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Diffstat (limited to 'extern/ceres/internal/ceres/corrector.cc')
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diff --git a/extern/ceres/internal/ceres/corrector.cc b/extern/ceres/internal/ceres/corrector.cc new file mode 100644 index 00000000000..720182868c1 --- /dev/null +++ b/extern/ceres/internal/ceres/corrector.cc @@ -0,0 +1,158 @@ +// Ceres Solver - A fast non-linear least squares minimizer +// Copyright 2015 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: sameeragarwal@google.com (Sameer Agarwal) + +#include "ceres/corrector.h" + +#include <cstddef> +#include <cmath> +#include "ceres/internal/eigen.h" +#include "glog/logging.h" + +namespace ceres { +namespace internal { + +Corrector::Corrector(const double sq_norm, const double rho[3]) { + CHECK_GE(sq_norm, 0.0); + sqrt_rho1_ = sqrt(rho[1]); + + // If sq_norm = 0.0, the correction becomes trivial, the residual + // and the jacobian are scaled by the squareroot of the derivative + // of rho. Handling this case explicitly avoids the divide by zero + // error that would occur below. + // + // The case where rho'' < 0 also gets special handling. Technically + // it shouldn't, and the computation of the scaling should proceed + // as below, however we found in experiments that applying the + // curvature correction when rho'' < 0, which is the case when we + // are in the outlier region slows down the convergence of the + // algorithm significantly. + // + // Thus, we have divided the action of the robustifier into two + // parts. In the inliner region, we do the full second order + // correction which re-wights the gradient of the function by the + // square root of the derivative of rho, and the Gauss-Newton + // Hessian gets both the scaling and the rank-1 curvature + // correction. Normaly, alpha is upper bounded by one, but with this + // change, alpha is bounded above by zero. + // + // Empirically we have observed that the full Triggs correction and + // the clamped correction both start out as very good approximations + // to the loss function when we are in the convex part of the + // function, but as the function starts transitioning from convex to + // concave, the Triggs approximation diverges more and more and + // ultimately becomes linear. The clamped Triggs model however + // remains quadratic. + // + // The reason why the Triggs approximation becomes so poor is + // because the curvature correction that it applies to the gauss + // newton hessian goes from being a full rank correction to a rank + // deficient correction making the inversion of the Hessian fraught + // with all sorts of misery and suffering. + // + // The clamped correction retains its quadratic nature and inverting it + // is always well formed. + if ((sq_norm == 0.0) || (rho[2] <= 0.0)) { + residual_scaling_ = sqrt_rho1_; + alpha_sq_norm_ = 0.0; + return; + } + + // We now require that the first derivative of the loss function be + // positive only if the second derivative is positive. This is + // because when the second derivative is non-positive, we do not use + // the second order correction suggested by BANS and instead use a + // simpler first order strategy which does not use a division by the + // gradient of the loss function. + CHECK_GT(rho[1], 0.0); + + // Calculate the smaller of the two solutions to the equation + // + // 0.5 * alpha^2 - alpha - rho'' / rho' * z'z = 0. + // + // Start by calculating the discriminant D. + const double D = 1.0 + 2.0 * sq_norm * rho[2] / rho[1]; + + // Since both rho[1] and rho[2] are guaranteed to be positive at + // this point, we know that D > 1.0. + + const double alpha = 1.0 - sqrt(D); + + // Calculate the constants needed by the correction routines. + residual_scaling_ = sqrt_rho1_ / (1 - alpha); + alpha_sq_norm_ = alpha / sq_norm; +} + +void Corrector::CorrectResiduals(const int num_rows, double* residuals) { + DCHECK(residuals != NULL); + // Equation 11 in BANS. + VectorRef(residuals, num_rows) *= residual_scaling_; +} + +void Corrector::CorrectJacobian(const int num_rows, + const int num_cols, + double* residuals, + double* jacobian) { + DCHECK(residuals != NULL); + DCHECK(jacobian != NULL); + + // The common case (rho[2] <= 0). + if (alpha_sq_norm_ == 0.0) { + VectorRef(jacobian, num_rows * num_cols) *= sqrt_rho1_; + return; + } + + // Equation 11 in BANS. + // + // J = sqrt(rho) * (J - alpha^2 r * r' J) + // + // In days gone by this loop used to be a single Eigen expression of + // the form + // + // J = sqrt_rho1_ * (J - alpha_sq_norm_ * r* (r.transpose() * J)); + // + // Which turns out to about 17x slower on bal problems. The reason + // is that Eigen is unable to figure out that this expression can be + // evaluated columnwise and ends up creating a temporary. + for (int c = 0; c < num_cols; ++c) { + double r_transpose_j = 0.0; + for (int r = 0; r < num_rows; ++r) { + r_transpose_j += jacobian[r * num_cols + c] * residuals[r]; + } + + for (int r = 0; r < num_rows; ++r) { + jacobian[r * num_cols + c] = sqrt_rho1_ * + (jacobian[r * num_cols + c] - + alpha_sq_norm_ * residuals[r] * r_transpose_j); + } + } +} + +} // namespace internal +} // namespace ceres |