Because the confidence measure that we use for selecting feature windows is  based  on  potential tracking  performance,  it  is  necessary   to  formalize the motion of an object that is computed by the tracking module.  The projection  of a moving object is modeled through perspective projection with focal length       /:'        This        model        projects      points p (t) —— (x$(I),y$(I), z,(t)) from the scene (reference frame   fi,   attached   to   the   camera)   to    points p,(/) —— (.ri ( ), i( )) in an image reference frame according   to  the  equation:

                                                              (4)

The scale factors c4 and cz account for pixel size and sampling. In this equation, «6 and c7 account for any displacement of the image reference frame with respect  to the optical axis.

If we suppose that the camera moves with a translational velocity T and a rotational velocity R with respect to a static environment, then we can use the following equation to describe the change in object coordinates with respect to the reference frame

  ——T — R ›‹ p$

The success of the tracking module will be based upon  the ability  to locate correctly:

which corresponds to the point that was previously at p,(/).    In   order   to   provide   enough   contrast   for

tracking, we use a window  of intensities  ID'  around a  point  p VG   We  assume  that  a  feature  window’s

intensity values remain relatively constant over the duration of their use. If  we assume that  p,(i + l) can be found within a neighborhood N$ (t) around p,(i), then we can locate it with a  matching-based technique known as the Sum-of-Squared Differences (SSD)."  The SSD algorithm selects the displacement

The assumption that the point can be found  within a neighborhood has  important  implications  when one considers issues relevant  to visual  tracking.

tracking.  Many  different  types  of  confidence mea-

sures are obtained through the use of an auto- correlation  algorithm.   15  auto-correlation  assumes

the image to be stationary (I  (x,y, t  l) = I,(a, y,  /)) and applies the SSD measure [Eq. (8)) to form a candidate feature window’s  auto-correlation  surface:

with  a  minimum  at  the origin.

Several possible confidence  measures  can  be applied to the surface in Eg. (9) to measure the suitability of a candidate feature  window.  A particularly robust confidence measure is a two- dimensional parabolic fit.  This  measure  takes advantage of the fact that better candidate feature windows will have auto-correlation surfaces that are paraboloids with steep surfaces on all sides.' The parabola s (X,) = cgA2 + 6» * < io ›S fitted to a candidate’s auto-correlation surface in each of four predefined orientations. Since better features have steeper auto-correlation sides all around, the con- fidence  measure   is  defined   as  the  minimum   of the

four  values  Clf  the  6’g  cCIe$JJcief1t.  The   CllRdidllte feature windows with the largest confidence measures are selected.