Finite-element methods for active contour models and balloons for2-D and 3-D images
Cohen, L.D.
Cohen, I.
CEREMADE, Paris IX Univ.;
This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Nov 1993
Volume: 15,
Issue: 11
On page(s): 1131-1147
ISSN: 0162-8828
References Cited: 36
CODEN: ITPIDJ
INSPEC Accession Number: 4580746
Digital Object Identifier: 10.1109/34.244675
Current Version Published: 2002-08-06
Abstract
The use of energy-minimizing curves, known as “snakes”
to extract features of interest in images has been introduced by Kass,
Witkin and Terzopoulos (1987). A balloon model was introduced by Cohen
(1991) as a way to generalize and solve some of the problems encountered
with the original method. A 3-D generalization of the balloon model as a
3-D deformable surface, which evolves in 3-D images, is presented. It is
deformed under the action of internal and external forces attracting the
surface toward detected edgels by means of an attraction potential. We
also show properties of energy-minimizing surfaces concerning their
relationship with 3-D edge points. To solve the minimization problem for
a surface, two simplified approaches are shown first, defining a 3-D
surface as a series of 2-D planar curves. Then, after comparing
finite-element method and finite-difference method in the 2-D problem,
we solve the 3-D model using the finite-element method yielding greater
stability and faster convergence. This model is applied for segmenting
magnetic resonance images
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