v01
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Ivan
408
thirdparty/basalt-headers/include/basalt/camera/unified_camera.hpp
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thirdparty/basalt-headers/include/basalt/camera/unified_camera.hpp
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/**
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BSD 3-Clause License
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This file is part of the Basalt project.
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https://gitlab.com/VladyslavUsenko/basalt-headers.git
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Copyright (c) 2019, Vladyslav Usenko and Nikolaus Demmel.
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All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are met:
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* Redistributions of source code must retain the above copyright notice, this
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list of conditions and the following disclaimer.
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* Redistributions in binary form must reproduce the above copyright notice,
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this list of conditions and the following disclaimer in the documentation
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and/or other materials provided with the distribution.
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* Neither the name of the copyright holder nor the names of its
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contributors may be used to endorse or promote products derived from
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this software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
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FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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@file
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@brief Implementation of unified camera model
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*/
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#pragma once
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#include <basalt/camera/camera_static_assert.hpp>
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#include <basalt/utils/sophus_utils.hpp>
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namespace basalt {
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using std::sqrt;
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/// @brief Unified camera model
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///
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/// \image html ucm.png
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/// This model has N=5 parameters \f$ \mathbf{i} = \left[f_x, f_y, c_x, c_y,
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/// \alpha \right]^T \f$ with \f$ \alpha \in [0,1] \f$.
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/// See \ref project and \ref unproject functions for more details.
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template <typename Scalar_ = double>
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class UnifiedCamera {
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public:
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using Scalar = Scalar_;
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static constexpr int N = 5; ///< Number of intrinsic parameters.
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using Vec2 = Eigen::Matrix<Scalar, 2, 1>;
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using Vec4 = Eigen::Matrix<Scalar, 4, 1>;
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using VecN = Eigen::Matrix<Scalar, N, 1>;
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using Mat24 = Eigen::Matrix<Scalar, 2, 4>;
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using Mat2N = Eigen::Matrix<Scalar, 2, N>;
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using Mat42 = Eigen::Matrix<Scalar, 4, 2>;
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using Mat4N = Eigen::Matrix<Scalar, 4, N>;
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/// @brief Default constructor with zero intrinsics
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UnifiedCamera() { param_.setZero(); }
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/// @brief Construct camera model with given vector of intrinsics
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///
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/// @param[in] p vector of intrinsic parameters [fx, fy, cx, cy, alpha]
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explicit UnifiedCamera(const VecN& p) { param_ = p; }
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/// @brief Cast to different scalar type
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template <class Scalar2>
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UnifiedCamera<Scalar2> cast() const {
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return UnifiedCamera<Scalar2>(param_.template cast<Scalar2>());
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}
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/// @brief Camera model name
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///
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/// @return "ucm"
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static std::string getName() { return "ucm"; }
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/// @brief Project the point and optionally compute Jacobians
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///
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/// Projection function is defined as follows:
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/// \f{align}{
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/// \pi(\mathbf{x}, \mathbf{i}) &=
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/// \begin{bmatrix}
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/// f_x{\frac{x}{\alpha d + (1-\alpha) z}}
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/// \\ f_y{\frac{y}{\alpha d + (1-\alpha) z}}
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/// \\ \end{bmatrix}
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/// +
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/// \begin{bmatrix}
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/// c_x
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/// \\ c_y
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/// \\ \end{bmatrix},
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/// \\ d &= \sqrt{x^2 + y^2 + z^2}.
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/// \f}
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/// A set of 3D points that results in valid projection is expressed as
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/// follows: \f{align}{
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/// \Omega &= \{\mathbf{x} \in \mathbb{R}^3 ~|~ z > -wd \},
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/// \\ w &= \begin{cases} \frac{\alpha}{1-\alpha}, & \mbox{if } \alpha \le
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/// 0.5,
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/// \\ \frac{1-\alpha}{\alpha} & \mbox{if } \alpha > 0.5, \end{cases} \f}
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///
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/// @param[in] p3d point to project
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/// @param[out] proj result of projection
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/// @param[out] d_proj_d_p3d if not nullptr computed Jacobian of projection
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/// with respect to p3d
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/// @param[out] d_proj_d_param point if not nullptr computed Jacobian of
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/// projection with respect to intrinsic parameters
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/// @return if projection is valid
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template <class DerivedPoint3D, class DerivedPoint2D,
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class DerivedJ3D = std::nullptr_t,
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class DerivedJparam = std::nullptr_t>
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inline bool project(const Eigen::MatrixBase<DerivedPoint3D>& p3d,
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Eigen::MatrixBase<DerivedPoint2D>& proj,
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DerivedJ3D d_proj_d_p3d = nullptr,
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DerivedJparam d_proj_d_param = nullptr) const {
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const typename EvalOrReference<DerivedPoint3D>::Type p3d_eval(p3d);
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const Scalar& fx = param_[0];
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const Scalar& fy = param_[1];
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const Scalar& cx = param_[2];
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const Scalar& cy = param_[3];
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const Scalar& alpha = param_[4];
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const Scalar& x = p3d_eval[0];
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const Scalar& y = p3d_eval[1];
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const Scalar& z = p3d_eval[2];
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const Scalar r2 = x * x + y * y;
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const Scalar rho2 = r2 + z * z;
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const Scalar rho = sqrt(rho2);
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const Scalar norm = alpha * rho + (Scalar(1) - alpha) * z;
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const Scalar mx = x / norm;
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const Scalar my = y / norm;
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proj = Vec2(fx * mx + cx, fy * my + cy);
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// Check if valid
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const Scalar w = alpha > Scalar(0.5) ? (Scalar(1) - alpha) / alpha
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: alpha / (Scalar(1) - alpha);
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const bool is_valid = (z > -w * rho);
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if constexpr (!std::is_same_v<DerivedJ3D, std::nullptr_t>) {
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BASALT_ASSERT(d_proj_d_p3d);
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const Scalar denom = norm * norm * rho;
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const Scalar mid = -(alpha * x * y);
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const Scalar add = norm * rho;
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const Scalar addz = (alpha * z + (Scalar(1) - alpha) * rho);
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d_proj_d_p3d->setZero();
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(*d_proj_d_p3d)(0, 0) = fx * (add - x * x * alpha);
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(*d_proj_d_p3d)(1, 0) = fy * mid;
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(*d_proj_d_p3d)(0, 1) = fx * mid;
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(*d_proj_d_p3d)(1, 1) = fy * (add - y * y * alpha);
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(*d_proj_d_p3d)(0, 2) = -fx * x * addz;
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(*d_proj_d_p3d)(1, 2) = -fy * y * addz;
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(*d_proj_d_p3d) /= denom;
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} else {
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UNUSED(d_proj_d_p3d);
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}
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if constexpr (!std::is_same_v<DerivedJparam, std::nullptr_t>) {
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BASALT_ASSERT(d_proj_d_param);
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const Scalar norm2 = norm * norm;
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(*d_proj_d_param).setZero();
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(*d_proj_d_param)(0, 0) = mx;
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(*d_proj_d_param)(0, 2) = Scalar(1);
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(*d_proj_d_param)(1, 1) = my;
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(*d_proj_d_param)(1, 3) = Scalar(1);
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const Scalar tmp_x = -fx * x / norm2;
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const Scalar tmp_y = -fy * y / norm2;
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const Scalar tmp4 = (rho - z);
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(*d_proj_d_param)(0, 4) = tmp_x * tmp4;
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(*d_proj_d_param)(1, 4) = tmp_y * tmp4;
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} else {
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UNUSED(d_proj_d_param);
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}
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return is_valid;
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}
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/// @brief Unproject the point and optionally compute Jacobians
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///
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/// The unprojection function is computed as follows: \f{align}{
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/// \pi ^ { -1 }(\mathbf{u}, \mathbf{i}) &=
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/// \frac{\xi + \sqrt{1 + (1 - \xi ^ 2) r ^ 2}} {
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/// 1 + r ^ 2
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/// }
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/// \begin{bmatrix} m_x \\ m_y \\ 1 \\ \end{bmatrix} -
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/// \begin {bmatrix} 0 \\ 0 \\ \xi \\ \end{bmatrix},
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/// \\ m_x &= \frac{u - c_x}{f_x}(1-\alpha),
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/// \\ m_y &= \frac{v - c_y}{f_y}(1-\alpha),
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/// \\ r^2 &= m_x^2 + m_y^2,
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/// \\ \xi &= \frac{\alpha}{1-\alpha}.
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/// \f}
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///
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/// The valid range of unprojections is \f{align}{
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/// \Theta &=
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/// \begin{cases}
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/// \mathbb{R}^2 & \mbox{if } \alpha \le 0.5
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/// \\ \{ \mathbf{u} \in \mathbb{R}^2 ~|~ r^2 \le
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/// \frac{(1-\alpha)^2}{2\alpha
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/// - 1} \} & \mbox{if } \alpha > 0.5 \end{cases}
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/// \f}
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///
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/// @param[in] proj point to unproject
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/// @param[out] p3d result of unprojection
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/// @param[out] d_p3d_d_proj if not nullptr computed Jacobian of
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/// unprojection with respect to proj
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/// @param[out] d_p3d_d_param point if not nullptr computed Jacobian of
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/// unprojection with respect to intrinsic parameters
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/// @return if unprojection is valid
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template <class DerivedPoint2D, class DerivedPoint3D,
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class DerivedJ2D = std::nullptr_t,
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class DerivedJparam = std::nullptr_t>
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inline bool unproject(const Eigen::MatrixBase<DerivedPoint2D>& proj,
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Eigen::MatrixBase<DerivedPoint3D>& p3d,
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DerivedJ2D d_p3d_d_proj = nullptr,
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DerivedJparam d_p3d_d_param = nullptr) const {
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checkUnprojectionDerivedTypes<DerivedPoint2D, DerivedPoint3D, DerivedJ2D,
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DerivedJparam, N>();
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const typename EvalOrReference<DerivedPoint2D>::Type proj_eval(proj);
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const Scalar& fx = param_[0];
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const Scalar& fy = param_[1];
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const Scalar& cx = param_[2];
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const Scalar& cy = param_[3];
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const Scalar& alpha = param_[4];
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const Scalar& u = proj_eval[0];
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const Scalar& v = proj_eval[1];
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const Scalar xi = alpha / (Scalar(1) - alpha);
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const Scalar mxx = (u - cx) / fx;
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const Scalar myy = (v - cy) / fy;
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const Scalar mx = (Scalar(1) - alpha) * mxx;
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const Scalar my = (Scalar(1) - alpha) * myy;
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const Scalar r2 = mx * mx + my * my;
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// Check if valid
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const bool is_valid = !static_cast<bool>(
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(alpha > Scalar(0.5)) &&
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(r2 >= Scalar(1) / ((Scalar(2) * alpha - Scalar(1)))));
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const Scalar xi2 = xi * xi;
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const Scalar n = sqrt(Scalar(1) + (Scalar(1) - xi2) * (r2));
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const Scalar m = (Scalar(1) + r2);
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const Scalar k = (xi + n) / m;
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p3d.setZero();
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p3d[0] = k * mx;
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p3d[1] = k * my;
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p3d[2] = k - xi;
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if constexpr (!std::is_same_v<DerivedJ2D, std::nullptr_t> ||
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!std::is_same_v<DerivedJparam, std::nullptr_t>) {
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const Scalar dk_dmx = -Scalar(2) * mx * (n + xi) / (m * m) +
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mx * (Scalar(1) - xi2) / (n * m);
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const Scalar dk_dmy = -Scalar(2) * my * (n + xi) / (m * m) +
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my * (Scalar(1) - xi2) / (n * m);
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constexpr int SIZE_3D = DerivedPoint3D::SizeAtCompileTime;
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Eigen::Matrix<Scalar, SIZE_3D, 1> c0, c1;
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c0.setZero();
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c0(0) = (dk_dmx * mx + k) / fx;
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c0(1) = dk_dmx * my / fx;
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c0(2) = dk_dmx / fx;
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c1.setZero();
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c1(0) = dk_dmy * mx / fy;
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c1(1) = (dk_dmy * my + k) / fy;
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c1(2) = dk_dmy / fy;
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c0 *= (1 - alpha);
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c1 *= (1 - alpha);
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if constexpr (!std::is_same_v<DerivedJ2D, std::nullptr_t>) {
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BASALT_ASSERT(d_p3d_d_proj);
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d_p3d_d_proj->col(0) = c0;
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d_p3d_d_proj->col(1) = c1;
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} else {
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UNUSED(d_p3d_d_proj);
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}
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if constexpr (!std::is_same_v<DerivedJparam, std::nullptr_t>) {
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BASALT_ASSERT(d_p3d_d_param);
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const Scalar d_xi_d_alpha =
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Scalar(1) / ((Scalar(1) - alpha) * (Scalar(1) - alpha));
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const Scalar d_m_d_alpha =
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-Scalar(2) * (Scalar(1) - alpha) * (mxx * mxx + myy * myy);
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const Scalar d_n_d_alpha = -(mxx * mxx + myy * myy) / n;
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const Scalar dk_d_alpha =
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((d_xi_d_alpha + d_n_d_alpha) * m - d_m_d_alpha * (xi + n)) /
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(m * m);
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d_p3d_d_param->setZero();
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d_p3d_d_param->col(0) = -mxx * c0;
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d_p3d_d_param->col(1) = -myy * c1;
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d_p3d_d_param->col(2) = -c0;
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d_p3d_d_param->col(3) = -c1;
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(*d_p3d_d_param)(0, 4) = dk_d_alpha * mx - k * mxx;
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(*d_p3d_d_param)(1, 4) = dk_d_alpha * my - k * myy;
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(*d_p3d_d_param)(2, 4) = dk_d_alpha - d_xi_d_alpha;
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} else {
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UNUSED(d_p3d_d_param);
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}
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} else {
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UNUSED(d_p3d_d_proj);
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UNUSED(d_p3d_d_param);
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}
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return is_valid;
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}
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/// @brief Set parameters from initialization
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///
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/// Initializes the camera model to \f$ \left[f_x, f_y, c_x, c_y, 0.5,
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/// \right]^T \f$
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///
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/// @param[in] init vector [fx, fy, cx, cy]
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inline void setFromInit(const Vec4& init) {
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param_[0] = init[0];
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param_[1] = init[1];
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param_[2] = init[2];
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param_[3] = init[3];
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param_[4] = 0.5;
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}
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/// @brief Increment intrinsic parameters by inc and clamp the values to the
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/// valid range
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///
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/// @param[in] inc increment vector
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void operator+=(const VecN& inc) {
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param_ += inc;
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// alpha in [0, 1]
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param_[4] = std::clamp(param_[4], Scalar(0), Scalar(1));
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}
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/// @brief Returns a const reference to the intrinsic parameters vector
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///
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/// The order is following: \f$ \left[f_x, f_y, c_x, c_y, \xi, \alpha
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/// \right]^T \f$
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/// @return const reference to the intrinsic parameters vector
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const VecN& getParam() const { return param_; }
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/// @brief Projections used for unit-tests
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static Eigen::aligned_vector<UnifiedCamera> getTestProjections() {
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Eigen::aligned_vector<UnifiedCamera> res;
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VecN vec1;
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// Euroc
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vec1 << 460.76484651566468, 459.4051018049483, 365.8937161309615,
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249.33499869752445, 0.5903365915227143;
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res.emplace_back(vec1);
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// TUM VI 512
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vec1 << 191.14799816648748, 191.13150946585135, 254.95857715233118,
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256.8815466235898, 0.6291060871161842;
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res.emplace_back(vec1);
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return res;
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}
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/// @brief Resolutions used for unit-tests
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static Eigen::aligned_vector<Eigen::Vector2i> getTestResolutions() {
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Eigen::aligned_vector<Eigen::Vector2i> res;
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res.emplace_back(752, 480);
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res.emplace_back(512, 512);
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return res;
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}
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW
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private:
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VecN param_;
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};
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} // namespace basalt
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