| // Ceres Solver - A fast non-linear least squares minimizer | |
| // Copyright 2020 Google Inc. All rights reserved. | |
| // http://ceres-solver.org/ | |
| // | |
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| // modification, are permitted provided that the following conditions are met: | |
| // | |
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| // specific prior written permission. | |
| // | |
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| // | |
| // Author: jodebo_beck@gmx.de (Johannes Beck) | |
| // | |
| namespace ceres { | |
| template <int AmbientSpaceDimension> | |
| bool LineParameterization<AmbientSpaceDimension>::Plus( | |
| const double* x_ptr, | |
| const double* delta_ptr, | |
| double* x_plus_delta_ptr) const { | |
| // We seek a box plus operator of the form | |
| // | |
| // [o*, d*] = Plus([o, d], [delta_o, delta_d]) | |
| // | |
| // where o is the origin point, d is the direction vector, delta_o is | |
| // the delta of the origin point and delta_d the delta of the direction and | |
| // o* and d* is the updated origin point and direction. | |
| // | |
| // We separate the Plus operator into the origin point and directional part | |
| // d* = Plus_d(d, delta_d) | |
| // o* = Plus_o(o, d, delta_o) | |
| // | |
| // The direction update function Plus_d is the same as for the homogeneous | |
| // vector parameterization: | |
| // | |
| // d* = H_{v(d)} [0.5 sinc(0.5 |delta_d|) delta_d, cos(0.5 |delta_d|)]^T | |
| // | |
| // where H is the householder matrix | |
| // H_{v} = I - (2 / |v|^2) v v^T | |
| // and | |
| // v(d) = d - sign(d_n) |d| e_n. | |
| // | |
| // The origin point update function Plus_o is defined as | |
| // | |
| // o* = o + H_{v(d)} [0.5 delta_o, 0]^T. | |
| static constexpr int kDim = AmbientSpaceDimension; | |
| using AmbientVector = Eigen::Matrix<double, kDim, 1>; | |
| using AmbientVectorRef = Eigen::Map<Eigen::Matrix<double, kDim, 1>>; | |
| using ConstAmbientVectorRef = | |
| Eigen::Map<const Eigen::Matrix<double, kDim, 1>>; | |
| using ConstTangentVectorRef = | |
| Eigen::Map<const Eigen::Matrix<double, kDim - 1, 1>>; | |
| ConstAmbientVectorRef o(x_ptr); | |
| ConstAmbientVectorRef d(x_ptr + kDim); | |
| ConstTangentVectorRef delta_o(delta_ptr); | |
| ConstTangentVectorRef delta_d(delta_ptr + kDim - 1); | |
| AmbientVectorRef o_plus_delta(x_plus_delta_ptr); | |
| AmbientVectorRef d_plus_delta(x_plus_delta_ptr + kDim); | |
| const double norm_delta_d = delta_d.norm(); | |
| o_plus_delta = o; | |
| // Shortcut for zero delta direction. | |
| if (norm_delta_d == 0.0) { | |
| d_plus_delta = d; | |
| if (delta_o.isZero(0.0)) { | |
| return true; | |
| } | |
| } | |
| // Calculate the householder transformation which is needed for f_d and f_o. | |
| AmbientVector v; | |
| double beta; | |
| // NOTE: The explicit template arguments are needed here because | |
| // ComputeHouseholderVector is templated and some versions of MSVC | |
| // have trouble deducing the type of v automatically. | |
| internal::ComputeHouseholderVector<ConstAmbientVectorRef, double, kDim>( | |
| d, &v, &beta); | |
| if (norm_delta_d != 0.0) { | |
| // Map the delta from the minimum representation to the over parameterized | |
| // homogeneous vector. See section A6.9.2 on page 624 of Hartley & Zisserman | |
| // (2nd Edition) for a detailed description. Note there is a typo on Page | |
| // 625, line 4 so check the book errata. | |
| const double norm_delta_div_2 = 0.5 * norm_delta_d; | |
| const double sin_delta_by_delta = | |
| std::sin(norm_delta_div_2) / norm_delta_div_2; | |
| // Apply the delta update to remain on the unit sphere. See section A6.9.3 | |
| // on page 625 of Hartley & Zisserman (2nd Edition) for a detailed | |
| // description. | |
| AmbientVector y; | |
| y.template head<kDim - 1>() = 0.5 * sin_delta_by_delta * delta_d; | |
| y[kDim - 1] = std::cos(norm_delta_div_2); | |
| d_plus_delta = d.norm() * (y - v * (beta * (v.transpose() * y))); | |
| } | |
| // The null space is in the direction of the line, so the tangent space is | |
| // perpendicular to the line direction. This is achieved by using the | |
| // householder matrix of the direction and allow only movements | |
| // perpendicular to e_n. | |
| // | |
| // The factor of 0.5 is used to be consistent with the line direction | |
| // update. | |
| AmbientVector y; | |
| y << 0.5 * delta_o, 0; | |
| o_plus_delta += y - v * (beta * (v.transpose() * y)); | |
| return true; | |
| } | |
| template <int AmbientSpaceDimension> | |
| bool LineParameterization<AmbientSpaceDimension>::ComputeJacobian( | |
| const double* x_ptr, double* jacobian_ptr) const { | |
| static constexpr int kDim = AmbientSpaceDimension; | |
| using AmbientVector = Eigen::Matrix<double, kDim, 1>; | |
| using ConstAmbientVectorRef = | |
| Eigen::Map<const Eigen::Matrix<double, kDim, 1>>; | |
| using MatrixRef = Eigen::Map< | |
| Eigen::Matrix<double, 2 * kDim, 2 * (kDim - 1), Eigen::RowMajor>>; | |
| ConstAmbientVectorRef d(x_ptr + kDim); | |
| MatrixRef jacobian(jacobian_ptr); | |
| // Clear the Jacobian as only half of the matrix is not zero. | |
| jacobian.setZero(); | |
| AmbientVector v; | |
| double beta; | |
| // NOTE: The explicit template arguments are needed here because | |
| // ComputeHouseholderVector is templated and some versions of MSVC | |
| // have trouble deducing the type of v automatically. | |
| internal::ComputeHouseholderVector<ConstAmbientVectorRef, double, kDim>( | |
| d, &v, &beta); | |
| // The Jacobian is equal to J = 0.5 * H.leftCols(kDim - 1) where H is | |
| // the Householder matrix (H = I - beta * v * v') for the origin point. For | |
| // the line direction part the Jacobian is scaled by the norm of the | |
| // direction. | |
| for (int i = 0; i < kDim - 1; ++i) { | |
| jacobian.block(0, i, kDim, 1) = -0.5 * beta * v(i) * v; | |
| jacobian.col(i)(i) += 0.5; | |
| } | |
| jacobian.template block<kDim, kDim - 1>(kDim, kDim - 1) = | |
| jacobian.template block<kDim, kDim - 1>(0, 0) * d.norm(); | |
| return true; | |
| } | |
| } // namespace ceres | |