706 int nIter1 = (int)summary.iterations.size(); 707 708 //2.AnalyzeError 709 double infrs0rs0 = norm(rs0, rs0 * errRatio, NORM_INF); 710 double infrs0rs1 = norm(rs0, rs1, NORM_INF); 711 double infts0ts0 = norm(ts0, ts0 * errRatioTrans, NORM_INF); 712 double infts0ts1 = norm(ts0, ts1, NORM_INF); 713 double infK0K0 = norm(K0, K0 * errRatio, NORM_INF); 714 double infK0K1 = norm(K0, K1, NORM_INF); 715 double infD0D0 = norm(D0, D0 * errRatio, NORM_INF); 716 double infD0D1 = norm(D0, D1, NORM_INF); 717 double infPTS0PTS0 = norm(point3D0, point3D0 * errRatio, NORM_INF); 718 double infPTS0PTS1 = norm(point3D0, point3D1, NORM_INF); 719 720 //3.PrintError 721 cout << fmt::format("LoopCount: {} AutoDeriv.iters: {} ", k, nIter1); 722 //if (infrs0rs1 > 1e-8 || infts0ts1 > 1e-8 || infK0K1 > 1e-8 || infD0D1 > 1e-8 ) 723 { 724 cout << fmt::format("infrs0rs1: {:<15.9} {:<15.9} ", infrs0rs1, infrs0rs0); 725 cout << fmt::format("infts0ts1: {:<15.9} {:<15.9} ", infts0ts1, infts0ts0); 726 cout << fmt::format("infK0K1 : {:<15.9} {:<15.9} ", infK0K1, infK0K0); 727 cout << fmt::format("infD0D1 : {:<15.9} {:<15.9} ", infD0D1, infD0D0); 728 cout << fmt::format("infPTS0PTS1 : {:<15.9} {:<15.9} ", infPTS0PTS1, infPTS0PTS0); 729 if (1) 730 { 731 //cout << endl << "" << << endl; 732 } 733 cout << "Press any key to continue" << endl; std::getchar(); 734 } 735 } 736 } 737 738 public: 739 struct ProjectionModelKDTP 740 { 741 const int nDist; 742 const Mat_<Vec2d> point2D; 743 ProjectionModelKDTP(const Mat_<Vec2d> point2D0, const int nDist0) : point2D(point2D0), nDist(nDist0) {} 744 template <typename tp> bool operator()(const tp* const point3D, const tp* const rot, const tp* const t, const tp* const K, const tp* const D, tp* errPoint2D) const 745 { 746 //1.Projection params 747 tp fx = K[0]; 748 tp fy = K[1]; 749 tp cx = K[2]; 750 tp cy = K[3]; 751 752 //2.Distortion params 753 tp k1 = D[0]; 754 tp k2 = D[1]; 755 tp p1 = D[2]; 756 tp p2 = D[3]; 757 tp k3, k4, k5, k6; 758 tp s1, s2, s3, s4; 759 if (nDist > 4) k3 = D[4]; 760 if (nDist > 5) { k4 = D[5]; k5 = D[6]; k6 = D[7]; } 761 if (nDist > 8) { s1 = D[8]; s2 = D[9]; s3 = D[10]; s4 = D[11]; } 762 763 //3.Translation params 764 tp tx = t[0]; 765 tp ty = t[1]; 766 tp tz = t[2]; 767 768 //4.Rotation params 769 tp R11, R12, R13, R21, R22, R23, R31, R32, R33; 770 { 771 R11 = rot[0]; R12 = rot[1]; R13 = rot[2]; 772 R21 = rot[3]; R22 = rot[4]; R23 = rot[5]; 773 R31 = rot[6]; R32 = rot[7]; R33 = rot[8]; 774 } 775 776 //5.ReProjection 777 const Vec2d* data2D = point2D.ptr<Vec2d>(); 778 Vec<tp, 3>* data3D = (Vec<tp, 3>*)point3D; 779 Vec<tp, 2>* err2D = (Vec<tp, 2>*)errPoint2D; 780 for (int k = 0; k < point2D.rows; ++k) 781 { 782 //5.1 WorldCoordinate 783 tp X = data3D[k][0]; 784 tp Y = data3D[k][1]; 785 tp Z = data3D[k][2]; 786 787 //5.2 CameraCoordinate 788 tp x = R11 * X + R12 * Y + R13 * Z + tx; 789 tp y = R21 * X + R22 * Y + R23 * Z + ty; 790 tp z = R31 * X + R32 * Y + R33 * Z + tz; 791 792 //5.3 StandardPhysicsCoordinate 793 tp iz = 1. / z; //if denominator==0 794 tp xc = x * iz; 795 tp yc = y * iz; 796 797 //5.4 DistortionPhysicsCoordinate 798 tp xc2 = xc * xc; 799 tp yc2 = yc * yc; 800 tp d2 = xc2 + yc2; 801 tp xcyc = 2. * xc * yc; 802 tp d4 = d2 * d2; 803 tp d6 = d2 * d4; 804 tp d2xc2 = d2 + 2. * xc2; 805 tp d2yc2 = d2 + 2. * yc2; 806 tp nu, de, xd, yd; 807 if (nDist < 5) 808 { 809 nu = 1. + k1 * d2 + k2 * d4; 810 xd = xc * nu + p1 * xcyc + p2 * d2xc2; 811 yd = yc * nu + p2 * xcyc + p1 * d2yc2; 812 } 813 else if (nDist < 8) 814 { 815 nu = 1. + k1 * d2 + k2 * d4 + k3 * d6; 816 xd = xc * nu + p1 * xcyc + p2 * d2xc2; 817 yd = yc * nu + p2 * xcyc + p1 * d2yc2; 818 } 819 else if (nDist < 12) 820 { 821 nu = 1. + k1 * d2 + k2 * d4 + k3 * d6; 822 de = 1. / (1. + k4 * d2 + k5 * d4 + k6 * d6);//if denominator==0 823 xd = xc * nu * de + p1 * xcyc + p2 * d2xc2; 824 yd = yc * nu * de + p2 * xcyc + p1 * d2yc2; 825 } 826 else if (nDist < 14) 827 { 828 nu = 1. + k1 * d2 + k2 * d4 + k3 * d6; 829 de = 1. / (1. + k4 * d2 + k5 * d4 + k6 * d6);//if denominator==0 830 xd = xc * nu * de + p1 * xcyc + p2 * d2xc2 + s1 * d2 + s2 * d4; 831 yd = yc * nu * de + p2 * xcyc + p1 * d2yc2 + s3 * d2 + s4 * d4; 832 } 833 err2D[k][0] = xd * fx + cx - data2D[k][0]; 834 err2D[k][1] = yd * fy + cy - data2D[k][1]; 835 } 836 return true; 837 } 838 }; 839 struct LocalParamRWithGeneralJ : public ceres::LocalParameterization 840 { 841 bool Plus(const double* preParam, const double* deltaParam, double* newParam) const 842 { 843 Matx33d ambientPre(preParam); 844 Matx33d ambientDelta; cv::Rodrigues(Matx31d(deltaParam), ambientDelta); 845 Matx33d ambientNew = ambientDelta * ambientPre; 846 memcpy(newParam, ambientNew.val, sizeof(double) * 9); 847 return true; 848 } 849 850 bool ComputeJacobian(const double* param, double* jacobian) const 851 { 852 Mat_<double> dRdr(9, 3, jacobian); 853 dRdr << 0, param[6], -param[3], 0, param[7], -param[4], 0, param[8], -param[5], 854 -param[6], 0, param[0], -param[7], 0, param[1], -param[8], 0, param[2], 855 param[3], -param[0], 0, param[4], -param[1], 0, param[5], -param[2], 0; 856 return true; 857 858 Matx33d R(param); 859 Mat_<double> dRdrT({ 3, 9 }, { 860 0, 0, 0, -R(2, 0), -R(2, 1), -R(2, 2), R(1, 0), R(1, 1), R(1, 2), 861 R(2, 0), R(2, 1), R(2, 2), 0, 0, 0, -R(0, 0), -R(0, 1), -R(0, 2), 862 -R(1, 0), -R(1, 1), -R(1, 2), R(0, 0), R(0, 1), R(0, 2), 0, 0, 0 }); 863 cout << endl << cv::norm(dRdr, dRdrT.t(), NORM_INF) << endl; 864 } 865 866 int GlobalSize() const { return 9; } 867 int LocalSize() const { return 3; } 868 }; 869 }; 870 871 int main(int argc, char** argv) { OptimizeKDTP::TestMe(argc, argv); return 0; }