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diff --git a/extern/ceres/include/ceres/internal/line_parameterization.h b/extern/ceres/include/ceres/internal/line_parameterization.h new file mode 100644 index 00000000000..eda390148df --- /dev/null +++ b/extern/ceres/include/ceres/internal/line_parameterization.h @@ -0,0 +1,183 @@ +// Ceres Solver - A fast non-linear least squares minimizer +// Copyright 2020 Google Inc. All rights reserved. +// http://ceres-solver.org/ +// +// 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 Google Inc. 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. +// +// Author: jodebo_beck@gmx.de (Johannes Beck) +// + +#ifndef CERES_PUBLIC_INTERNAL_LINE_PARAMETERIZATION_H_ +#define CERES_PUBLIC_INTERNAL_LINE_PARAMETERIZATION_H_ + +#include "householder_vector.h" + +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 + +#endif // CERES_PUBLIC_INTERNAL_LINE_PARAMETERIZATION_H_ |