Biomedical Engineering Reference
In-Depth Information
clustering. One thing in common for all regularizers is the application of region
information.
One intriguing issue in a hybrid level set is minimization of the energy func-
tion. The energy function is a natural way to model a preferred segment, and many
methods have been put forward to optimize it. Among these methods, one effective
way is to convert init to a Partial Differential Equation (PDE), so that handling
the segmentation problem corresponds to solution of the associated PDE. Unfor-
tunately, since we often use region integrals to model region information and the
integral regions are often variants corresponding to segments, it has to go through
an unnatural step of converting region integrals into boundary integrals [54, 57].
Recently, Chan and Vese [58] proposed a similar but more natural method to model
region information by introducing the Heaviside function. This excellent strategy
is adopted in this chapter to model cortical structures.
Hybrid models driven by both region and boundary information have achieved
great success in medical image processing [47, 59]. The main reason behind this
success is that it simultaneously takes advantage of local information, which is
accurate, and global information, which is robust.
In addition, neural networks have been widely used in medical segmentation
problems [30, 60-62]. Chiou and Hwang [60] constructed a two-layer perceptron
to train on MR image data to better identify pixels on the boundary of the brain.
Alirezaie et al. [61] used Learning-Vector Quantization (LVQ), a typical self-
organization map network, for segmenting 2D MR images of the brain, where
they treat the segmentation problem as classifying pixels based upon features
that are extracted from multispectral images and incorporate spatial information.
Shareef et al. [30] utilized a new biologically inspired oscillator network to perform
segmentation on 2D and 3D CT and MRI medical-image datasets, and the results
were promising. A comparison between the neural network and fuzzy clustering
techniques in segmenting brain MR images was presented by Hall et al. [25].
2.
DEFORMABLE MODELS
As mentioned earlier, deformable models can be classified as either para-
metric deformable models or geometric deformable models according to their
representation and implementation. In particular, parametric deformable models,
also referred to as snakes or active contour models, are represented explicitly as
parameterized curves in a Lagrangian formulation. Geometric deformable models
are represented implicitly as level sets of two-dimensional distance functions that
evolve according to an Eulerian formulation [47].
2.1. Parametric Deformable Models
A snake is a curve driven by using partial differential equations based on the
theory of elasticity [13]. The famous external forces for parametric deformable
