Biomedical Engineering Reference
In-Depth Information
came in the form of inclusion of topological adaptability, where the snake can
merge and split to capture complex geometries and topologies.
The equations in this chapter mostly deal with a 2D space. However, they
are extendable to 3D in all cases [25, 60]. The basic energy equation remains the
same for all dimensionalities. Only the computation of geometric properties and
image forces is changed. The geometric properties then need to be evaluated for
a surface rather than a line segment. This makes the estimation computationally
expensive, but the main essence is retained. The snake framework can be utilized
in a different form often to segment 3D volumes. Rather than using the surface, the
3D volume can be broken down into an array of 2D slices (which comes naturally
in medical images). Each of the 2D slices can be separately segmented and stacked
up to form a 3D volume. However, in this approach the 3D information of the
medical data is not utilized optimally.
A similar approach has also been used for motion tracking in various medical
applications like tracking heart motion [64] and cell deformation [28, 65-69]. De-
formable models have been used to track nonrigid microscopic and macroscopic
structures in motion, such as blood cells [65] and neurite growth cones [70] in
cine-microscopy, as well as coronary arteries in cine-angiography [71]. However,
the primary use of deformable models for tracking in medical image analysis is
to measure the dynamic behavior of the human heart, especially the left ventricle.
Regional characterization of heart wall motion is necessary to isolate the severity
and extent of diseases such as ischemia. The most conventional approach is to
track the 2D contour in an image frame and propagate the contour to the temporally
next frame for deformation. Some approaches have utilized motion vectors and
Kalman filtering approaches [66] to boost snake performance in tracking motions
of this kind.
The increasingly important role of medical imaging in the diagnosis and treat-
ment of disease and the rapid advancement in imaging devices have opened up
challenging problems for the medical image analysis community. Deformable
models offer an attractive solution to situations where we intend to capture complex
shapes and wide shape variability of anatomical structures. Deformable models
overcome many of the limitations of traditional low-level image processing tech-
niques by providing compact and analytical representations of object shape, by
incorporating anatomic knowledge, and by providing interactive capabilities.
APPENDIX A
Energyminimization of the snake is accomplishedwithin an Euler-Lagrangian
framework of solving PDEs or a dynamic programming approach that uses neigh-
borhood information on an energy surface. Note that the energy-based approach
of dynamic programming and the greedy snake does not optimally use the image
