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3.7 Objects of unknown topology
If nothing, or very few is known about the topology of
objects, like in many topographic or medical applications,
approaches have to be made more robust and should include
techniques for handling division of contours and surfaces.
Malladi et al., 1993 model arbitrarily complex shapes with
protrusions, whereas snakes tend to prefer regular shapes.
The contour can split freely if more than one object occurs
independent from the initial state, due to the application of
front advancement instead of optimization. This approach is
not limited to 2D contours only. Larsen et al., 1995 observe
a stable behaviour of their multiple and dividing snake given
objects of a certain minimal size.
Delingette et al., 1991 work with free form surfaces based on
points and features and a Lagrangian deformation that
enables segmentation and allows coarse approximations. It
requires minimal and maximal sizes of expected objects,
which can be accepted in many applications. Szeliski and
Tonnesen, 1992 use molecular dynamics to model surfaces of
arbitrary topology, like surface fitting to sparse data. The
surfaces are based on interacting particle systems, they are
elastic and dynamic and can stretch and grow. In Szeliski et.
al., 1993 this approach is extended by an explicitly
triangulated surface based on Bézier curves to derive at a
globally consistent analytic surface. Being more flexible
than spline-based surfaces the particle surfaces require more
computational efforts and due to discretization effects do not
always allow exact mathematical shape control without
further constraints.
3.8 Quality estimates
Any automated procedure should have validation features and
should be thoroughly checked against ground truth.
Szeliski and Terzopoulos, 1991 describe an uncertainty
measures of snake estimates. They either use a reduced
description of uncertainty based on the variance of each
nodal variable (neglecting covariances) or a Monte-Carlo
approach to generate random examples from the posterior
distribution and to derive a confidence envelope for a
contour. In Giilch, 1993, information on the quality of image
energies are made available, but not propagated further. In
Giilch, 1995 the performance of 2D-snakes compared to
mask matching and manual measurement of signalized
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
control points shows a similar or better performance in the
range of sub-pixel accuracy. Trinder and Li, 1995 report on
examinations on the pull-in-range and the absolute accuracy
of 2D and 3D snakes. Given a very precise initial estimate of
better than 5 pixels then relative accuracies of 0.5 pixels for
2D and 1.0 pixels for 3D snakes could be achieved. Larsen et
al., 1995 require a maximal movement of half of the width of
the edge of the object to be tracked.
Very few is done about quality estimates, due to the fact that
most often user interaction is involved at several stages in
the shape extraction and visual inspection alone decides on
success or failure. Poor initial values are obviously the
dominating error source for deformable models.
4. POTENTIAL AND PROBLEMS
We can see that snakes have been tested for many different
measurement tasks under different spezialized conditions,
and proved to be a quite flexible measurement tool, but still
there are some severe drawbacks.
4.1 Potential
As a summary from own and external experience it seems to
be clear, that the major potential is the extraction of generic
contours and surfaces in an interactive environment or guided
by high-level interpretation. Deformable models differ
substantially from manual contour or surface measurement.
The user quickly traces a boundary or give some seed points
of a surface and the measurement is refined by a dynamic
solution that attracts the deformable model to the shape. The
support of neighbouring contour or surface segments to
bridge over low texture areas is an essential strength. The
user has the possibility to guide the deformable model by
implying constraints of different nature.
Simple geometric models of a road together with some
automatically derived or user defined seed points allow
already now the extraction of a large amount of roads in an
aerial or satellite scene. Vegetation boundaries can be
extracted under relaxed modeling conditions. Snakes perform
rather good in the tracking of image sequences, as initial
states have to be given usually just at the beginning of a
sequence and the parameter don't have to be strongly
adapted. The work on free form surfaces and unknown
topology could be very well used in the analysis of digital
surface models from automated image matching or from laser
scanning.
Snakes allow the introduction of many different, image
energies and can practically be trimmed to every desired
internal behaviour. This manifold of possibilities is on the
other hand side responsible for some the major drawbacks.
4.2 Problems
To summarize the discussion in chapter 3, we observe that
different applications have different requirements and
different conditions, that aren't always met by deformable
models. In topographic mapping we have to deal with natural
and man-made contours and surfaces. We are dealing with
different sensors, with single and multiple views, with
sequences and multispectral scenes. The result should be
interpretable and required parameters and quality estimates
connected to geometry, object, scene and task. It is very
difficult to predict the behaviour of snakes in not well-
defined measurement tasks. It is difficult to set stopping
criteria and to get quality criteria. It is not easy to weight
different image energies and it is difficult to derive
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