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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.
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