International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
VANISHING LSQ GERMAN McCLURE 
LIES N W V W 
1 1.084 1 0.08571 0.9855 
2 0.2714 1 0.07246 0.9896 
3 0.07606 1 0.00314 1 
4 0.2352 1 0.01095 0.9998 
5 0.6622 1 0.001638 1 
6 0.3377 1 0.007453 0.9999 
7 0.1313 1 0.004276 1 
8 3:23 1 0.07332 0.9893 
9 1.325 1 0.0622 0.9923 
10 1.501 1 1.867 0.04968 
11 2.028 1 2.147 0.0318 
12 6.61 1 6.425 0.000559 
  
  
  
  
  
  
  
Fig.6: LSQ vs. German estimator in vanishing points detection 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
VANISHING LSQ DANISH 
Lows V W V Ww 
1 1.08 1 0.05816 0.9964 
2 0.2714 1 0.06716 0.9933 
3 0.07606 1 0.0031 1 
4 0.2332 1 0.01083 0.9999 
5 0.6622 1 0.0163 0.9998 
6 0.3377 ] 0.00764 0.9999 
7 0.1513 1 0.00825 0.9999 
8 3,32 1 0.01987 0.9996 
9 1.835 1 0.02339 0.9994 
10 1.501 1 1.877 0.03957 
11 2.028 1 2,149 0.009837 
12 6.61 1 6.425 1.18e-018 
  
  
  
  
  
  
  
Fig. 7: LSQ vs. Danish estimator in vanishing points detection 
In summary, Minimum Cost estimators (Minimum Sum and 
Huber) distribute blunder errors among the other observations, 
and make more difficult the right estimation of vanishing 
‘points. Contrarily, Danish and German & McClure estimators 
detect perfectly the computation by residuals of vanishing lines, 
discard the erroneous artificially introduced vanishing line, 
reject blunders errors out of adjustment by virtue of low weight 
and keep very small the other residuals. 
4. CONCLUSIONS AND FUTURE WORK 
We have developed several methods for a robust estimation of 
vanishing points inside the views corresponding to projections 
of indoor and outdoor scenes, and we have compared on a 
specially designed program. From the comparison between 
them, we have obtained robust and accurate results for Danish 
and German operators. 
But, apart from the results obtained by applying Danish and 
German estimators are more accurate than the others in 
performed experiments, in general, the robust methodology 
developed overcomes in power and effectiveness to the 
classical method (LSQ), in blunders detection and vanishing 
point compute. The main reason about the discrepancy between 
estimators is that the oblique images and their structural 
elements present a great weakness, what increase the 
complexity of our algorithms when we face real situations, 
demanding us, to experiment and adapt our robust estimator to 
our particular problem. On the other hand, we are aware that to 
get that the user doesn’t take part in the whole process will be a 
mete difficult to overcome. In this way, an interactive 
behaviour is still needed for the treatment of alternant 
behaviour in buildings. An automatic approach to be developed 
in the next future requires to improve our graphical model, by 
developing a low-cost implementation of algorithms allowing 
us to add variable visibility constraints linked to an automatic 
robust estimation of oriented facets in terms of inserting- 
deleting 
voxels. 
5. REFERENCES 
[Agu03] Aguilera D.G, M.Gonzalo and J.Finat: "Grouping 
criteria in architectural scenes from compatible orientations of 
polygonal regions", The Intl Arch.of the Photogrammetry, 
Remote Sensing and Spatial Information Sciences, 
Vol. XXXIV, Part 5/W 12, 13-16. 
[Ame79] Amer, F., Theoretical Reliability Studies for Some 
Elementary Photogrametric Procedures, Proceedings of the 
Aerial Triangulation Symposium, Department of Surveying, 
University of Queensland, Brisbane, Australia ,1979. 
[Ber97] M.de Berg, M.Van Kreveld, M.Overmars, and O. 
Schwarzkopf: "Computational Geometry. Algorihtms and 
Applications", Springer-Verlag, 1997. 
[Brd99] Brauer Christian, Burchardt, Klauss Voss. “Robust 
Vanishing Point Determination in Noisy Images”. Digital 
Image Processing Group. Institute for Compute Science. 
University of Jena. Germany. 
[Bri91] B. Brillault-O'Mahoney. New method for vanishing 
point detection. Computer Vision, Graphics, and Image 
Processing. Image Understanding, 54(2):289-300, September 
1991. 
[Dom00] Domingo Preciado Ana: "Investigación sobre los 
Métodos de Estimación Robusta aplicados a la resolución de los 
problemas fundamentales de la Fotogrametría". Tesis Doctoral. 
Universidad de Cantabria. Febrero 2000. 
[Fin02] J.Finat , M.Gonzalo, M.J. Antolinez y S. Aguilar: 
"Dynamic Trapezoidal Maps For Coarse Perspective Models In 
Indoor Scenes", ISPRS'02. 
[Hak81] El-Hakim. S. F., À practical Study of Gross-Error 
Detection in a Blundle Adjust-ment, Canadian Surveyor. 
"Blunder Detection in Horizontal Survey Networks” (1981). 
[Har00] R.Hartley and A .Zisserman; "Multiple View Geometry 
in Computer Vision", Cambridge Univ. Press, 2000. 
[Gom01] Gómez J. "Apuntes de Tercer Ciclo". E.PS. Ávila. 
Departamento de Ingeniería Cartográfica y del Terreno. Aio 
2001. 
[Heu98] F.A. van den Heuvel. Vanishing point detection for 
architectural photogrammetry. In International Archives of 
Photogrammetry and Remote Sensing Vol. XXXII part 5, pages 
652-659, 1998. 
[Kan93] K.Kanatani: "Geometric Computation for Machine 
Vision", Oxford Univ. Press,1993. 
[Kra93] Kraus, K . Advanced Methods and Applications Vol.2. 
Fundamentals and Estándar Processes Voll. Institute for 
Photogrammetry Vienna University of Technology. Ferd. 
Dummler Verlag. Bonn 1993. 
    
  
      
        
     
     
     
   
   
    
  
    
   
    
   
    
     
   
    
   
     
       
  
    
     
Internatioi 
[Lut94] E. 
to the dete 
[n IEEE 
intelligenc 
[Mag84] 
vanishing 
Graphics, : 
[Rth00] C 
detection i 
British M 
September 
[Shf96] J. 
vanishing 
Understan 
Kaufmann 
[Str93] M. 
vanishing 
Image anc 
1005, 
[Tor03] P. 
Importance 
Trans on P 
[Wil02] M 
using geon 
Proc of EC