MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Structure from Motion: a New Look from the Point of View of Invariant Theory.

Pierre-Louis Bazin and Mireille Boutin


We present a novel, simple formulation of the problem of 3D object reconstruction from images. In this formulation, the object is seen as lying at the intersection of the projection of orbits of custom-built Lie group actions. The group parameters correspond to unknown, irrelevant quantities such as the camera orientation, the depth parameters of the object with respect to the camera plane and the focal length. We then use an algorithmic method based on moving frames "a la Fels-Olver" to obtain a fundamental set of invariants of these group actions. The invariants are used to define a set of equations detemining the 3D object, thus providing a mathematical formulation of the problem where the irrelevant parameters do not appear.

MSC Codes:
53, 22, 68
structure from motion, moving frame method, invariants

Related publications

2004 Repository Open Access
PL Bazin and Mireille Boutin

Structure from motion: A new look from the point of view of invariant theory

In: SIAM journal on applied mathematics, 64 (2004) 4, pp. 1156-1174