# Abstract for mendonca_affine-tensor

BMVC98

ANALYSIS AND COMPUTATION OF AN AFFINE TRIFOCAL TENSOR

P.R.D.S. Mendonça and R. Cipolla

1998

This paper investigates the trifocal tensor for an affine trinocular rig and defines an {\em affine trifocal tensor}. The question of the degrees of freedom of the tensor entries will be addressed, and a novel algorithm to compute the tensor by a linear technique is presented. It will be shown that 4 point or 8 line correspondences along the three images are enough for a reliable computation of the trifocal tensor in the affine case (uncalibrated, weak perspective camera model), in contrast to the projective case, where at least 7 point or 13 line correspondences are needed for a linear computation (and usually with poor results).

An analysis of the error in the approximation of a generic trifocal tensor by the affine trifocal tensor is carried out and preliminary experiments with synthetic and real data show the reliability and robustness of the approximation under a wide range of conditions.

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