Full text: Proceedings, XXth congress (Part 5)

   
   
     
   
    
   
    
    
   
    
     
   
   
     
     
    
    
    
    
    
     
   
       
    
       
  
    
    
    
   
    
       
     
    
    
    
    
   
    
   
   
   
   
    
ıral perspective 
ts. In this paper 
"he intersection 
which provide 
on. Triplets of 
zation tasks by 
ple junctions in 
introduction of 
ng of adjacent 
h can occlude 
cuboids in the 
rvention it is 
mation about 
their incidence 
ied in terms of 
ojective flags". 
f an incidence 
ition relative to 
tive lines) and 
). The relative 
d to the image 
nd T-type) and 
€ intersections 
val assigned to 
rom a Deriche's 
s in automatic 
ractive visual 
management of 
ion of pairs of 
lines. Both of 
collinearity and 
itic grouping of 
pective lines in 
void sensitivity 
ted by a robust 
ice perspective 
way, by taking 
| are grouped 
n or RANSAC 
: of perspective 
F least squares 
mini-segments, 
highly textured 
to recover and 
primitive-based 
yed a primitive- 
based approach for perspective models because it supports 
better vectorized information. Robust and accurate estimation 
of vanishing points is obtained integrating different 
methodologies belonging to Photometry and Computer Vision 
with robust procedures. Parameters linked to transformations 
between views are expressed in terms of affine maps between 
quadrilaterals determined by intersections of perspective lines. 
Planar collineations between pairs of views are lifted to 
collineations in the ambient 3D space by constructing cuboids 
from the third vanishing point. We have developed a symbolic 
management of information based on propagation models from 
an initial cuboid located around the focal point and generated 
from pencils of lines through vanishing points. Perspective lines 
provide the main directions for propagation phenomena in our 
model. Thus, the robust identification of vanishing points 
allows to avoid "tedious" local compatibility and global 
coherence conditions for homologue cuboids in different 
constructions, and simplify the tracking in presence of self- 
motion [Fin02]. We have restricted ourselves to simple indoor 
and outdoor scenes with a static camera, by avoiding occlusion 
problems and possible cumbersome alternance between 
concave/convex regions for evaluating the goodness of our 
results. 
2. METHODOLOGY 
With the goal of investigating and testing the behavior of our 
robust methodology, we have developed a program that allows 
us to test and analyze under different geometric and stochastic 
conditions several perspectives models and oblique images. The 
next scheme shows the steps of the methodology developed: 
| SINGLE IMAGE | 
Canny's feature 
extraction | | 
v 
Automatic or 
| Image preprocessing | 
Human assistance 
v 
  
  
  
  
  
  
  
  
  
  
  
Labelling and | 
grouping 
  
  
  
  
  
  
  
Compute of 
Rd ^ Support by Area 
vanishing points 
Minimization and Robust E. 
  
  
  
  
  
  
  
Quadrilaterals and 
cuboids decomposition 
  
  
  
  
Y 
Perspective 
reconstruction 
  
  
  
  
  
  
  
  
Fig.1: Methodology developed. 
2.1 Automatic extraction of basic elements 
Automatic grouping in Computational Geometry is usually 
performed by using auxiliary constructions such | as 
decompositions in triangles, trapezoids or, more generally, 
convex sets associated to a multivectorized treatment of data 
[Ber97] Minisegments are obtained from Canny's detector. 
Minisegments are grouped along lines to determine ordinary 
multiple junctions. Large segments are grouped depending on 
the slope and collinearity restrictions. In this way, we attenuate 
the striped effect which appears from boundaries and 
minisegments obtained from the application of Canny's 
detector. Furthermore, we eliminate short segments with length 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
under a selected threshold. In indoor scenes, we apply an active 
discrimination for vertical lines, due to the characteristics of 
scene and bad illumination (reflectances, irradiance of the 
ground and floor, etc). Large segments make part of putative 
candidates to become perspective lines. To validate them as 
perspective lines, we must have a robust an accurate estimation 
of the vanishing points, and verify incidence conditions of large 
segments through vanishing points. 
2.2 Elements of perspective 
Vanishing points are computed from bundles of perspective 
lines in the framework of Projective Geometry [Har00]. The 
relative location of vanishing points w.r.t. the image determines 
the perspective model (frontal view, angular perspective, and 
oblique perspective, respectively) which is useful for 
visualization tasks (linked to one, two or three vanishing points 
to finite distance, respectively). Selection of constraints in 
manually driven reconstruction is typical of photogrammetry, 
and it depends on the perspective model chosen. In frontal and 
angular perspective, rigidity constraints relative to motions and 
objects are translated to parallelism and perpendicularity 
constraints for typical representations of architectural scenes. 
The projective extension of Euclidian approach is clearly very 
useful for oblique perspective. It is based on maps of cuboids 
appearing as the image of parallelepipeds by a projective 
transformation. This kind of volumetric representation has been 
extensively developed and applied for reconstruction from a 
single view and their applications [Wil02]. : 
2.3 Robust estimators for vanishing points 
In scenes with bad illumination or annoying architectural 
elements, sometimes it is difficult to identify perspective 
elements to visualize 3D scenes. In this case, we have 
developed a real-time implementation based on the intersection 
of putative perspective lines obtained by regression and Hough 
transform [Fin02]. A weighted average around a vanishing line 
allows to identify a coarse approach to a putative vanishing 
point 7, and retracing perspective lines through V. The high 
rate of errors (around a 59$) can be corrected in mobile 
navigation [Fin02]. However, this error is not allowed in more 
accurate 3D Reconstruction. Thus, we have concentrated our 
attention in the implementation of algorithms for robust 
estimation of vanishing points. In this section we compare 
different several estimators for vanishing points: Danish 
method, Minimal Sum, Huber, German-McClure. The main 
goal of all of them is the automatic elimination of lines which 
are not adequate for the "right" determination of vanishing 
points. The rightness is measured in terms of the area 
minimization. In typical architectural scenes we have a high 
redundancy degree, more precisely, we have enough elements 
arising from an automatic vectorization to provide bundle of 
errors in perspective lines. 
Robust estimators provide an adjustment method, and detect 
wrong observations appearing as outliers in an efficient way. 
Robustness corresponds to their independence w.r.t. the errors 
distribution. Robust estimators are based on applying variable 
weight functions P(w) , and they can be written as Pow!) 
where i is a residual number and £ the iteration number. The 
function P allows to modify original weights in order to reject 
observations having blunders errors in the adjustment. We have 
considered the following robust estimators:
	        
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