TY - GEN
T1 - Critical curves and surfaces for euclidean reconstruction
AU - Kahl, Fredrik
AU - Hartley, Richard
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.
PY - 2002
Y1 - 2002
N2 - The problem of recovering scene structure and camera motion from images has a number of inherent ambiguities. In this paper, configurations of points and cameras are analyzed for which the image points alone are insufficient to recover the scene geometry uniquely. Such configurations are said to be critical. For two views, it is well-known that a configuration is critical only if the two camera centres and all points lie on a ruled quadric. However, this is only a necessary condition. We give a complete characterization of the critical surfaces for two calibrated cameras and any number of points. Both algebraic and geometric characterizations of such surfaces are given. The existence of critical sets for n-view projective reconstruction has recently been reported in the literature. We show that there are critical sets for n-view Euclidean reconstruction as well. For example, it is shown that for any placement of three calibrated cameras, there always exists a critical set consisting of any number of points on a fourth-degree curve.
AB - The problem of recovering scene structure and camera motion from images has a number of inherent ambiguities. In this paper, configurations of points and cameras are analyzed for which the image points alone are insufficient to recover the scene geometry uniquely. Such configurations are said to be critical. For two views, it is well-known that a configuration is critical only if the two camera centres and all points lie on a ruled quadric. However, this is only a necessary condition. We give a complete characterization of the critical surfaces for two calibrated cameras and any number of points. Both algebraic and geometric characterizations of such surfaces are given. The existence of critical sets for n-view projective reconstruction has recently been reported in the literature. We show that there are critical sets for n-view Euclidean reconstruction as well. For example, it is shown that for any placement of three calibrated cameras, there always exists a critical set consisting of any number of points on a fourth-degree curve.
UR - http://www.scopus.com/inward/record.url?scp=84948949988&partnerID=8YFLogxK
U2 - 10.1007/3-540-47967-8_30
DO - 10.1007/3-540-47967-8_30
M3 - Conference contribution
SN - 9783540437444
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 447
EP - 462
BT - Computer Vision - 7th European Conference on Computer Vision, ECCV 2002, Proceedings
A2 - Heyden, Anders
A2 - Sparr, Gunnar
A2 - Nielsen, Mads
A2 - Johansen, Peter
PB - Springer Verlag
T2 - 7th European Conference on Computer Vision, ECCV 2002
Y2 - 28 May 2002 through 31 May 2002
ER -