Biomedical Engineering Reference
In-Depth Information
When a snake collides with itself or with another snake, or when a snake
breaks into two or more parts, a topological transformation must take place. In
order to effect consistent topological changes, consistent decisions must be made
about disconnecting and reconnecting snake nodes. The simplicial grid provides
us with an unambiguous framework from which to make these decisions. Each
boundary triangle can contain only one line segment to approximate a closed snake
in that triangle. This line segment must intersect the triangle on two distinct edges.
Furthermore, each vertex of a boundary triangle can be unambiguously classified
as inside or outside the snake. When a snake collides with itself, or when two
or more snakes collide, there are some boundary triangles that will contain two
or more line segments. We then choose two line segment endpoints on different
edges of these boundary triangles and connect them to form a new line segment.
The two endpoints are chosen such that they are the closest endpoints to the outside
vertices of the triangle and such that the line segment joining them separates the
inside and outside vertices (Figure 22c). Any unused node points are discarded.
Once the topological transformations have taken place, the list of nodes gen-
erated can be visited and contour tracings perform via the grid cells, marking off
all nodes visited during the tracings. All new snakes generated are determined by
the topological transformation phase and assign each a unique identifier.
Topological adaptive snakes are widely used [59, 60, 63] for their ability to
handle complex structures which are so often encountered in medical imaging.
Figure 23 illustrates some of the implementation results for tracking blood vessels
in a retinal angiogram, on the cerebral vasculature surface (3D), and in different
regions of brain. It is important to notice that topological adaptability has allowed
an immense amount of flexibility in the snake framework, and thus enabled it to
segment geometrically and topologically complex structures.
6.
DISCUSSION AND CONCLUSIONS
The basic snake algorithm thus developed originally for computer vision ap-
plications has found widespread application in medical image analysis for its abil-
ity to capture local image statistics within a global geometric framework. This
framework is widely appreciated in segmenting anatomical structures and quanti-
fying various features in images of different modalities, including MR, x-ray, CT,
and ultrasound. The task of segmentation using an active contour model ranges
throughout the anatomical atlas, covering areas, like spine, heart, brain, cere-
brum, kidney, lungs, and liver, and various artery segmentation, like the carotid
and the aorta. An extensive amount of work has been done in delineating and
quantifying the growth of objects like tumors, multiple sclerosis lesions, a fetus,
micro-calcifications in breast frommammography images, etc. Thus, applications
range from identifying white matter in the brain to quantifying diseases through
imaging. Also, application of the active contour model has gone a step further in
