Tonnesen, 1992, Malladı et. al., 1993 or Neuenschwander et
al., 1995, together with other contributions that pick out
single aspects for optimization and improvement. The major
feature of deformable models is the ability to bridge over low
texture areas. Most approaches are based on an interactive
setting of seed points along the contour or on a surface.
There snakes are primarily a tool for the last step in a
mensuration process and not for detecting a contour or a
surface from very far away. There exist many families of
deformable models. Different implementations of 2D snakes
are used in mono-images, like open, closed snakes or snake
networks (Ruskoné et al., 1994). Approaches for 3D contour
snakes (e.g. Trinder and Li, 1995) and 3D surface type snakes
(e.g. Delinguette et al., 1991, Szeliski, 1992, Guéziec and
Ayache, 1993) have been reported, integrating also
stereoscopic correspondence and motion models for contours
in the approach (e.g. Bascle and Deriche, 1993).
2.3 Application areas
In Kass et al., 1987 the major intention was the interactive
specification of image contours, matching and motion
tracking. Since then many new application areas have
emerged. We can clearly see a large influence of development
ın medicine and aerial imagery. for contour extraction and
tracking ın multiple frames, in 2D and 3D.
We can see applications in satellite and aerial imagery, in
industrial scenes and medical images. Snakes work on
panchromatic and colour images as well as on medical
ultrasonic images, magnetic resonance images and are used
in computer tomography. The method is applicable to single
images, multiple images or image sequences.
The flexibility of this tool to handle different sensor types
and applications makes it interesting for photogrammetric
applications, like interactive topographic mapping or other
mensuration problems. Considerable work has been
performed the last decade to improve the performance of
deformable models, still we can see only a limited, very
specialized application of them in classical
photogrammetric measurement tasks. We will first look at
some of the improvements that have been undertaken and
discuss then potential and remaining problems for further
acceptance in photogrammetry.
3. IMPROVING THE PERFORMANCE
We examine the important modules of deformable models in
more detail and include contributions to handle objects of
unknown topology.
3.1 Regularization and energy minimization
Physically based models when applied to static data reduce to
energy minimization methods, like regularization, which is
a common approach to solve visual inverse problems.
Different improvements for the iterative optimization have
been reported.
Leclerc and Fua, 1987 describe a guided gradient ascent
method for optimization, which is, however, too slow if
many vertices are involved. Fua and Leclerc, 1988 give a
better optimization method by using a viscous medium and
solving the equation of dynamics. In Gülch, 1990 a
hierarchy in the amount of contour points is applied within a
coarse-to-fine strategy to gradually increase the number of
vertices. Szeliski and Terzopoulos, 1991 combine
physically based models with probabalistic models to a
Kalman filter applied to noisy dynamic tracking data.
280
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Ronfar, 1994 designs a heuristic optimization procedure,
that accounts for internal and external energy in separate
steps and uses adaptive neighbourhood structures and
diffusion processes for a region based strategy. Larsen et al.,
1995 stabilize the variational approach by introducing a
decay function for the step size that gradually reduces
oscillations.
The search for alternate approaches to Lagrangian dynamics
were influenced by Amini et al., 1988. They propagate
'time'delayed' dynamic programming instead of the
variational method to get a more stable behaviour of 2D
snakes. Hard constraints were integrated to avoid merging of
points along the contour. A considerable further
improvement is reported by Olstad and Tysdahl, 1993, Their
approach requires some reasonable constraints on the
selection of candidate points and usage of a second order
energy model.
Statements on criteria for reaching convergence are rare,
especially in cases of dynamic moving objects. A clear
choice of best optimization method is not possible yet. The
number of iterations are seldom reported, but are usually very
high and can range from 10 to 400 and much more. High
numbers, however, make the approach unattractive for all
real-time and interactive applications.
3.2 Internal Energies
The setting of the material parameters, additional constraints
and the handling of discontinuities are major problems.
Fua and Leclerc, 1988 state the inefficiency of local
geometric constraints and give examples for global
constraints to enforce rectilinearity or parallelity. They can
set the smoothness parameter given only the initial state of
the curve and a rough guess of its quality.
In Gülch, 1990 an elimination and densification step for
contour points based on finite elements avoids observed
uncontrolled drifting and clustering of points along the
curve. It ensures an almost equal point distribution along the
whole length of the contour. Breakpoints are introduced not
in the internal energies but by image energies (3.3). Grün
and Li, 1994 adopted the dynamic programming method and
introduced an alternate restriction for point movements
combined with a dynamic insertion and deletion of vertices.
Cohen, 1991 introduced an additional inflation force and a
numerical choice of the material parameters and their
relations to the space discretization step. It will fail when
significant protrusions occur, due to the curvature
minimization properties. Malladi et al., 1993 give solutions
to extract also protrusions.
Samadani, 1991 develops the automated parameter setting
further and introduced an adaptive control of the material
parameters, based on monitoring deformation energies.
However it seems that this heuristic approach requires still
some user assistance for more complex scenes. Rougon and
Préteux, 1993 propose an adapting of material and damping
factors based on differential group-invariant representations
of local image structures.
Jasiobedzki, 1993, uses a network of active contours, where
the whole network or graph can be deformed by internal and
external energies, keeping the connectivity at the nodes,
thus keeping the topology during the deformation process.
Cohen et al., 1993 combine surfaces of different type as lake
and deformable mountainous area with a separated
determination of the lake border by an active contour based
on a variational formulation.
Solutions for isolated problems are visible, but no overall
success to automate the selection of internal energies and
constraints.
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