Validation
==========

Single Particle Bounce
----------------------

For a very simple test case, a series of synthetic images were constructed of
a single particle bouncing. The X velocity is fixed at :math:`5 pixels/frame`
and the Y velocity is initially set at :math:`10 pixels/frame`. An acceleration
of :math:`4 pixels/frame^2` is applied in the Y direction. When the particle
collides with the walls, 85% of the Y velocity is retained.

This set of images was tracked using the :ref:`poly_projection_ref` with the
default settings and no velocity filters. The particle center was found by using
the `Label` method.

.. image:: images/single_bounce.gif
    :align: center

Almost all of the particle positions are found and included in tracks except for
some of the positions at the wall as well as at the top of the arcs. At the
walls, the true particle centers are not found because the particles are being
clipped. At the top of the arcs, the default search radius is to small.

.. image:: images/single_bounce_position.png
    :align: center

Overall, the `True` and `Tracked` velocities compare very well. However there
are some discrepancies due to the missed particle centers.

.. image:: images/single_bounce_velocity_dist.png
    :align: center


SSCP July 17, 2012, 4Umf Run 1
------------------------------

The small scale challenge problem (SSCP) 4Umf Run 1 video (resolution of
1280x800, 21,090 frames) was processed on a Dell Precision 9710 with an Intel
Xeon E5-2667 v4 running at 3.2GHz with 32 cores and 188.7GB of RAM, running
CentOS7. Using 15 workers and multiprocessing, the video was processed in
33 minutes. 42,001,791 individual velocity measurements were recorded.

Comparing to the previous work performed by Gopalan et al. as part of the SSCP
:cite:`GOPALAN2016299`:

+-----------------------+------------+------------+
| Value                 | Tracker    | Gopalan    |
+=======================+============+============+
| Velocity measurements | 41,356,169 | 34,479,966 |
+-----------------------+------------+------------+
| Mean X Velocity       | -0.0042    | -0.0060    |
+-----------------------+------------+------------+
| Mean Y Velocity       | -0.1299    | -0.1457    |
+-----------------------+------------+------------+
| Mean Magnitude        | 0.4589     | 0.4704     |
+-----------------------+------------+------------+

Comparing the velocity distributions of the X velocity, Y velocity, and
magnitude between the two techniques shows good agreement in the X velocity.
However, the results of Gopalan show a bi-model distribution in the Y velocity
and consequently a bi-model distribution in the magnitude.

.. image:: images/17_Jul_4umf_dist.png
    :align: center

Comparing the centers between to two codes for the first 20 frames shows that
both codes track the same particles. Tracker does seem to find more particles,
especially ones that are further back in the bed.

.. image:: images/17_Jul_4umf_frame.png
    :align: center

Comparing the binned and averaged velocities, both codes show the same structure
with the two vortices.

.. image:: images/17_Jul_4umf_quiver.png
    :align: center

.. bibliography:: refs.bib