I am currently investigating a process represented by a time series of
arrays (each of size m X 2n) of intensity values.  During the process,
a cluster of high-intensity values in the center of the array moves
towards the edge of the array.  When the edge of the high-intensity
cluster reaches the edge of the array, this is the signal for the
process to end.


What I would like to know is, how do I determine the least number of
units in the array that are needed to faithfully track the movement of
the cluster of high intensity values?  For example, could I delete
every other column of the arrays (now of size mXn) and still be able to track
the progression of the mass towards the edge of the array?  And what’s
the best way to quantify the “goodness” of the tracking?  I think the
calls for a sensitivity analysis (with number of intensity values as a
parameter), but my experience with this, and the sites that I have
found on the web deal mostly with linear programming models, not
images.  Any suggestions?

Hello Noisy,

The short answer to your first question is "it depends". The primary
factor is the contrast between the object and the background. A major
secondary effect is the amount of noise present in the image. Let me
use a few web sites that have some illustrations to describe what can
and cannot be done.

  http://www.cs.bris.ac.uk/~majid/Research/SmallObj/
Titled "Detection and Tracking of Very Small Low Constrast Objects",
they describe the problems with FLIR (Forward Looking Infrared) and
include images showing the original images as well as the effects of
the tracking algorithm used to track a high speed airplane and cars on
a road. In addition to the movies, there are references to other
papers with additional information.

  http://vision.stanford.edu/~birch/klt/
Titled "KLT: An Implementation of the Kanade-Lucas-Tomasi Feature
Tracker" this site has source code and documentation for a software
library that can track a number of features in an object. On the page
above, they mention that 2x2 gradient matricies are used - this would
imply that very small features can be tracked with this method (with
enough contrast).

  http://www.fmrib.ox.ac.uk/~steve/review/review/node5.html
Titled "Image Segmentation and Object Tracking", this brings you to a
series of pages that describe a number of different methods. On the
fourth page, it describes methods used to track objects that are a
single pixel in size, even in noisy images.

So, to recap the initial answer - your results will depend on the
quality of the image. There are a number of different methods that
have a number of performance characteristics. That kind of answer
would also address your second question (decimation of the image) - if
the contrast is sufficient, you would have no problems with using
every other pixel of the image.

To look at measuring the quality of the tracking - these same sites
generally address that relative to an independent reference (usually
human perception). This may imply you need to use more than one
algorithm and look at the relative error between the tracking results
to determine the "goodness" automatically. The Intel report I refer to
below touches on this as well - comparing their results with
commercial products.

A few other sites that may be helpful:

A page providing links to a number of computer vision sites.
  http://www-2.cs.cmu.edu/~cil/v-source.html

A report on head tracking at Intel, describes methods used to operate
in the presence of noise or "distractors".
  http://www.intel.com/technology/itj/q21998/articles/art_2g.htm

To find additional resources, try search phrases such as:
  image tracking "object size"
  image tracking object source code
As I was searching, I also found some sites that appeared to have good
demonstration programs, but I can't tell for sure which ones are
appropriate. Please use the clarification request if you want those
listed or add some more detail on your application so I can more
properly focus the answer.

Another suggestion I might make - consider an "area of interest" once
the cluster is located. Do more processing in the area where the
cluster was seen in the last frame (in lieu of processing the entire
image). This is touched on briefly in the first paper - it suggests
using variable optics to improve the resolution of the image to make
detection and tracking easier.

  --Maniac