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Using collineations to compute motion and structure in an uncalibrated image sequence

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Abstract

We address the well-known problem of estimating the motion and structure of a plane, but in the case where the visual system is not calibrated and in a monocular image-sequence.

We first define plane collineations and analyse some of their properties when used to analyse the retinal motion in an uncalibrated image sequence. We show how to relate them to the Euclidean parameters of the scene. In particular, we discuss how to detect and estimate the collineation of the plane at infinity and use this quantity for auto-calibration.

More precisely

  • - We have been able to elaborate a method to estimate robustly any collineation in the image as soon as at least four projections have been established, especially for points at infinity and the collineation of this virtual infinite plane;

  • - It is shown that, given at least four points of a stationary plane and two stationary points not on the plane (or equivalently 2 planes) we can compute the focus of expansion;

  • - A step further, we have defined a bi-ratio of distances for a point with respect to a plane which allows us to analyse not only the relative position of this point with respect to the plane but also quantify this distance;

  • - Moreover a necessary and sufficient condition for a collineation to correspond to a stationary plane is given in the affine case;

  • - It is also discussed that when given three views and the plane at infinity, the intrinsics calibration parameters of the camera can be recovered from linear equations.

Robust estimations of collineation and statistical tests are then developed and illustrated by some experimental results.

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Authors and Affiliations

  1. INRIA, Sophia, BP93, 06902, Valbonne, France

    Thierry Viéville, Cyril Zeller & Luc Robert

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  1. Thierry Viéville
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  2. Cyril Zeller
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  3. Luc Robert
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Viéville, T., Zeller, C. & Robert, L. Using collineations to compute motion and structure in an uncalibrated image sequence. Int J Comput Vision 20, 213–242 (1996). https://doi.org/10.1007/BF00208720

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  • DOI: https://doi.org/10.1007/BF00208720

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