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Proc. of the 6th Europ. Conf. on Comp. Vision ECCV 2000, Dublin, LNCS 1842, pp. 84-99 1 A Minimal Set of Constraints for the Trifocal
 

Summary: Proc. of the 6th Europ. Conf. on Comp. Vision ECCV 2000, Dublin, LNCS 1842, pp. 84-99 1
A Minimal Set of Constraints for the Trifocal
Tensor
Nikos Canterakis
Albert-Ludwigs-Universitat Freiburg
Computer Science Department
Institute for Pattern Recognition and Image Processing
D-79110 Freiburg, Germany
email: canterakis@informatik.uni-freiburg.de
Abstract. In this paper we derive a minimal set of suÆcient constraints
in order for 27 numbers to constitute a trifocal tensor. It is shown that,
in general, eight nonlinear algebraic constraints are enough.This result
is in accordance with the theoretically expected number of eight inde-
pendent constraints and novel since the to date known sets of suÆcient
constraints contain at least 12 conditions. Up to now, research and for-
mulation of constraints for the trifocal tensor has concentrated mainly on
the correlation slices and has produced sets of constraints that are nei-
ther minimal ( 12) nor independent. We show that by turning attention
from correlation to homographic slices, simple geometric considerations
yield the desired result. Having the minimal set of constraints is impor-

  

Source: Albert-Ludwigs-Universität Freiburg, Institut für Informatik,, Lehrstuhls für Mustererkennung und Bildverarbeitung

 

Collections: Computer Technologies and Information Sciences