![](bg4.png)
time expensive for huge images like those from the re-
search in G
¨
ottingen. This saves a little time because
in the meantime the user is able to perform indepen-
dent tasks like setting up one or more initial contours
or adjusting parameter values.
3.2 Multiresolution with an
Automation Approach
We use a multiresolution approach which is very sim-
ilar to Leroy (Leroy et al., 1996). After a huge im-
age has been loaded several smaller scales of the im-
age are computed. Each scale has half the width
and height of the above scale. This computation is
repeated until the coarsest image size is about one
megapixel.
Starting with a rough initial contour with a few
points in the coarsest scale, we can set up an iter-
ative process. By solving small systems of linear
equations our approach determines a suitable solu-
tion curve very rapidly. Furthermore, the tendency to
shrink is stronger if the active contour has only a few
points, due to the structure of the internal forces, i.e.
the snake needs less iterations. A simple polygonal
initialized snake is filled with many collinear points
on the edges of the polygon. If these points are lo-
cated in regions without a potential image force they
have a minimal energy. So they will not move unless
a discrete curvature is present which can be found,
of course, at the polygon’s vertices. That means that
these vertices are the first deforming parts of the snake
spreading a smaller curvature to their neighbors. One
can imagine that the snake is shrinking faster the less
points it has. In fact, this behavior can be desired,
though it is commonly seen as a disadvantage. Often,
a snake has to move across regions without any edge
information when detecting object boundaries from
outside by contraction. Therefore, it has to deform
while being exposed only to the internal forces.
In order to keep an approximate point distance, new
points are inserted when switching to a higher resolu-
tion next to scaling the contour to an appropriate size.
That means the result of the last lower scale is used
as the initial curve for the current scale. When the
original resolution is reached the snake should be al-
ready very close to the desired curve and therefore
only a few iterations are needed for a more detailed
extraction. This approach leads to an acceleration,
because the biggest distance of the contour is covered
in coarse scales with only a few points and in higher
scales just minimal refinements are needed.
User interaction can be further reduced if accept-
able results can be achieved without the need of pa-
rameter adjustments during the deforming process.
Based on that multiresolution strategy, we have de-
signed an automation technique, that allows an auto-
matic image segmentation for images with a sufficient
quality. We start with a given initial contour in the
coarsest scale with the traditional image forces (no
GVF). Besides we use the opposite image forces for
the beginning convergence process, i.e. using
~
F
img
instead of −
~
F
img
in equation (5). That way, we can
keep the snake slightly distant from the desired object
boundaries. Otherwise we observed the contour of-
ten moving across weak edges in lower scales. The
deformation procedure automatically switches to the
next scale after the snake has stabilized its position.
It is scaled to double size and additional points are
inserted. For each reached scale the potential im-
age forces are recomputed, according to the new size.
These steps are repeated until we reached the original
size of the image. Then the classical image energy
(with the correct sign) or the GVF field is used for
the last time the deforming process gets started. Con-
verged close to the desired edges in the meantime the
snake can now fit to them very quickly.
3.3 Using Segments
Kerschner (Kerschner, 2003) proposed an approach
that uses segments in order to overcome local min-
ima. A traffic light system enables the snake to diag-
nose the quality of the segmentation result of itself.
Thereby segments in different colors (red for rejected
results, yellow for unsure results, green for trustwor-
thy results) are presented to the operator who can in-
fluence the accepting procedure of the automatic rat-
ing system. Typically, yellow and red parts are linked
and deform afterward with a modified energy func-
tion, e.g. by changing parameter values.
We use segments to gain another acceleration. Dur-
ing the deforming process parts of a snake often reach
the desired object boundaries faster than others, e.g.
an active contour has not moved into an concave
boundary region yet while the rest of the object has
been detected already. Points in these parts will not
move anymore and thus can be excluded from the it-
erative minimization procedure. This can be done by
subdividing the snake into segments and treating them
as open snakes.
The segmentation process is started with one seg-
ment – one closed contour. The movement of each
point of the snake is traced for the last few iterations.
If the position of several adjacent points does not
change significantly within that time, two segments
are formed. The first segment contains these adja-
cent points and is locked, i.e. is ignored in the future
minimization process. The second segment is filled
with the remaining points and further on deforming
as open snake by solving a respectively smaller sys-
tem of equations. Figure 2 shows the use of segments.
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