001/******************************************************************************* 002 * Permission to use and distribute this software is granted under the BSD 2-Clause 003 * "Simplified" License (see http://opensource.org/licenses/BSD-2-Clause). 004 * Copyright (c) 2016-2023 Wilhelm Burger. All rights reserved. 005 * Visit https://imagingbook.com for additional details. 006 ******************************************************************************/ 007package imagingbook.calibration.zhang; 008 009import imagingbook.common.geometry.basic.Pnt2d; 010import org.apache.commons.math3.analysis.MultivariateMatrixFunction; 011import org.apache.commons.math3.analysis.MultivariateVectorFunction; 012 013import static java.lang.Math.cos; 014import static java.lang.Math.pow; 015import static java.lang.Math.sin; 016import static java.lang.Math.sqrt; 017 018/** 019 * Nonlinear optimizer based on the Levenberg-Marquart method, where the Jacobian matrix 020 * is calculated analytically, with the first partial derivatives derived from the calibration model. 021 * As an alternative see {@link NonlinearOptimizerNumeric} which uses numeric differentiation. 022 * 023 * @author WB 024 */ 025public class NonlinearOptimizerAnalytic extends NonlinearOptimizer { 026 027 NonlinearOptimizerAnalytic(Pnt2d[] modelPts, Pnt2d[][] obsPts) { 028 super(modelPts, obsPts); 029 } 030 031 @Override 032 MultivariateVectorFunction makeValueFun() { 033 return new ValueFun(); 034 } 035 036 @Override 037 MultivariateMatrixFunction makeJacobianFun() { 038 return new JacobianFun(); 039 } 040 041 private class JacobianFun implements MultivariateMatrixFunction { 042 /** 043 * Calculates a "stacked" Jacobian matrix with 2MN rows and K = 7 + 6M columns (for M views with N points each, 044 * K parameters). For example, with M = 5 views and N = 256 points each, J is of size 2560 × 37. Each pair of 045 * rows in the Jacobian corresponds to one point. 046 */ 047 @Override 048 public double[][] value(double[] params) { 049 final double[][] J = new double[2 * M * N][]; 050 int r = 0; // row 051 for (int i = 0; i < M; i++) { // for all views 052 for (int j = 0; j < N; j++) { // for all points 053 final double[][] Jij = subJacobian(i, j, params); 054 J[r + 0] = Jij[0]; // row 0 (x-coordinate) 055 J[r + 1] = Jij[1]; // row 1 (y-coordinate) 056 r = r + 2; 057 } 058 } 059 return J; 060 } 061 062 /** 063 * Calculates the sub-Jacobian for view 'i' / model point 'j' with the current parameter vector 'params' . 064 * 065 * @param i the point index (= 0,...,M) 066 * @param j the view index (= 0,...,N) 067 * @param params the current parameters (of length K) 068 * @return the two rows (2 x K sub-matrix) of the Jacobian for the given point 069 */ 070 private double[][] subJacobian(int i, int j, double[] params) { 071 final double[][] A0 = new double[2][camParLength + viewParLength]; 072 073 final double X = modelPts[j].getX(); 074 final double Y = modelPts[j].getY(); 075 076 final double alpha = params[0]; 077 final double beta = params[1]; 078 final double gamma = params[2]; 079 final double uc = params[3]; 080 final double vc = params[4]; 081 final double k0 = params[5]; 082 final double k1 = params[6]; 083 084 final double wx = params[i * viewParLength + camParLength + 0]; 085 final double wy = params[i * viewParLength + camParLength + 1]; 086 final double wz = params[i * viewParLength + camParLength + 2]; 087 final double tx = params[i * viewParLength + camParLength + 3]; 088 final double ty = params[i * viewParLength + camParLength + 4]; 089 final double tz = params[i * viewParLength + camParLength + 5]; 090 091 // begin matlab code 092 final double t2 = wx * wx; 093 final double t3 = wy * wy; 094 final double t4 = wz * wz; 095 final double t5 = t2 + t3 + t4; 096 final double t6 = sqrt(t5); 097 final double t7 = sin(t6); 098 final double t8 = 1.0 / sqrt(t5); 099 final double t9 = cos(t6); 100 final double t10 = t9 - 1.0; 101 final double t11 = 1.0 / t5; 102 final double t12 = t7 * t8 * wy; 103 final double t13 = t10 * t11 * wx * wz; 104 final double t14 = t12 + t13; 105 final double t15 = t7 * t8 * wz; 106 final double t16 = t7 * t8 * wx; 107 final double t18 = t10 * t11 * wy * wz; 108 final double t17 = t16 - t18; 109 final double t19 = Y * t17; 110 final double t39 = X * t14; 111 final double t20 = t19 - t39 + tz; 112 final double t21 = 1.0 / t20; 113 final double t22 = t10 * t11 * wx * wy; 114 final double t23 = t3 + t4; 115 final double t24 = t10 * t11 * t23; 116 final double t25 = t24 + 1.0; 117 final double t26 = alpha * t25; 118 final double t27 = t15 + t22; 119 final double t28 = t17 * uc; 120 final double t29 = t2 + t4; 121 final double t30 = t10 * t11 * t29; 122 final double t31 = t30 + 1.0; 123 final double t32 = gamma * t31; 124 final double t45 = alpha * t27; 125 final double t33 = t28 + t32 - t45; 126 final double t34 = Y * t33; 127 final double t35 = alpha * tx; 128 final double t36 = gamma * ty; 129 final double t37 = tz * uc; 130 final double t40 = t15 - t22; 131 final double t41 = gamma * t40; 132 final double t42 = t14 * uc; 133 final double t43 = t26 + t41 - t42; 134 final double t44 = X * t43; 135 final double t46 = t34 + t35 + t36 + t37 + t44; 136 final double t47 = t21 * t46; 137 final double t38 = -t47 + uc; 138 final double t48 = 1.0 / (alpha * alpha * alpha); 139 final double t49 = t38 * t38; 140 final double t50 = t48 * t49 * 2.0; 141 final double t51 = 1.0 / (alpha * alpha); 142 final double t52 = X * t25; 143 final double t57 = Y * t27; 144 final double t53 = t52 - t57 + tx; 145 final double t54 = t21 * t38 * t51 * t53 * 2.0; 146 final double t55 = t50 + t54; 147 final double t60 = beta * ty; 148 final double t61 = beta * t40; 149 final double t62 = t14 * vc; 150 final double t63 = t61 - t62; 151 final double t64 = X * t63; 152 final double t65 = tz * vc; 153 final double t66 = t17 * vc; 154 final double t67 = beta * t31; 155 final double t68 = t66 + t67; 156 final double t69 = Y * t68; 157 final double t70 = t60 + t64 + t65 + t69; 158 final double t71 = t21 * t70; 159 final double t56 = -t71 + vc; 160 final double t58 = t49 * t51; 161 final double t59 = 1.0 / (beta * beta); 162 final double t72 = t56 * t56; 163 final double t73 = t59 * t72; 164 final double t74 = t58 + t73; 165 final double t75 = 1.0 / (beta * beta * beta); 166 final double t76 = t72 * t75 * 2.0; 167 final double t77 = X * t40; 168 final double t78 = Y * t31; 169 final double t79 = t77 + t78 + ty; 170 final double t80 = t21 * t56 * t59 * t79 * 2.0; 171 final double t81 = t76 + t80; 172 final double t82 = k0 * t74; 173 final double t83 = t74 * t74; 174 final double t84 = k1 * t83; 175 final double t85 = t82 + t84; 176 final double t86 = 1.0 / pow(t5, 3.0 / 2.0); 177 final double t87 = 1.0 / (t5 * t5); 178 final double t88 = t9 * t11 * wx * wz; 179 final double t89 = t2 * t7 * t86 * wy; 180 final double t90 = t2 * t10 * t87 * wy * 2.0; 181 final double t91 = t7 * t86 * wx * wy; 182 final double t92 = t2 * t7 * t86 * wz; 183 final double t93 = t2 * t10 * t87 * wz * 2.0; 184 final double t105 = t10 * t11 * wz; 185 final double t106 = t9 * t11 * wx * wy; 186 final double t94 = t91 + t92 + t93 - t105 - t106; 187 final double t95 = t7 * t8; 188 final double t96 = t2 * t9 * t11; 189 final double t97 = t10 * t87 * wx * wy * wz * 2.0; 190 final double t98 = t7 * t86 * wx * wy * wz; 191 final double t103 = t2 * t7 * t86; 192 final double t99 = t95 + t96 + t97 + t98 - t103; 193 final double t100 = t10 * t29 * t87 * wx * 2.0; 194 final double t101 = t7 * t29 * t86 * wx; 195 final double t116 = t10 * t11 * wx * 2.0; 196 final double t102 = t100 + t101 - t116; 197 final double t104 = t7 * t86 * wx * wz; 198 final double t107 = X * t94; 199 final double t108 = Y * t99; 200 final double t109 = t107 + t108; 201 final double t110 = 1.0 / (t20 * t20); 202 final double t111 = t10 * t23 * t87 * wx * 2.0; 203 final double t112 = t7 * t23 * t86 * wx; 204 final double t113 = t111 + t112; 205 final double t117 = t10 * t11 * wy; 206 final double t114 = t88 + t89 + t90 - t104 - t117; 207 final double t115 = t94 * uc; 208 final double t118 = t99 * uc; 209 final double t119 = beta * t102; 210 final double t262 = t99 * vc; 211 final double t120 = t119 - t262; 212 final double t121 = Y * t120; 213 final double t122 = beta * t114; 214 final double t123 = t94 * vc; 215 final double t124 = t122 + t123; 216 final double t263 = X * t124; 217 final double t125 = t121 - t263; 218 final double t126 = t21 * t125; 219 final double t127 = t70 * t109 * t110; 220 final double t128 = t126 + t127; 221 final double t129 = gamma * t114; 222 final double t141 = alpha * t113; 223 final double t130 = t115 + t129 - t141; 224 final double t131 = X * t130; 225 final double t132 = -t88 + t89 + t90 + t104 - t117; 226 final double t133 = alpha * t132; 227 final double t142 = gamma * t102; 228 final double t134 = t118 + t133 - t142; 229 final double t135 = Y * t134; 230 final double t136 = t131 + t135; 231 final double t137 = t21 * t136; 232 final double t143 = t46 * t109 * t110; 233 final double t138 = t137 - t143; 234 final double t139 = t38 * t51 * t138 * 2.0; 235 final double t264 = t56 * t59 * t128 * 2.0; 236 final double t140 = t139 - t264; 237 final double t144 = t3 * t7 * t86 * wz; 238 final double t145 = t3 * t10 * t87 * wz * 2.0; 239 final double t146 = -t91 - t105 + t106 + t144 + t145; 240 final double t147 = t3 * t7 * t86; 241 final double t156 = t3 * t9 * t11; 242 final double t148 = -t95 + t97 + t98 + t147 - t156; 243 final double t149 = t10 * t29 * t87 * wy * 2.0; 244 final double t150 = t7 * t29 * t86 * wy; 245 final double t151 = t149 + t150; 246 final double t152 = t9 * t11 * wy * wz; 247 final double t153 = t3 * t7 * t86 * wx; 248 final double t154 = t3 * t10 * t87 * wx * 2.0; 249 final double t155 = t7 * t86 * wy * wz; 250 final double t157 = Y * t146; 251 final double t158 = X * t148; 252 final double t159 = t157 + t158; 253 final double t161 = t10 * t11 * wx; 254 final double t160 = t152 + t153 + t154 - t155 - t161; 255 final double t162 = beta * t160; 256 final double t163 = t148 * vc; 257 final double t164 = t162 + t163; 258 final double t165 = X * t164; 259 final double t166 = beta * t151; 260 final double t267 = t146 * vc; 261 final double t167 = t166 - t267; 262 final double t268 = Y * t167; 263 final double t168 = t165 - t268; 264 final double t169 = t21 * t168; 265 final double t269 = t70 * t110 * t159; 266 final double t170 = t169 - t269; 267 final double t171 = t56 * t59 * t170 * 2.0; 268 final double t172 = -t152 + t153 + t154 + t155 - t161; 269 final double t173 = alpha * t172; 270 final double t174 = t146 * uc; 271 final double t189 = gamma * t151; 272 final double t175 = t173 + t174 - t189; 273 final double t176 = Y * t175; 274 final double t177 = t10 * t23 * t87 * wy * 2.0; 275 final double t178 = t7 * t23 * t86 * wy; 276 final double t190 = t10 * t11 * wy * 2.0; 277 final double t179 = t177 + t178 - t190; 278 final double t180 = gamma * t160; 279 final double t181 = t148 * uc; 280 final double t191 = alpha * t179; 281 final double t182 = t180 + t181 - t191; 282 final double t183 = X * t182; 283 final double t184 = t176 + t183; 284 final double t185 = t21 * t184; 285 final double t192 = t46 * t110 * t159; 286 final double t186 = t185 - t192; 287 final double t187 = t38 * t51 * t186 * 2.0; 288 final double t188 = t171 + t187; 289 final double t193 = t4 * t9 * t11; 290 final double t194 = t4 * t7 * t86 * wx; 291 final double t195 = t4 * t10 * t87 * wx * 2.0; 292 final double t196 = -t152 + t155 - t161 + t194 + t195; 293 final double t197 = t4 * t7 * t86; 294 final double t198 = t10 * t29 * t87 * wz * 2.0; 295 final double t199 = t7 * t29 * t86 * wz; 296 final double t204 = t10 * t11 * wz * 2.0; 297 final double t200 = t198 + t199 - t204; 298 final double t201 = t4 * t7 * t86 * wy; 299 final double t202 = t4 * t10 * t87 * wy * 2.0; 300 final double t203 = t88 - t104 - t117 + t201 + t202; 301 final double t205 = t10 * t23 * t87 * wz * 2.0; 302 final double t206 = t7 * t23 * t86 * wz; 303 final double t207 = t196 * uc; 304 final double t208 = t95 + t97 + t98 + t193 - t197; 305 final double t209 = t203 * uc; 306 final double t210 = -t95 + t97 + t98 - t193 + t197; 307 final double t211 = alpha * t210; 308 final double t231 = gamma * t200; 309 final double t212 = t209 + t211 - t231; 310 final double t213 = Y * t212; 311 final double t214 = X * t196; 312 final double t215 = Y * t203; 313 final double t216 = t214 + t215; 314 final double t217 = t196 * vc; 315 final double t218 = beta * t208; 316 final double t219 = t217 + t218; 317 final double t220 = X * t219; 318 final double t221 = beta * t200; 319 final double t273 = t203 * vc; 320 final double t222 = t221 - t273; 321 final double t274 = Y * t222; 322 final double t223 = t220 - t274; 323 final double t224 = t21 * t223; 324 final double t275 = t70 * t110 * t216; 325 final double t225 = t224 - t275; 326 final double t226 = t56 * t59 * t225 * 2.0; 327 final double t227 = -t204 + t205 + t206; 328 final double t228 = gamma * t208; 329 final double t237 = alpha * t227; 330 final double t229 = t207 + t228 - t237; 331 final double t230 = X * t229; 332 final double t232 = t213 + t230; 333 final double t233 = t21 * t232; 334 final double t238 = t46 * t110 * t216; 335 final double t234 = t233 - t238; 336 final double t235 = t38 * t51 * t234 * 2.0; 337 final double t236 = t226 + t235; 338 final double t239 = 1.0 / alpha; 339 final double t240 = 1.0 / beta; 340 final double t241 = t21 * t56 * t240 * 2.0; 341 final double t242 = gamma * t21 * t38 * t51 * 2.0; 342 final double t243 = t241 + t242; 343 final double t244 = t21 * uc; 344 final double t248 = t46 * t110; 345 final double t245 = t244 - t248; 346 final double t246 = t70 * t110; 347 final double t285 = t21 * vc; 348 final double t247 = t246 - t285; 349 final double t249 = t38 * t51 * t245 * 2.0; 350 final double t286 = t56 * t59 * t247 * 2.0; 351 final double t250 = t249 - t286; 352 final double t251 = k0 * t55; 353 final double t252 = k1 * t55 * t74 * 2.0; 354 final double t253 = t251 + t252; 355 final double t254 = k0 * t81; 356 final double t255 = k1 * t74 * t81 * 2.0; 357 final double t256 = t254 + t255; 358 final double t257 = t21 * t79; 359 final double t258 = t21 * t79 * t85; 360 final double t259 = k0 * t21 * t38 * t51 * t79 * 2.0; 361 final double t260 = k1 * t21 * t38 * t51 * t74 * t79 * 4.0; 362 final double t261 = t259 + t260; 363 final double t265 = k0 * t140; 364 final double t266 = k1 * t74 * t140 * 2.0; 365 final double t270 = k0 * t188; 366 final double t271 = k1 * t74 * t188 * 2.0; 367 final double t272 = t270 + t271; 368 final double t276 = k0 * t236; 369 final double t277 = k1 * t74 * t236 * 2.0; 370 final double t278 = t276 + t277; 371 final double t279 = k0 * t21 * t38 * t239 * 2.0; 372 final double t280 = k1 * t21 * t38 * t74 * t239 * 4.0; 373 final double t281 = t279 + t280; 374 final double t282 = k0 * t243; 375 final double t283 = k1 * t74 * t243 * 2.0; 376 final double t284 = t282 + t283; 377 final double t287 = k0 * t250; 378 final double t288 = k1 * t74 * t250 * 2.0; 379 final double t289 = t287 + t288; 380 // alpha 381 A0[0][0] = t21 * t53 + t253 382 * (uc - t21 * (t34 + t35 + t36 + t37 + X * (t26 - t14 * uc + gamma * (t15 - t10 * t11 * wx * wy)))) 383 + t21 * t53 * t85; 384 // beta 385 A0[0][1] = t38 * t256; 386 // uc 387 A0[0][3] = 1.0; 388 // vc 389 A0[0][4] = 0.0; 390 // gamma 391 A0[0][2] = t257 + t258 + t38 * t261; 392 // k1 393 A0[0][5] = -t38 * t74; 394 // k2 395 A0[0][6] = -t38 * t83; 396 A0[0][7] = t137 - t143 + t38 * (t265 + t266) + t85 * 397 (t21 * (X * (t115 - alpha * t113 + gamma * (t88 + t89 + t90 - t10 * t11 * wy - t7 * t86 * wx * wz)) + Y 398 * (t118 + alpha * (-t88 + t89 + t90 + t104 - t10 * t11 * wy) - gamma * t102)) - t46 * t109 * t110); 399 A0[0][8] = t185 - t192 + t85 * t186 + t38 * t272; 400 A0[0][9] = -t238 + t38 * t278 + t85 * t234 + t21 401 * (t213 + X * (t207 + gamma * (t95 + t97 + t98 + t193 - t4 * t7 * t86) - alpha 402 * (t205 + t206 - t10 * t11 * wz * 2.0))); 403 A0[0][10] = alpha * t21 + t38 * t281 + alpha * t21 * t85; 404 A0[0][11] = gamma * t21 + t38 * t284 + gamma * t21 * t85; 405 A0[0][12] = t244 - t46 * t110 + t38 * t289 + t85 * t245; 406 407 // alpha 408 A0[1][0] = t56 * t253; 409 // beta 410 A0[1][1] = t257 + t258 + t56 * t256; 411 // uc 412 A0[1][3] = 0.0; 413 // vc 414 A0[1][4] = 1.0; 415 // gamma 416 A0[1][2] = t56 * t261; 417 // k1 418 A0[1][5] = -t56 * t74; 419 // k2 420 A0[1][6] = -t56 * t83; 421 422 A0[1][7] = -t126 - t127 + t56 * (t265 + t266) - t85 * t128; 423 A0[1][8] = t169 - t269 + t85 * t170 + t56 * t272; 424 A0[1][9] = t224 - t275 + t85 * t225 + t56 * t278; 425 A0[1][10] = t56 * t281; 426 A0[1][11] = beta * t21 + t56 * t284 + beta * t21 * t85; 427 A0[1][12] = -t246 + t285 - t85 * t247 + t56 * t289; 428 // end of matlab code 429 430 final double[][] Jij = new double[2][camParLength + viewParLength * M]; 431 System.arraycopy(A0[0], 0, Jij[0], 0, camParLength); 432 System.arraycopy(A0[1], 0, Jij[1], 0, camParLength); 433 System.arraycopy(A0[0], 7, Jij[0], camParLength + i * viewParLength, viewParLength); 434 System.arraycopy(A0[1], 7, Jij[1], camParLength + i * viewParLength, viewParLength); 435 //System.out.format("**** Jij = %d / %d\n", Jij.length, Jij[0].length); 436 return Jij; 437 } 438 } 439 440}