Biomedical Engineering Reference
In-Depth Information
where
λ
1
and
λ
2
are two parameters that balance the influence of the gradient-
curvature term and the shape-model term.
proposed further refinements of their method by
introducing prior intensity and curvature models using statistical image-surface
relationships in the regularizer terms. Some clinical validation has reported show-
ing efficient and robust performance of the method.
In [56], Leventon et al.
4.3.4. Coupling-surfaces regularizers
This kind of regularizer was motivated by segmentation of embedded organs
such as the brain cortical gray matter. The application is to attempt to employ
a level set segmentation framework to perform simultaneous segmentation of the
inner and outer organ surfaces with coupled level set functions. This method was
proposed by Zeng et al. [32]. In this framework, segmentation is performed with
the following system of equations:
Φ
in
+
F
in
|∇
Φ
in
|
=0
,
Φ
out
+
F
out
|∇
Φ
out
|
=0
.
(19)
where the terms
F
in
and
F
out
are functions of the surface normal direction (e.g.,
curvature), image-derived information and the distance between the two surfaces.
When this distance is within the desired range, the two surfaces propagate ac-
cording to the first two terms of the speed term. When the distance is outside the
desired range, the speed term based on the distance controls the deformation so as
to correct for the surface positions.
4.4. Region-Based Active Contour Models
These classical snakes and active contour models rely on the edge function, de-
pending on the image gradient, to stop curve evolution, and these models can detect
only objects with edges defined by the gradient. Some of the typical edge functions
are illustrated in Figure 13. In practice, the discrete gradients are bounded, and then
the stopping function is never zero on the edges, and the curve may pass through
the boundary. If the image is very noisy, the isotropic smoothing Gaussian has to
be strong, which will smooth the edges as well. This region-based active contour
method is a different active contour model, without a stopping edge-function, i.e.,
a model that is not based on the gradient of the image for the stopping process.
4.4.1. Mumford-Shah (MS) function
One kind of stopping term is based on the Mumford-Shah [57] segmentation
techniques. In this way, the model can detect contours with or without gradient,
for instance, objects with very smooth boundaries or even with discontinuous
