From e47d87fdd6fbedfe6290223fb81587d1f81f5a31 Mon Sep 17 00:00:00 2001 From: Sameer Agarwal Date: Fri, 24 Sep 2021 05:02:40 -0700 Subject: [PATCH] Add a note about Trigg's correction Add a pointer about how the theory and practice of Trigg's correction for loss function differs when the second derivative of the loss function becomes positive. https://github.com/ceres-solver/ceres-solver/issues/573 Change-Id: Ic22ce91cc230f7ed7fa7b70a1cc2050919039828 --- docs/source/nnls_modeling.rst | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/docs/source/nnls_modeling.rst b/docs/source/nnls_modeling.rst index 9f62aa659..cac3d1cb4 100644 --- a/docs/source/nnls_modeling.rst +++ b/docs/source/nnls_modeling.rst @@ -1154,7 +1154,6 @@ the case, then its possible to re-weight the residual and the Jacobian matrix such that the robustified Gauss-Newton step corresponds to an ordinary linear least squares problem. - Let :math:`\alpha` be a root of .. math:: \frac{1}{2}\alpha^2 - \alpha - \frac{\rho''}{\rho'}\|f(x)\|^2 = 0. @@ -1178,6 +1177,11 @@ least squares algorithm to robustified non-linear least squares problems. +While the theory described above is elegant, in practice we observe +that using the Triggs correction when :math:`\rho'' > 0` leads to poor +performance, so we upper bound it by zero. For more details see +`corrector.cc `_ + :class:`LocalParameterization` ==============================