A minimal set of constraints for the trifocal tensor

Abstract

In this paper we derive a minimal set of suficient 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 independent constraints and novel since the to date known sets of suficient 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 neither 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 important for constrained estimation of the tensor, as well as for deepening the understanding of the multiple view relations that are valid in the projective framework.