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Camera calibration techniques and associated code
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/**
* Copyright (c) 2011, The University of Southampton and the individual contributors.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification,
* are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* * Neither the name of the University of Southampton nor the names of its
* contributors may be used to endorse or promote products derived from this
* software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
* ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
* ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
package org.openimaj.image.camera.calibration;
import static java.lang.Math.cos;
import static java.lang.Math.pow;
import static java.lang.Math.sin;
import static java.lang.Math.sqrt;
import java.util.ArrayList;
import java.util.List;
import org.apache.commons.math3.analysis.MultivariateMatrixFunction;
import org.apache.commons.math3.analysis.MultivariateVectorFunction;
import org.apache.commons.math3.fitting.leastsquares.LeastSquaresFactory;
import org.apache.commons.math3.fitting.leastsquares.LeastSquaresOptimizer.Optimum;
import org.apache.commons.math3.fitting.leastsquares.LevenbergMarquardtOptimizer;
import org.apache.commons.math3.fitting.leastsquares.MultivariateJacobianFunction;
import org.apache.commons.math3.linear.ArrayRealVector;
import org.apache.commons.math3.linear.RealVector;
import org.openimaj.image.camera.Camera;
import org.openimaj.image.camera.CameraIntrinsics;
import org.openimaj.math.geometry.point.Point2d;
import org.openimaj.math.geometry.transforms.HomographyRefinement;
import org.openimaj.math.geometry.transforms.TransformUtilities;
import org.openimaj.util.pair.IndependentPair;
import Jama.Matrix;
public class CameraCalibration extends CameraCalibrationZhang {
public CameraCalibration(List>> points,
int width, int height)
{
super(points, width, height);
}
@Override
protected void performCalibration(int width, int height) {
// compute the homographies
final List homographies = new ArrayList();
for (int i = 0; i < points.size(); i++) {
final List> data = points.get(i);
final Matrix h = HomographyRefinement.SINGLE_IMAGE_TRANSFER.refine(
TransformUtilities.homographyMatrixNorm(data), data);
homographies.add(h);
}
// intial estimate of intrisics and extrinsics
estimateIntrisicAndExtrinsics(homographies, width, height);
// non-linear optimisation using analytic jacobian
refine();
}
/**
* This is the implementation of the value function for the optimiser. It
* computes the predicted location of an image point by projecting a model
* point through the camera homography and then applying the distortion. The
* implementation is converted from the C code produced by the following
* matlab symbolic code:
*
*
*
* syms u0 v0 fx fy sk real
* syms tx ty tz wx wy wz real
* syms k1 k2 k3 p1 p2 real
* syms X Y real
*
* % the intrinsic parameter matrix
* K=[fx sk u0; 0 fy v0; 0 0 1];
*
* % Expression for the rotation matrix based on the Rodrigues formula
* theta=sqrt(wx^2+wy^2+wz^2);
* omega=[0 -wz wy; wz 0 -wx; -wy wx 0];
* R = eye(3) + (sin(theta)/theta)*omega + ((1-cos(theta))/theta^2)*(omega*omega);
*
* % Expression for the translation vector
* t=[tx;ty;tz];
*
* % perspective projection of the model point (X,Y)
* uvs=K*[R(:,1) R(:,2) t]*[X; Y; 1];
* u=uvs(1)/uvs(3);
* v=uvs(2)/uvs(3);
*
* % application of 2-term radial distortion
* uu0 = u - u0;
* vv0 = v - v0;
* x = uu0/fx;
* y = vv0/fy;
* r2 = x*x + y*y;
* r4 = r2*r2;
* r6 = r2*r2*r2;
* uv = [u + uu0*(k1*r2 + k2*r4 + k3*r6) + 2*p1*vv0 + p2*(r2 + 2*uu0^2);
* v + vv0*(k1*r2 + k2*r4 + k3*r6) + p1*(r2 + 2*vv0^2) + 2*p2*uu0];
* ccode(uv, 'file', 'calibrate-value.c')
*
*
*
* @author Jonathon Hare ([email protected])
*
*/
private class Value implements MultivariateVectorFunction {
@Override
public double[] value(double[] params) throws IllegalArgumentException {
int totalPoints = 0;
for (int i = 0; i < points.size(); i++)
totalPoints += points.get(i).size();
final double[] result = new double[2 * totalPoints];
for (int i = 0, k = 0; i < points.size(); i++) {
for (int j = 0; j < points.get(i).size(); j++, k++) {
final double[] tmp = computeValue(i, j, params);
result[k * 2 + 0] = tmp[0];
result[k * 2 + 1] = tmp[1];
}
}
return result;
}
private double[] computeValue(int img, int point, double[] params) {
final double[][] A0 = new double[2][1];
final double X = points.get(img).get(point).firstObject().getX();
final double Y = points.get(img).get(point).firstObject().getY();
final double fx = params[0];
final double fy = params[1];
final double u0 = params[2];
final double v0 = params[3];
final double sk = params[4];
final double k1 = params[5];
final double k2 = params[6];
final double k3 = params[7];
final double p1 = params[8];
final double p2 = params[9];
final double wx = params[img * 6 + 10];
final double wy = params[img * 6 + 11];
final double wz = params[img * 6 + 12];
final double tx = params[img * 6 + 13];
final double ty = params[img * 6 + 14];
final double tz = params[img * 6 + 15];
// begin matlab code
final double t2 = wx * wx;
final double t3 = wy * wy;
final double t4 = wz * wz;
final double t5 = t2 + t3 + t4;
final double t6 = sqrt(t5);
final double t7 = sin(t6);
final double t8 = 1.0 / sqrt(t5);
final double t9 = cos(t6);
final double t10 = t9 - 1.0;
final double t11 = 1.0 / t5;
final double t12 = t7 * t8 * wy;
final double t13 = t10 * t11 * wx * wz;
final double t14 = t12 + t13;
final double t15 = t7 * t8 * wz;
final double t16 = t7 * t8 * wx;
final double t18 = t10 * t11 * wy * wz;
final double t17 = t16 - t18;
final double t19 = Y * t17;
final double t38 = X * t14;
final double t20 = t19 - t38 + tz;
final double t21 = 1.0 / t20;
final double t22 = t10 * t11 * wx * wy;
final double t23 = t3 + t4;
final double t24 = t10 * t11 * t23;
final double t25 = t24 + 1.0;
final double t26 = fx * t25;
final double t27 = t15 + t22;
final double t28 = t17 * u0;
final double t29 = t2 + t4;
final double t30 = t10 * t11 * t29;
final double t31 = t30 + 1.0;
final double t32 = sk * t31;
final double t43 = fx * t27;
final double t33 = t28 + t32 - t43;
final double t34 = Y * t33;
final double t35 = fx * tx;
final double t36 = sk * ty;
final double t37 = tz * u0;
final double t39 = t15 - t22;
final double t40 = sk * t39;
final double t48 = t14 * u0;
final double t41 = t26 + t40 - t48;
final double t42 = X * t41;
final double t44 = t34 + t35 + t36 + t37 + t42;
final double t49 = t21 * t44;
final double t45 = -t49 + u0;
final double t53 = fy * ty;
final double t54 = fy * t39;
final double t55 = t14 * v0;
final double t56 = t54 - t55;
final double t57 = X * t56;
final double t58 = tz * v0;
final double t59 = t17 * v0;
final double t60 = fy * t31;
final double t61 = t59 + t60;
final double t62 = Y * t61;
final double t63 = t53 + t57 + t58 + t62;
final double t64 = t21 * t63;
final double t46 = -t64 + v0;
final double t47 = 1.0 / (fx * fx);
final double t50 = t45 * t45;
final double t51 = t47 * t50;
final double t52 = 1.0 / (fy * fy);
final double t65 = t46 * t46;
final double t66 = t52 * t65;
final double t67 = t51 + t66;
final double t68 = t67 * t67;
final double t69 = k1 * t67;
final double t70 = k2 * t68;
final double t71 = k3 * t67 * t68;
final double t72 = t69 + t70 + t71;
A0[0][0] = -t45 * t72 + t21
* (t34 + t35 + t36 + t37 + X * (t26 - t14 * u0 + sk * (t15 - t10 * t11 * wx * wy))) + p2
* (t50 * 2.0 + t51 + t66) + p1 * t45 * t46 * 2.0;
A0[1][0] = t64 - t46 * t72 + p1 * (t51 + t65 * 2.0 + t66) + p2 * t45 * t46 * 2.0;
// end matlab code
return new double[] { A0[0][0], A0[1][0] };
}
}
/**
* This is the implementation of the Jacobian function for the optimiser; it
* is the partial derivative of the value function with respect to the
* parameters. The implementation is based on the matlab symbolic code:
*
*
*
* syms u0 v0 fx fy sk real
* syms tx ty tz wx wy wz real
* syms k1 k2 k3 p1 p2 real
* syms X Y real
*
* % the intrinsic parameter matrix
* K=[fx sk u0; 0 fy v0; 0 0 1];
*
* % Expression for the rotation matrix based on the Rodrigues formula
* theta=sqrt(wx^2+wy^2+wz^2);
* omega=[0 -wz wy; wz 0 -wx; -wy wx 0];
* R = eye(3) + (sin(theta)/theta)*omega + ((1-cos(theta))/theta^2)*(omega*omega);
*
* % Expression for the translation vector
* t=[tx;ty;tz];
*
* % perspective projection of the model point (X,Y)
* uvs=K*[R(:,1) R(:,2) t]*[X; Y; 1];
* u=uvs(1)/uvs(3);
* v=uvs(2)/uvs(3);
*
* % application of 2-term radial distortion
* uu0 = u - u0;
* vv0 = v - v0;
* x = uu0/fx;
* y = vv0/fy;
* r2 = x*x + y*y;
* r4 = r2*r2;
* r6 = r2*r2*r2;
* uv = [u + uu0*(k1*r2 + k2*r4 + k3*r6) + 2*p1*vv0 + p2*(r2 + 2*uu0^2);
* v + vv0*(k1*r2 + k2*r4 + k3*r6) + p1*(r2 + 2*vv0^2) + 2*p2*uu0];
* J=jacobian(uv,[fx,fy,u0,v0,sk,k1,k2,k3,p1,p2 wx wy wz tx ty tz]);
* ccode(J, 'file', 'calibrate-jacobian.c')
*
*
*
* @author Jonathon Hare ([email protected])
*
*/
private class Jacobian implements MultivariateMatrixFunction {
@Override
public double[][] value(double[] params) {
// Note that we're building the jacobian for all cameras/images and
// points. The params vector is 10 + 6*numCameras elements long (10
// intrinsic params and 6 extrinsic per camera)
int totalPoints = 0;
for (int i = 0; i < points.size(); i++)
totalPoints += points.get(i).size();
final double[][] result = new double[2 * totalPoints][];
for (int i = 0, k = 0; i < points.size(); i++) {
for (int j = 0; j < points.get(i).size(); j++, k++) {
final double[][] tmp = computeJacobian(i, j, params);
result[k * 2 + 0] = tmp[0];
result[k * 2 + 1] = tmp[1];
}
}
return result;
}
private double[][] computeJacobian(int img, int point, double[] params) {
final double[][] A0 = new double[2][16];
final double X = points.get(img).get(point).firstObject().getX();
final double Y = points.get(img).get(point).firstObject().getY();
final double fx = params[0];
final double fy = params[1];
final double u0 = params[2];
final double v0 = params[3];
final double sk = params[4];
final double k1 = params[5];
final double k2 = params[6];
final double k3 = params[7];
final double p1 = params[8];
final double p2 = params[9];
final double wx = params[img * 6 + 10];
final double wy = params[img * 6 + 11];
final double wz = params[img * 6 + 12];
final double tx = params[img * 6 + 13];
final double ty = params[img * 6 + 14];
final double tz = params[img * 6 + 15];
// begin matlab code
final double t2 = wx * wx;
final double t3 = wy * wy;
final double t4 = wz * wz;
final double t5 = t2 + t3 + t4;
final double t6 = sqrt(t5);
final double t7 = sin(t6);
final double t8 = 1.0 / sqrt(t5);
final double t9 = cos(t6);
final double t10 = t9 - 1.0;
final double t11 = 1.0 / t5;
final double t12 = t7 * t8 * wy;
final double t13 = t10 * t11 * wx * wz;
final double t14 = t12 + t13;
final double t15 = t7 * t8 * wz;
final double t16 = t7 * t8 * wx;
final double t18 = t10 * t11 * wy * wz;
final double t17 = t16 - t18;
final double t19 = Y * t17;
final double t39 = X * t14;
final double t20 = t19 - t39 + tz;
final double t21 = 1.0 / t20;
final double t22 = t10 * t11 * wx * wy;
final double t23 = t3 + t4;
final double t24 = t10 * t11 * t23;
final double t25 = t24 + 1.0;
final double t26 = fx * t25;
final double t27 = t15 + t22;
final double t28 = t17 * u0;
final double t29 = t2 + t4;
final double t30 = t10 * t11 * t29;
final double t31 = t30 + 1.0;
final double t32 = sk * t31;
final double t45 = fx * t27;
final double t33 = t28 + t32 - t45;
final double t34 = Y * t33;
final double t35 = fx * tx;
final double t36 = sk * ty;
final double t37 = tz * u0;
final double t40 = t15 - t22;
final double t41 = sk * t40;
final double t42 = t14 * u0;
final double t43 = t26 + t41 - t42;
final double t44 = X * t43;
final double t46 = t34 + t35 + t36 + t37 + t44;
final double t47 = t21 * t46;
final double t38 = -t47 + u0;
final double t48 = 1.0 / (fx * fx * fx);
final double t49 = t38 * t38;
final double t50 = t48 * t49 * 2.0;
final double t51 = 1.0 / (fx * fx);
final double t52 = X * t25;
final double t57 = Y * t27;
final double t53 = t52 - t57 + tx;
final double t54 = t21 * t38 * t51 * t53 * 2.0;
final double t55 = t50 + t54;
final double t60 = fy * ty;
final double t61 = fy * t40;
final double t62 = t14 * v0;
final double t63 = t61 - t62;
final double t64 = X * t63;
final double t65 = tz * v0;
final double t66 = t17 * v0;
final double t67 = fy * t31;
final double t68 = t66 + t67;
final double t69 = Y * t68;
final double t70 = t60 + t64 + t65 + t69;
final double t71 = t21 * t70;
final double t56 = -t71 + v0;
final double t58 = t49 * t51;
final double t59 = 1.0 / (fy * fy);
final double t72 = t56 * t56;
final double t73 = t59 * t72;
final double t74 = t58 + t73;
final double t75 = t74 * t74;
final double t76 = 1.0 / (fy * fy * fy);
final double t77 = t72 * t76 * 2.0;
final double t78 = X * t40;
final double t79 = Y * t31;
final double t80 = t78 + t79 + ty;
final double t81 = t21 * t56 * t59 * t80 * 2.0;
final double t82 = t77 + t81;
final double t83 = k1 * t74;
final double t84 = k2 * t75;
final double t85 = k3 * t74 * t75;
final double t86 = t83 + t84 + t85;
final double t87 = 1.0 / pow(t5, 3.0 / 2.0);
final double t88 = 1.0 / (t5 * t5);
final double t89 = t7 * t87 * wx * wy;
final double t90 = t2 * t7 * t87 * wz;
final double t91 = t2 * t10 * t88 * wz * 2.0;
final double t102 = t10 * t11 * wz;
final double t103 = t9 * t11 * wx * wy;
final double t92 = t89 + t90 + t91 - t102 - t103;
final double t93 = t7 * t8;
final double t94 = t2 * t9 * t11;
final double t95 = t10 * t88 * wx * wy * wz * 2.0;
final double t96 = t7 * t87 * wx * wy * wz;
final double t109 = t2 * t7 * t87;
final double t97 = t93 + t94 + t95 + t96 - t109;
final double t98 = t9 * t11 * wx * wz;
final double t99 = t2 * t7 * t87 * wy;
final double t100 = t2 * t10 * t88 * wy * 2.0;
final double t107 = t10 * t11 * wy;
final double t108 = t7 * t87 * wx * wz;
final double t101 = t98 + t99 + t100 - t107 - t108;
final double t104 = t10 * t29 * t88 * wx * 2.0;
final double t105 = t7 * t29 * t87 * wx;
final double t114 = t10 * t11 * wx * 2.0;
final double t106 = t104 + t105 - t114;
final double t110 = X * t92;
final double t111 = Y * t97;
final double t112 = t110 + t111;
final double t113 = 1.0 / (t20 * t20);
final double t115 = fy * t106;
final double t142 = t97 * v0;
final double t116 = t115 - t142;
final double t117 = Y * t116;
final double t118 = fy * t101;
final double t119 = t92 * v0;
final double t120 = t118 + t119;
final double t143 = X * t120;
final double t121 = t117 - t143;
final double t122 = t21 * t121;
final double t123 = t70 * t112 * t113;
final double t124 = t122 + t123;
final double t125 = t10 * t23 * t88 * wx * 2.0;
final double t126 = t7 * t23 * t87 * wx;
final double t127 = t125 + t126;
final double t128 = sk * t101;
final double t129 = t92 * u0;
final double t145 = fx * t127;
final double t130 = t128 + t129 - t145;
final double t131 = X * t130;
final double t132 = -t98 + t99 + t100 - t107 + t108;
final double t133 = fx * t132;
final double t134 = t97 * u0;
final double t146 = sk * t106;
final double t135 = t133 + t134 - t146;
final double t136 = Y * t135;
final double t137 = t131 + t136;
final double t138 = t21 * t137;
final double t147 = t46 * t112 * t113;
final double t139 = t138 - t147;
final double t140 = t38 * t51 * t139 * 2.0;
final double t144 = t56 * t59 * t124 * 2.0;
final double t141 = t140 - t144;
final double t148 = t7 * t87 * wy * wz;
final double t149 = t3 * t7 * t87 * wx;
final double t150 = t3 * t10 * t88 * wx * 2.0;
final double t151 = t10 * t29 * t88 * wy * 2.0;
final double t152 = t7 * t29 * t87 * wy;
final double t153 = t151 + t152;
final double t154 = t9 * t11 * wy * wz;
final double t155 = t3 * t7 * t87 * wz;
final double t156 = t3 * t10 * t88 * wz * 2.0;
final double t157 = -t89 - t102 + t103 + t155 + t156;
final double t158 = t157 * u0;
final double t159 = t10 * t23 * t88 * wy * 2.0;
final double t160 = t7 * t23 * t87 * wy;
final double t174 = t10 * t11 * wy * 2.0;
final double t161 = t159 + t160 - t174;
final double t170 = t10 * t11 * wx;
final double t162 = -t148 + t149 + t150 + t154 - t170;
final double t163 = sk * t162;
final double t164 = t3 * t7 * t87;
final double t169 = t3 * t9 * t11;
final double t165 = -t93 + t95 + t96 + t164 - t169;
final double t166 = t165 * u0;
final double t175 = fx * t161;
final double t167 = t163 + t166 - t175;
final double t168 = X * t167;
final double t171 = Y * t157;
final double t172 = X * t165;
final double t173 = t171 + t172;
final double t176 = t148 + t149 + t150 - t154 - t170;
final double t177 = fx * t176;
final double t183 = sk * t153;
final double t178 = t158 + t177 - t183;
final double t179 = Y * t178;
final double t180 = t168 + t179;
final double t181 = t21 * t180;
final double t184 = t46 * t113 * t173;
final double t182 = t181 - t184;
final double t185 = fy * t162;
final double t186 = t165 * v0;
final double t187 = t185 + t186;
final double t188 = X * t187;
final double t189 = fy * t153;
final double t196 = t157 * v0;
final double t190 = t189 - t196;
final double t197 = Y * t190;
final double t191 = t188 - t197;
final double t192 = t21 * t191;
final double t198 = t70 * t113 * t173;
final double t193 = t192 - t198;
final double t194 = t56 * t59 * t193 * 2.0;
final double t195 = t38 * t51 * t182 * 2.0;
final double t199 = t194 + t195;
final double t200 = t4 * t9 * t11;
final double t201 = t4 * t7 * t87 * wx;
final double t202 = t4 * t10 * t88 * wx * 2.0;
final double t203 = t148 - t154 - t170 + t201 + t202;
final double t204 = t4 * t7 * t87 * wy;
final double t205 = t4 * t10 * t88 * wy * 2.0;
final double t206 = t98 - t107 - t108 + t204 + t205;
final double t207 = t4 * t7 * t87;
final double t208 = t10 * t29 * t88 * wz * 2.0;
final double t209 = t7 * t29 * t87 * wz;
final double t214 = t10 * t11 * wz * 2.0;
final double t210 = t208 + t209 - t214;
final double t211 = X * t203;
final double t212 = Y * t206;
final double t213 = t211 + t212;
final double t215 = t10 * t23 * t88 * wz * 2.0;
final double t216 = t7 * t23 * t87 * wz;
final double t217 = t203 * u0;
final double t218 = t93 + t95 + t96 + t200 - t207;
final double t219 = t206 * u0;
final double t220 = -t93 + t95 + t96 - t200 + t207;
final double t221 = fx * t220;
final double t238 = sk * t210;
final double t222 = t219 + t221 - t238;
final double t223 = Y * t222;
final double t224 = t203 * v0;
final double t225 = fy * t218;
final double t226 = t224 + t225;
final double t227 = X * t226;
final double t228 = fy * t210;
final double t244 = t206 * v0;
final double t229 = t228 - t244;
final double t245 = Y * t229;
final double t230 = t227 - t245;
final double t231 = t21 * t230;
final double t246 = t70 * t113 * t213;
final double t232 = t231 - t246;
final double t233 = t56 * t59 * t232 * 2.0;
final double t234 = -t214 + t215 + t216;
final double t235 = sk * t218;
final double t247 = fx * t234;
final double t236 = t217 + t235 - t247;
final double t237 = X * t236;
final double t239 = t223 + t237;
final double t240 = t21 * t239;
final double t248 = t46 * t113 * t213;
final double t241 = t240 - t248;
final double t242 = t38 * t51 * t241 * 2.0;
final double t243 = t233 + t242;
final double t249 = 1.0 / fx;
final double t250 = 1.0 / fy;
final double t251 = t21 * t56 * t250 * 2.0;
final double t252 = sk * t21 * t38 * t51 * 2.0;
final double t253 = t251 + t252;
final double t254 = t21 * u0;
final double t255 = t70 * t113;
final double t260 = t21 * v0;
final double t256 = t255 - t260;
final double t262 = t46 * t113;
final double t257 = t254 - t262;
final double t258 = t38 * t51 * t257 * 2.0;
final double t261 = t56 * t59 * t256 * 2.0;
final double t259 = t258 - t261;
final double t263 = k1 * t55;
final double t264 = k2 * t55 * t74 * 2.0;
final double t265 = k3 * t55 * t75 * 3.0;
final double t266 = t263 + t264 + t265;
final double t267 = k1 * t82;
final double t268 = k3 * t75 * t82 * 3.0;
final double t269 = k2 * t74 * t82 * 2.0;
final double t270 = t267 + t268 + t269;
final double t271 = t21 * t80;
final double t272 = t21 * t80 * t86;
final double t273 = k1 * t21 * t38 * t51 * t80 * 2.0;
final double t274 = k2 * t21 * t38 * t51 * t74 * t80 * 4.0;
final double t275 = k3 * t21 * t38 * t51 * t75 * t80 * 6.0;
final double t276 = t273 + t274 + t275;
final double t277 = t38 * t56 * 2.0;
final double t278 = k1 * t141;
final double t279 = k2 * t74 * t141 * 2.0;
final double t280 = k3 * t75 * t141 * 3.0;
final double t281 = k1 * t199;
final double t282 = k2 * t74 * t199 * 2.0;
final double t283 = k3 * t75 * t199 * 3.0;
final double t284 = t281 + t282 + t283;
final double t285 = k1 * t243;
final double t286 = k2 * t74 * t243 * 2.0;
final double t287 = k3 * t75 * t243 * 3.0;
final double t288 = t285 + t286 + t287;
final double t289 = k1 * t21 * t38 * t249 * 2.0;
final double t290 = k2 * t21 * t38 * t74 * t249 * 4.0;
final double t291 = k3 * t21 * t38 * t75 * t249 * 6.0;
final double t292 = t289 + t290 + t291;
final double t293 = k1 * t253;
final double t294 = k3 * t75 * t253 * 3.0;
final double t295 = k2 * t74 * t253 * 2.0;
final double t296 = t293 + t294 + t295;
final double t297 = k1 * t259;
final double t298 = k2 * t74 * t259 * 2.0;
final double t299 = k3 * t75 * t259 * 3.0;
final double t300 = t297 + t298 + t299;
A0[0][0] = t21 * t53 + t266
* (u0 - t21 * (t34 + t35 + t36 + t37 + X * (t26 - t14 * u0 + sk * (t15 - t10 * t11 * wx * wy)))) - p2
* (t50 + t54 + t21 * t38 * t53 * 4.0) + t21 * t53 * t86 - p1 * t21 * t53 * t56 * 2.0;
A0[0][1] = -p2 * t82 + t38 * t270 - p1 * t21 * t38 * t80 * 2.0;
A0[0][2] = 1.0;
A0[0][4] = t271 + t272 - p2 * (t21 * t38 * t80 * 4.0 + t21 * t38 * t51 * t80 * 2.0) + t38 * t276 - p1 * t21
* t56 * t80 * 2.0;
A0[0][5] = -t38 * t74;
A0[0][6] = -t38 * t75;
A0[0][7] = -t38 * t74 * t75;
A0[0][8] = t277;
A0[0][9] = t49 * 2.0 + t58 + t73;
A0[0][10] = t138 - t147 + t86 * t139 + t38 * (t278 + t279 + t280) - p2 * (t140 - t144 + t38 * t139 * 4.0)
+ p1 * t38 * t124 * 2.0 - p1 * t56 * t139 * 2.0;
A0[0][11] = -t184 + t86 * t182 + t38 * t284 - p2 * (t194 + t195 + t38 * t182 * 4.0) + t21
* (t168 + Y * (t158 - sk * t153 + fx * (t148 + t149 + t150 - t10 * t11 * wx - t9 * t11 * wy * wz)))
- p1 * t38 * t193 * 2.0 - p1 * t56 * t182 * 2.0;
A0[0][12] = t240
- t248
+ t38
* t288
- p2
* (t233 + t242 + t38 * t241 * 4.0)
+ t86
* (t21
* (t223 + X
* (t217 + sk * (t93 + t95 + t96 + t200 - t4 * t7 * t87) - fx
* (t215 + t216 - t10 * t11 * wz * 2.0))) - t46 * t113 * t213) - p1 * t38
* t232 * 2.0 - p1 * t56 * t241 * 2.0;
A0[0][13] = fx * t21 + t38 * t292 - p2 * (fx * t21 * t38 * 4.0 + t21 * t38 * t249 * 2.0) + fx * t21 * t86
- fx * p1 * t21 * t56 * 2.0;
A0[0][14] = sk * t21 + t38 * t296 - p2 * (t251 + t252 + sk * t21 * t38 * 4.0) + sk * t21 * t86 - fy * p1
* t21 * t38 * 2.0 - p1 * sk * t21 * t56 * 2.0;
A0[0][15] = t254 - t46 * t113 + t38 * t300 + t86 * t257 - p2 * (t258 - t261 + t38 * t257 * 4.0) - p1 * t56
* t257 * 2.0 + p1 * t38 * (t255 - t260) * 2.0;
A0[1][0] = -p1 * t55 + t56 * t266 - p2 * t21 * t53 * t56 * 2.0;
A0[1][1] = t271 + t272 + t56 * t270 - p1 * (t77 + t81 + t21 * t56 * t80 * 4.0) - p2 * t21 * t38 * t80 * 2.0;
A0[1][3] = 1.0;
A0[1][4] = t56 * t276 - p2 * t21 * t56 * t80 * 2.0 - p1 * t21 * t38 * t51 * t80 * 2.0;
A0[1][5] = -t56 * t74;
A0[1][6] = -t56 * t75;
A0[1][7] = -t56 * t74 * t75;
A0[1][8] = t58 + t72 * 2.0 + t73;
A0[1][9] = t277;
A0[1][10] = -t122 - t123 - t86 * t124 + t56 * (t278 + t279 + t280) + p1 * (-t140 + t144 + t56 * t124 * 4.0)
+ p2 * t38 * t124 * 2.0 - p2 * t56 * t139 * 2.0;
A0[1][11] = t192 - t198 + t86 * t193 + t56 * t284 - p1 * (t194 + t195 + t56 * t193 * 4.0) - p2 * t38 * t193
* 2.0 - p2 * t56 * t182 * 2.0;
A0[1][12] = t231 - t246 + t86 * t232 + t56 * t288 - p1 * (t233 + t242 + t56 * t232 * 4.0) - p2 * t38 * t232
* 2.0 - p2 * t56 * t241 * 2.0;
A0[1][13] = t56 * t292 - fx * p2 * t21 * t56 * 2.0 - p1 * t21 * t38 * t249 * 2.0;
A0[1][14] = fy * t21 + t56 * t296 - p1 * (t251 + t252 + fy * t21 * t56 * 4.0) + fy * t21 * t86 - fy * p2
* t21 * t38 * 2.0 - p2 * sk * t21 * t56 * 2.0;
A0[1][15] = -t255 + t260 - t86 * t256 + t56 * t300 + p1 * (-t258 + t261 + t56 * t256 * 4.0) - p2 * t56 * t257
* 2.0 + p2 * t38 * (t255 - t260) * 2.0;
// end matlab code
final double[][] result = new double[2][10 + 6 * points.size()];
System.arraycopy(A0[0], 0, result[0], 0, 10);
System.arraycopy(A0[1], 0, result[1], 0, 10);
System.arraycopy(A0[0], 10, result[0], 10 + img * 6, 6);
System.arraycopy(A0[1], 10, result[1], 10 + img * 6, 6);
// result[0][7] = 0;
// result[1][7] = 0;
// result[0][8] = 0;
// result[1][8] = 0;
// result[0][9] = 0;
// result[1][9] = 0;
return result;
}
}
/**
* Stack the observed image locations of the calibration pattern points into
* a vector
*
* @return the observed vector
*/
@Override
protected RealVector buildObservedVector()
{
int totalPoints = 0;
for (int i = 0; i < points.size(); i++)
totalPoints += points.get(i).size();
final double[] vec = new double[totalPoints * 2];
for (int i = 0, k = 0; i < points.size(); i++) {
for (int j = 0; j < points.get(i).size(); j++, k++) {
vec[k * 2 + 0] = points.get(i).get(j).secondObject().getX();
vec[k * 2 + 1] = points.get(i).get(j).secondObject().getY();
}
}
return new ArrayRealVector(vec, false);
}
/**
* Perform Levenburg-Marquardt non-linear optimisation to get better
* estimates of the parameters
*/
private void refine()
{
final LevenbergMarquardtOptimizer lm = new LevenbergMarquardtOptimizer();
final RealVector start = buildInitialVector();
final RealVector observed = buildObservedVector();
final int maxEvaluations = 1000;
final int maxIterations = 1000;
final MultivariateVectorFunction value = new Value();
final MultivariateMatrixFunction jacobian = new Jacobian();
final MultivariateJacobianFunction model = LeastSquaresFactory.model(value, jacobian);
final Optimum result = lm.optimize(LeastSquaresFactory.create(model,
observed, start, null, maxEvaluations, maxIterations));
updateEstimates(result.getPoint());
}
/**
* Extract the data from the optimised parameter vector and put it back into
* our camera model
*
* @param point
* the optimised parameter vector
*/
private void updateEstimates(RealVector point) {
final CameraIntrinsics intrinsic = cameras.get(0).intrinsicParameters;
intrinsic.setFocalLengthX(point.getEntry(0));
intrinsic.setFocalLengthY(point.getEntry(1));
intrinsic.setPrincipalPointX(point.getEntry(2));
intrinsic.setPrincipalPointY(point.getEntry(3));
intrinsic.setSkewFactor(point.getEntry(4));
intrinsic.k1 = point.getEntry(5);
intrinsic.k2 = point.getEntry(6);
intrinsic.k3 = point.getEntry(7);
intrinsic.p1 = point.getEntry(8);
intrinsic.p2 = point.getEntry(9);
for (int i = 0; i < cameras.size(); i++) {
final Camera e = cameras.get(i);
final double[] rv = new double[] { point.getEntry(i * 6 + 10), point.getEntry(i * 6 + 11),
point.getEntry(i * 6 + 12) };
e.rotation = TransformUtilities.rodrigues(rv);
e.translation.setX(point.getEntry(i * 6 + 13));
e.translation.setY(point.getEntry(i * 6 + 14));
e.translation.setZ(point.getEntry(i * 6 + 15));
}
}
private RealVector buildInitialVector() {
final CameraIntrinsics intrinsic = cameras.get(0).intrinsicParameters;
final double[] vector = new double[10 + cameras.size() * 6];
vector[0] = intrinsic.getFocalLengthX();
vector[1] = intrinsic.getFocalLengthY();
vector[2] = intrinsic.getPrincipalPointX();
vector[3] = intrinsic.getPrincipalPointY();
vector[4] = intrinsic.getSkewFactor();
vector[5] = intrinsic.k1;
vector[6] = intrinsic.k2;
vector[7] = intrinsic.k3;
vector[8] = intrinsic.p1;
vector[9] = intrinsic.p2;
for (int i = 0; i < cameras.size(); i++) {
final Camera e = cameras.get(i);
final double[] rv = TransformUtilities.rodrigues(e.rotation);
vector[i * 6 + 10] = rv[0];
vector[i * 6 + 11] = rv[1];
vector[i * 6 + 12] = rv[2];
vector[i * 6 + 13] = e.translation.getX();
vector[i * 6 + 14] = e.translation.getY();
vector[i * 6 + 15] = e.translation.getZ();
}
return new ArrayRealVector(vector, false);
}
}