Biomedical Engineering Reference
In-Depth Information
δφ
=
(
)(
ν
+
(
∇φ
/|
∇φ
|
))
|
∇φ
|∗
δ
g
I
div
t
(34)
where
φ
0
is initialized as the signed distance function of
C
0
and (
34
) is iterated until
δφ
<
ε
.
Importantly, in order for the update (
34
) to work correctly, the level set property
of
must be
periodically re-initialized. This is costly and has led to the development of efficient
narrow banding
techniques that limit updates to
φ
must be maintained at all times. In practice, this requires that
φ
φ
near the zero level set, while
further constraining
to be a distance function in this neighborhood. Techniques
have also been developed that optimize and adapt the level set technique specifically
for image segmentation tasks. A novel discrete framework was introduced by [
75
]
which achieves unparalleled speedup by avoiding the solution of any costly pdes.
Some interesting aspects of the algorithm include the adoption of a level set function
with a range limited to the set (
φ
−
,−
1,1,3). The level set function updates based on
neighborhood connectivity over a minimally sparse set of active boundary points,
and never needs re-initialization. Smoothing is achieved by periodically convolving
the level set function with a Gaussian kernel.
3
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