Appl Math Optim 55:127–144 (2007)
2007 Springer Science+Business Media, Inc.
A New Implicit Method for Surface Segmentation
by Minimal Paths in 3D Images
Laurent D. Cohen,
and Anthony Yezzi
51 rue Carnot, 92156 Suresnes, France
CEREMADE-Universit´e Paris Dauphine,
Place du Mar´echal de Lattre de Tassigny, 75775 Paris Cedex 16, France
Georgia Institute of Technology,
Atlanta, GA 30322, USA
Abstract. We introduce a novel implicit approach for single-object segmentation
in 3D images. The boundary surface of this object is assumed to contain two known
curves (the constraining curves), given by an expert. The aim of our method is to
ﬁnd the wanted surface by exploiting as much as possible the information given in
the supplied curves and in the image. As for active surfaces, we use a cost potential
that penalizes image regions of low interest (most likely areas of low gradient or too
far from the surface to be extracted). In order to avoid local minima, we introduce a
new partial differential equation and use its solution for segmentation. We show that
the zero level set of this solution contains the constraining curves as well as a set
of paths joining them. We present a fast implementation that has been successfully
applied to 3D medical and synthetic images.
Key Words. Image segmentation, Active contours, Minimal paths, Level set
method, Stationary transport equation.
AMS Classiﬁcation. 68U10, 92C55, 35Q80, 49L25, 74G65.
The common use of deformable models, introduced by Kass et al. , in 2D and 3D image
segmentation consists of introducing an initial object in the image and deforming it until