@article{1073.68095,
author="Hinterm\"uller, Michael and Ring, Wolfgang",
title="{A second order shape optimization approach for image segmentation.}",
language="English",
journal="SIAM J. Appl. Math. ",
volume="64",
number="2",
pages="442-467",
year="2003",
doi={10.1137/S0036139902403901},
abstract="{Summary: The problem of segmentation of a given image using the
    active contour technique is considered. An abstract calculus to find
    appropriate speed functions for active contour models in image segmentation
    or related problems based on variational principles is presented. The speed
    method from shape sensitivity analysis is used to derive speed functions
    which correspond to gradient or Newton-type directions for the underlying
    optimization problem. The Newton-type speed function is found by solving an
    elliptic problem on the current active contour in every time step. Numerical
    experiments comparing the classical gradient method with Newton's method are
    presented.}",
keywords="{segmentation; active contours; level set method; shape sensitivity
    analysis; Newton's method}",
classmath="{*68U10 (Image processing)
49Q10 (Optimization of the shape other than minimal surfaces)
49Q12 (Sensitivity analysis)
65K05 (Mathematical programming (numerical methods))
}",
}