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Topologically adaptable snakes, or simply Tsnakes, are
a standard tool for automatically identifying multiple segments
in an image. This work introduces a novel approach
for controlling the topology of a Tsnake. It focuses on the
loops formed by the socalled projected curve which is obtained
at every stage of the snake evolution. The idea is to
make that curve the image of a piecewise linear mapping
of an adequate class. Then, with the help of an additional
structure—the LoopTree—it is possible to decide in O(1)
time whether the region enclosed by each loop has already
been explored by the snake. This makes it possible to construct
an enhanced algorithm for evolving Tsnakes whose
performance is assessed by means of statistics and examples.
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