of the object using quadratic spline function. There are a couple of advantages
of this representation. First, this representation enforces the smoothness
inherent in the object contour. Second, this turns out to be more robust
to measurement noise than edge-based representation, and it reduces the
dimensionality considerably.
However, the control point representation(Q) is not simple enough
to maintain over time since the number of control points( 
) is quite big for the most of objects. Also, it allows for the arbitrary
deformation of the contour , which does not happen for any real object.
There exists a more compact representation of an object contour, which
has lower dimensio and allows for only meaningful deformation. This representation
of an object contour is called ``shape-space'' representation, and can
obtained from the following equation.
where 
, W, 
and 
are defined as in the previous section.
is usually drawn by hand, and W can be obtained from
considering possible motion model of the contour. In this report, the affine
model is used and, thus, the dimensionality of the shape-space vector
is only six. The details about this representation is well explained in
[2] .
