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Sameer Agarwal
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1. Unused variable warnings and fixes. 2. Minor documentation update. Change-Id: I815588a5806df1030a7c8750f4fb594c503f8998
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2.7 KiB
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80 lines
2.7 KiB
ReStructuredText
.. _chapter-introduction:
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============
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Introduction
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============
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Solving nonlinear least squares problems [#f1]_ comes up in a broad
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range of areas across science and engineering - from fitting curves in
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statistics, to constructing 3D models from photographs in computer
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vision. Ceres Solver [#f2]_ [#f3]_ is a portable C++ library for
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solving non-linear least squares problems. It is designed to solve
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small and large sparse problems accurately and efficiently.
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At Google, Ceres Solver has been used for solving a variety of
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problems in computer vision and machine learning. e.g., it is used to
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to estimate the pose of Street View cars, aircrafts, and satellites;
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to build 3D models for PhotoTours; to estimate satellite image sensor
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characteristics, and more.
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Features:
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#. A friendly :ref:`chapter-modeling`.
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#. Automatic and numeric differentiation.
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#. Robust loss functions and local parameterizations.
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#. Multithreading.
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#. Trust-Region (Levenberg-Marquardt and Dogleg) and Line Search
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(Nonlinear CG and L-BFGS) solvers.
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#. Variety of linear solvers.
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a. Dense QR and Cholesky factorization (using `Eigen
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<http://eigen.tuxfamily.org/index.php?title=Main_Page>`_) for
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small problems.
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b. Sparse Cholesky factorization (using `SuiteSparse
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<http://www.cise.ufl.edu/research/sparse/SuiteSparse/>`_ and
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`CXSparse <http://www.cise.ufl.edu/research/sparse/CSparse/>`_) for
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large sparse problems.
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c. Specialized solvers for bundle adjustment problems in computer
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vision.
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d. Iterative linear solvers with perconditioners for general sparse
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and bundle adjustment problems.
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#. Portable: Runs on Linux, Windows, Mac OS X and Android. An iOS port is
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underway.
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.. rubric:: Footnotes
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.. [#f1] For a gentle but brief introduction to non-linear least
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squares problems, please start by reading the
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:ref:`chapter-tutorial`.
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.. [#f2] While there is some debate as to who invented the method of
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Least Squares [Stigler]_, there is no debate that it was
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`Carl Friedrich Gauss
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<http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss>`_ who
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brought it to the attention of the world. Using just 22
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observations of the newly discovered asteroid `Ceres
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<http://en.wikipedia.org/wiki/Ceres_(dwarf_planet)>`_, Gauss
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used the method of least squares to correctly predict when
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and where the asteroid will emerge from behind the Sun
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[TenenbaumDirector]_. We named our solver after Ceres to
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celebrate this seminal event in the history of astronomy,
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statistics and optimization.
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.. [#f3] For brevity, in the rest of this document we will just use
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the term Ceres.
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