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Snake Tracking
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We use B-spline snakes [3][7]
to represent image tag lines. The
spline is given by the following expression:
where 
is a column vector of powers of 
, the spline
parameter,
is a sequence of control points, and 
is a matrix which blends the control points.
The approach is to minimize the following expression
along tags:
In equation (6), the first term maximizes
along the length of the snake, and second
and third terms attract the snake to the endpoint
of tag lines.
The discrete form of 
, for a quadric
spline may be written as:
where 
are the B-spline control points. Dynamic
Programming (DP) [1] may be
used to optimize the curve in the control
point space to minimize 
using the following
recurrence
for 
, and
.
In general, for an order 
B-spline,
is a function of control points. Also,
note that the minimization yields the optimal
open spline, as is the case for a tag line.
In order to find a closed snake,
one performs 
applications of the above recurrence,
where is the number of possible choices for
the endpoint , and for each optimization fixing
the end point to be one of the choices,
repeating for all possibilities,
and finally choosing the minimum.
Figure 2 shows the initial star-burst
image and results from the DP
algorithm. Figure 3 shows the energy field
for a diagonal tag line, and for one endpoint of
the same tag line.