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.. _chapter-introduction:
============
Introduction
============
Solving nonlinear least squares problems [#f1]_ comes up in a broad
range of areas across science and engineering - from fitting curves in
statistics, to constructing 3D models from photographs in computer
vision. Ceres Solver [#f2]_ [#f3]_ is a portable C++ library for
solving non-linear least squares problems accurately and efficiently.
**Features**
#. A friendly :ref:`chapter-modeling` API.
#. Automatic and numeric differentiation.
#. Robust loss functions and local parameterizations.
#. Multithreading.
#. Trust-Region (Levenberg-Marquardt and Dogleg) and Line Search
(Nonlinear CG and L-BFGS) solvers.
#. Variety of linear solvers.
a. Dense QR and Cholesky factorization (using `Eigen
<http://eigen.tuxfamily.org/index.php?title=Main_Page>`_) for
small problems.
b. Sparse Cholesky factorization (using `SuiteSparse
<http://www.cise.ufl.edu/research/sparse/SuiteSparse/>`_ and
`CXSparse <http://www.cise.ufl.edu/research/sparse/CSparse/>`_) for
large sparse problems.
c. Specialized solvers for bundle adjustment problems in computer
vision.
d. Iterative linear solvers with preconditioners for general sparse
and bundle adjustment problems.
#. Portable: Runs on Linux, Windows, Mac OS X and Android.
At Google, Ceres Solver has been used for solving a variety of
problems in computer vision and machine learning. e.g., it is used to
to estimate the pose of Street View cars, aircrafts, and satellites;
to build 3D models for PhotoTours; to estimate satellite image sensor
characteristics, and more.
`Blender <http://www.blender.org>`_ uses Ceres for `motion tracking
<http://mango.blender.org/development/planar-tracking-preview/>`_ and
`bundle adjustment
<http://wiki.blender.org/index.php/Dev:Ref/Release_Notes/2.67/Motion_Tracker>`_.
.. rubric:: Footnotes
.. [#f1] For a gentle but brief introduction to non-linear least
squares problems, please start by reading the
:ref:`chapter-tutorial`.
.. [#f2] While there is some debate as to who invented the method of
Least Squares [Stigler]_, there is no debate that it was
`Carl Friedrich Gauss
<http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss>`_ who
brought it to the attention of the world. Using just 22
observations of the newly discovered asteroid `Ceres
<http://en.wikipedia.org/wiki/Ceres_(dwarf_planet)>`_, Gauss
used the method of least squares to correctly predict when
and where the asteroid will emerge from behind the Sun
[TenenbaumDirector]_. We named our solver after Ceres to
celebrate this seminal event in the history of astronomy,
statistics and optimization.
.. [#f3] For brevity, in the rest of this document we will just use
the term Ceres.
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