Image Processing Reference

In-Depth Information

3 Shape Prior for Geometric Active Contours

Geometric active contours are iterative segmentation methods which use the level set ap-

posed in literature that we can classify into edge-based or region-based active contours.

In Ref. [
4
], the level set approach is used to model the shape of objects using an evolving

front. The evolution's equation of the level set function ∅ is

(24)

F
is a speed function of the form
F
=
F
0
+
F
1
(
K
) where
F
0
is a constant advection term equals to

(± 1) depends of the object inside or outside the initial contour. The second term is of the form

−
εK
where
K
is the curvature at any point and
ε
> 0. To detect the objects in the image, the

authors proposed to use the following function which stops the level set function's evolution

at the object boundaries.

(25)

where
f
is the image and
G
σ
is a Gaussian filter with a deviation equals to
σ
. This stopping

function has values that are closer to zero in regions of high image gradient and values that

are closer to unity in regions with relatively constant intensity. Hence, the discrete evolution

equation is:

(26)

It's obvious that the evolution is based on the stopping function
g
which depends on the im-

age gradient. That's why this model leads to unsatisfactory results in presence of occlusions,

low contrast, and even noise. To make the level set function evolve in the regions of variability

between the shape of reference and the target shape, we propose the new stopping function as

follows:

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