Refactor the landing page to be a bit more compact.

Also minor changes to the introduction.

Change-Id: Iaa71f576b95c869f075d6837dbb60ba4bb608ee7

docs/source/index.rst

@@ -23,36 +23,28 @@ Ceres Solver
    bibliography
    license
 
-Solving `nonlinear least squares`_ problems 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 is an industrial-grade C++ library for modeling and
+solving `nonlinear least squares`_ problems. These problems 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 features an integrated modeling layer with automatic
+differentiation (you can also use numeric and/or analytic
+derivatives), well optimized code with extensive tests and state of
+the art performance on a variety of problems.
+
+Ceres Solver is used in Google `Street View`_, Google `PhotoTours`_,
+Google `PhotoSphere`_, `Project Tango`_, `Blender`_, and more.
 
 .. _nonlinear least squares: http://en.wikipedia.org/wiki/Non-linear_least_squares
 .. _fitting curves: http://en.wikipedia.org/wiki/Nonlinear_regression
 .. _3D models from photographs: http://en.wikipedia.org/wiki/Structure_from_motion
-
-What is Ceres Solver?
----------------------
-Ceres is an industrial-grade C++ library for modeling and solving large and
-small nonlinear least squares problems of the form
-
-.. math:: \frac{1}{2}\sum_{i} \rho_i\left(\left\|f_i\left(x_{i_1}, ... ,x_{i_k}\right)\right\|^2\right).
-
-For a brief introduction to nonlinear solving in general, see the
-:ref:`chapter-tutorial`.
-
-Who uses Ceres Solver?
-----------------------
-There are many users of Ceres, including Google Street View, Google Maps,
-several SLAM pipelines, Blender, and more. See the :ref:`chapter-introduction`
-for more users.
-
-Why use Ceres Solver?
----------------------
-Ceres is a world-class least squares solver for a variety of reasons, including
-an integrated modelling layer, automatic differentiation, optimized code,
-extensive tests, and more. See the :ref:`chapter-introduction` for a detailed
-list.
+.. _Street View: http://youtu.be/z00ORu4bU-A
+.. _PhotoTours: http://google-latlong.blogspot.com/2012/04/visit-global-landmarks-with-photo-tours.html
+.. _PhotoSphere: http://www.google.com/maps/about/contribute/photosphere/
+.. _Project Tango: https://www.google.com/atap/projecttango/
+.. _Blender: http://mango.blender.org/development/planar-tracking-preview/
 
 Getting started
 ---------------
@@ -67,18 +59,17 @@ Getting started
 
        git clone https://ceres-solver.googlesource.com/ceres-solver
 
-* Read the :ref:`chapter-tutorial`
-* Browse the :ref:`chapter-modeling` and :ref:`chapter-solving`.
+* Read the :ref:`chapter-tutorial`, browse :ref:`chapter-modeling` and :ref:`chapter-solving`.
 * Join the `mailing list
   <https://groups.google.com/forum/?fromgroups#!forum/ceres-solver>`_
   and ask questions.
 * File bugs, feature requests in the `issue tracker
   <https://code.google.com/p/ceres-solver/issues/list>`_.
-* Improve Ceres by :ref:`chapter-contributing`
+
 
 Cite Us
 -------
-If you use Ceres Solver for a publication, you must cite it as::
+If you use Ceres Solver for a publication, please cite it as::
 
     @misc{ceres-solver,
       author = "Sameer Agarwal and Keir Mierle and Others",