Biomedical Engineering Reference
In-Depth Information
resolution, different tissue signals may be present in one voxel). Moreover, some
anatomical structures may have different signal intensities, which is an inherent
property of brain tissue [1], and increases the difficulty of accurate segmentation.
To precisely extract objects from medical images, robust and efficient algorithms
that are insensitive to noise and poor image contrast are required.
There are many segmentation algorithms in the literature. Some have been
successfully applied in medical image analysis. Classification techniques group
voxels into different subsets. The fundamental principle of such algorithms is
to partition images in desired features space, under prior knowledge constraints.
For brain MR images segmentation, the fuzzy C-means (FCM) algorithm [2, 1]
has been successfully applied. The algorithm is fast and effective but difficult to
combine with prior knowledge and is prone to be affected by outliers. The edge
detection technique similarly distinguishes voxels with features (e.g., gradient)
prominently different from others. In the present work, we consider active con-
tour models that are techniques used to move the segmenting hypersurface toward
the boundaries of the objects to be segmented in the image. Although they have
been developing for many years, these models are still in use and are quite popular.
As in [3], active contour models can be classified into two categories: one para-
metric and the other geometric. Parametric active contour models (e.g., snakes [4])
represent shapes explicitly in their parametric form. Thus, motion of parametric
points represent evolution of the hypersurface. The models experience difficulty in
handling topology changes and are hard to be implemented for 3D image applica-
tions. Another drawback is the numerical instability when two parametric points
are very close. Moreover, the energy functional is dependent on the parameteriza-
tion, which is counterintuitive. On the other hand, geometric active contour models
can overcome these shortcomings, as they use an implicit function to represent the
hypersurface. The hypersurface is embedded into a higher-dimension function.
The geometric active contour models are based on the level set theory [5], which
was first developed in fluid dynamics. With the long development of computa-
tional fluid dynamics, numerous numerical techniques have been proposed to solve
conservation-type partial differential equations (PDEs). The evolution equation
of a level set is a conservation form of the Hamilton-Jacobi equation, which can
be solved using numerical techniques developed in computational fluid dynamics
(CFD). The authors of [6] first applied the level set method to solve segmenta-
tion problems. In that work the level set motion equation was obtained directly
by analogy with interface motion in physics. At the same time, the authors of
[7, 8] independently derived a curve evolution equation represented with a level
set function from a variational approach.
Many well-known segmentation methods are formulated for minimization of
energy functional. Early geometric deformable models only considered edge in-
formation to move the hypersurface toward the object boundary. The segmentation
results based on these models are very sensitive to noise and highly dependent on
initialization. To overcome these shortcomings, region information is then intro-
