Parametric Segmentation
Short description
This segmentation method relies on a parametric representation of the object contour.
The solution is expressed as the minimizer of an energy which general form is a linear combination
of a line integral along the contour, a domain integral on the contour interior, and a domain
integral on the contour exterior. The energy is therefore a function of the parameters
defining the contour, e.g., center and radius for a circle.
![\mathcal E(\Gamma = \Gamma(x,y,r))
=
\alpha
\oint_\Gamma
v_c(\Gamma, s)
\ \mbox ds
\ \dots
\left\{
\begin{array}{@{}l@{}l@{}l@{}l@{}}
\ +\ \beta_1 &
\displaystyle
\ \int_{D(\Gamma)} &
v_{r_1}(D(\Gamma), u,v) &
\ \mbox du
\mbox dv
\\[2em]
\ +\ \beta_2 &
\displaystyle
\ \int_{\bar D(\Gamma)} &
v_{r_2}(\bar D(\Gamma), u,v) &
\ \mbox du
\mbox dv
\end{array}
\right.](image/segmentation/energy.png)
The solution is computed with a gradient descent, noting that the energy gradient
with respect to the contour parameters writes as a chain rule with
the parameter-related contour deformation fields and
the shape derivative of the energy (see ICIP 2006 on the page
Conferences for complete reference and preprint).
Illustrative result
The picture below used to illustrate the method was downloaded from
WikipediA,
The Free Encyclopedia. It was taken by Lee R. Berger at Palau, Micronesia,
and shows a stingless jellyfish. The original picture and its licensing information
can be found at:
http://en.wikipedia.org/wiki/File:Palau_stingless_jellyfish.jpg
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