Abstract
Many applications in computer vision require robust linear regression on photogrammetrically reconstructed point clouds. Due to the modeling process from perspective images the uncertainty of an object point depends heavily on its location in object space w.r.t. the cameras. Standard algorithms for robust regression are based on distance measures from the regression surface to the points, but these distances are biased by varying uncertainties. In this paper a description of the local object point precision is given and the Mahalanobis distance to a plane is derived to allow unbiased regression. Illustrative examples are presented to demonstrate the effect of the statistically motivated distance measure.
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References
Werner, T., Zisserman, A.: New techniques for automated architecture reconstruction from photographs. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2351, pp. 541–555. Springer, Heidelberg (2002)
Varady, T., Martin, R., Cox, J.: Reverse engineering of geometric models - an introduction. Computer Aided Design 29, 255–268 (1997)
Rousseeuw, P., Leroy, A.: Robust Regression and Outlier Detection. John Wiley and Sons, Chichester (1987)
Fischler, M., Bolles, R.: RANSAC random sampling concensus: A paradigm for model fitting with applications to image analysis and automated cartography. Communications of ACM 26, 381–395 (1981)
Triggs, B.: A new approach to geometric fitting (1998), Available from http://www.inrialpes.fr/movi/people/Triggs
Kraus, K.: Photogrammetrie, Band 1. Dümmler Verlag (1994)
Förstner, W.: Algebraic projective geometry and direct optimal estimation of geometric entities. In: Proc. 25th AAPR Workshop, Berchtesgaden, pp. 67–86 (2001)
Duda, R.O., Hart, P., Stork, D.: Pattern Classification. John Wiley and Sons, Chichester (2001)
Ohta, Y., Kanade, T.: Stereo by intra- and inter-scanline search. Pattern Analsis and Machine Intelligence 7, 139–154 (1985)
Yuille, A., Poggio, T.: A generalized ordering constraint for stereo correspondence. MIT, A.I. Memo 777 (1984)
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Schindler, K., Bischof, H. (2003). On Robust Regression in Photogrammetric Point Clouds. In: Michaelis, B., Krell, G. (eds) Pattern Recognition. DAGM 2003. Lecture Notes in Computer Science, vol 2781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45243-0_23
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DOI: https://doi.org/10.1007/978-3-540-45243-0_23
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