| procedure,
in separate
uctures and
_arsen et al.,
troducing a
lly reduces
an dynamics
y propagate
ead. of. the
viour of 2D
| merging of
le further
1993. Their
nts on the
econd order
Ce are rare,
ts. A clear
ble yet. The
usually very
more. High
tive for all
| constraints
blems.
y of local
for global
y. They can
tial state of
on step for
Is observed
| along the
n along the
roduced not
(3.3). Grün
method and
movements
X vertices.
force and a
and their
] fail when
curvature
je solutions
eter setting
he material
1 energies.
quires still
Rougon and
id damping
'esentations
ours, where
internal and
the nodes,
on process.
ype as lake
separated
1tour based
no overall
lergies and
3.3 Image Energies
Image energies are improved or extended to allow for less
accurate initial states and to yield a better extracted shape.
The balloon model by Cohen, 199] uses edge points
previously extracted by a local edge detector to avoid
instabilities due to image forces and to enlarge the area of
attraction
In Gülch, 1993 a common image energy map for edge and
point type features is presented based on the Fórstner
interest operator (Fórstner and Gülch, 1987). It is an
extension of an earlier approach (Gülch, 1990). The interest-
and shape values, allow to localize and classify edge and
point type features and the derived energy values can be
geometrically interpreted. Breakpoints in the contour are
enforced by image energies (corners). A theoretically well
understood method is at hand that combines point and edge
energies and eliminates the problem of combining image
energy measures of different nature. In order to increase the
area of attraction an energy pit/canyon around each
point/edgel is created, based on the interest measures, with
highly interesting points/edges receiving minimal energy
contribution. À pit is centred at the sub-pixel position of the
interesting point (fig. 1). For edges the area of attraction is
chosen parallel to the edge direction and forms a canyon (fig.
2). Edges and corners are weighted in the same way and in
both cases the contribution of neighbouring pixels are taken
into account. By placing the centre of the attraction area at a
sub-pixel position the energy map can be spatially refined.
To avoid the pre-setting of a specific window size a sequence
of windows is applied to the image. The derived image
energies from the sequence of windows are combined to
derive a final energy map as input for the snakes.
Energy contribution (de) in a "point" window
Point (dez min)
d de<10
[1 $1
Window
Fig. 1: Example of energy contributions (de) for
a pixel in a point element window.
(de) is dependent on the location in relation to the centre of the
energy ellipse.
Edge (de-min)
Fig. 2: Energy contributions (de) for a pixel in
an edge element window.
(de) is dependent on the perpendicular distance of the pixel to the
edge. s,,4y I$ the maximal distance for a pixel to obtain an energy
contribution of de«1 .0.
The energy map for an aerial scene is given in fig. 3. The
distinction between edges and corners is set to be even. 60%
of the weakest points and 1% of the weakest edges are
excluded. The darkest areas are most attractive for the snakes.
The outline of the roof structure of a large building is visible.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Sn 3
Fig. 3: Image energy map for an aerial scene.
In the energy map a low energy contribution is given as a black
area. This is the position where the snake should attract to, bright
areas show maximal energy. The outline of the roof of a building
is clearly visible.
Trinder and Li, 1995 use in a similar way a chamfer image
derived from the feature image, but apply it also for 3D
snakes. Ronfard, 1994 uses a region-based energy criterion,
rather than an edge detection step, with the argument of non-
availability or expensive generation of edge maps.
3.4 Parameter settings
Besides the material parameters and parameters for the image
energies (window sizes, thresholds) the parameters for the
optimization have to be computed or chosen.
As one of the rare examples Delingette et al., 1991, give a
clear description of parameters, their meaning and their
settings.
Griin and Li, 1994, allow an interactive settings of
parameters, based on empirical observations.
In Giilch, 1993 an attempt has been made to unify the image
energies for contour extraction and limit the number of
necessary parameters to three. Those are:
Minimal interest operator window size in the sequence of
windows
- Maximal interest operator window size in the sequence of
windows
- Definition of point/edge element.
All of them can easily be related to task, size of objects and
image scale. In addition to that the material parameters, a
factor which weights the internal forces against the external
forces and the step size have to be given as well as the
sequence of starting level in the resolution hierarchy and
start/end level in the desired point density.
All other approaches require the same or similar parameters,
but usually few is reported on the used parameters and their
possible range and selection. Very few work is done on
automation of settings of parameters, except the above
mentioned automated settings of the internal parameters. In
very many contributions this is not regarded as a major
problem and mostly neglected. Nevertheless this is one of
the most critical point for photogrammetric applications.
3.5 Initial state
A major drawback of snakes is a strong dependency on the
initial state. Improvements in this respect would be very
welcome to relax the requirement of a very precise initial
281
