Three-Dimensional Pose Estimation and Segmentation Methods - 3D Computer Vision: Efficient Methods and Applications - page 96

improvements of the original snake algorithm have been proposed, such as 'bal-
loon snakes' (Cohen, 1991 ), 'ziplock snakes' (Neuenschwander et al., 1997 ), 'gra-
dient vector field snakes' (Xu and Prince, 1998 ), and implicit active contour models
(Caselles et al., 1995 , 1997 ; Sethian, 1999 ).
In the balloon snake approach of Cohen ( 1991 ), the adaptation of the curve to
intensity gradients in the image is based on an 'inflation force', which increases the
robustness of the contour adaptation in the presence of small edge segments which
do not correspond to the true object border. The ziplock snake algorithm of Neuen-
schwander et al. ( 1997 ) is described in Sect. 2.2.2 . Xu and Prince ( 1998 ) adapt a
contour to the intensity gradients in the image based on a 'generalised gradient vec-
tor field'. In their approach, the process of the adaptation of the curve to the image
is described by a set of partial differential equations modelling a force exerted on
the contour, which decreases smoothly with increasing distance from an intensity
gradient. In the approach by Caselles et al. ( 1997 ), the contour adaptation process is
performed in a Riemannian space with a metric defined according to the image in-
tensities. The contour adaptation thus corresponds to the minimisation of the length
of a curve in that space, leading to a set of partial differential equations describing
the adaptation of the curve to the image.
In many medical imaging applications, volumetric data need to be analysed, lead-
ing to the three-dimensional extension of the snake approach by Cohen and Cohen
( 1993 ). For pose estimation of non-rigid objects from multiple images, it is as-
sumed by most approaches that the non-rigid object is adequately described by a
one-dimensional curve in three-dimensional space. Such techniques are primarily
useful for applications in medical imaging, e.g. for the extraction of blood vessels
from a set of angiographies (Cañero et al., 2000 ) or for the inspection of bonding
wires on microchips (Ye et al., 2001 ). A related method for extracting the three-
dimensional pose of non-rigid objects such as tubes and cables from stereo image
pairs of the scene based on three-dimensional ribbon snakes is described in detail
later in this section.
For the segmentation of synthetic aperture radar images, which typically dis-
play strong noise, Gambini et al. ( 2004 ) adapt B-spline curves to the fractal di-
mension map extracted from the image, where gradients of the inferred frac-
tal dimension are assumed to correspond to the borders of contiguous image re-
gions.
Mongkolnam et al. ( 2006 ) perform a colour segmentation of the image in a
first step and then adapt B-spline curves to the resulting image regions. The bor-
der points extracted by the colour segmentation step do not have to lie on the
adapted curve, such that the approach yields smooth borders of the extracted re-
gions.
Another approach to two-dimensional curve fitting is the contracting curve den-
sity (CCD) algorithm introduced by Hanek and Beetz ( 2004 ). The CCD algorithm
employs a likelihood function as a quantitative measure of how well a curve is able
to describe the boundary between different image regions, where the degree of sim-
ilarity is described by the local probability distributions of the pixel grey values
determined based on the local vicinity of the expected curve. The posterior prob-
ability density is iteratively maximised with respect to the parameters of the curve