Camillo Ressl
dimension of *dangerous surfaces' in practice always appears higher by one. [Luong, Faugeras 1996] use in this context
the term ‘critical volume’ for emphasizing that depending on the image noise ambiguities and inaccuracies of the
unknowns may also appear for configurations quite far away from the ‘exact’ dangerous surface. In [Maybank, Shaghy,
1998] it is shown that reconstruction from three images of six points is subject to a three way ambiguity which i;
preserved as long as the optical center of the camera remains on a certain quadric surface; i.e. if 6 points are used fo;
computing the trifocal tensor a real dangerous surface can exist, which is of a special interest for the 6 point algorithm
proposed by [Torr, Zisserman 1997]. The question arises if this ambiguity due to six points can be broken by any
seventh point, or are there some constraints which such a ‘point of deliverance’ must meet.
The topics of gross-error-detection, dangerous situations, constraints within the TFT (also for calibrated images) and the
inclusion of image-distortion into the TFT-framework will be investigated in more detail in the near future in the course
of a research-project subsidized by the Austrian Science Fund FWF (P13901-INF).
REFERENCES
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R. Hartley, 1994. Lines and Points in Three Views — a Unified Approach. Proc. of an Image Understanding Workshop
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R. Hartley, 1998. Computation of the Quadrifocal Tensor. Proc. of 5" European Conf. on Computer Vision, Springer.
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K. Rinner, 1963. Studien über eine allgemeine, voraussetzungslose Lósung des Folgebildanschlusses. Sonderheft 23 der
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K. Rinner, R. Burkhardt, 1972. Photogrammetrie. In: Handbuch der Vermessungskunde. (Hsgb. Jordan, Eggert,
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A. Shashua, 1995. Algebraic Functions For Recognition. PAMI Vol. 17 No. 8, pp. 779-788.
A. Shashua, S. Maybank, 1996. Degenerate N Point Configurations of Three Views: Do Critical Surfaces Exist?
Technical Report TR 96-19, Hebrew University of Jerusalem.
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M.E. Spetsakis, J. Aloimonos, 1990. A Unified Theory of Structure from Motion. Proc. of an Image Understanding
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776 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
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