Full text: XVIIIth Congress (Part B3)

  
   
   
   
   
   
   
   
   
   
     
  
     
  
       
     
    
  
   
  
  
   
   
    
   
     
    
    
   
     
    
    
    
   
   
  
  
  
   
   
   
    
   
  
   
    
   
    
   
    
    
   
   
     
     
   
   
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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