Abstract
In this paper, we address the problem of the recovery of the Euclidean geometry of a scene from a sequence of images without any prior knowledge either about the parameters of the cameras, or about the motion of the cam-era(s). We do not require any knowledge of the absolute coordinates of some control points in the scene to achieve this goal. Using various computer vision tools, we establish correspondences between images and recover the epipolar geometry of the set of images, from which we show how to compute the complete set of perspective projection matrices for each camera position. These being known, we proceed to reconstruct the scene. This reconstruction is defined up to an unknown projective transformation (i.e. is parameterized with 15 arbitrary parameters). Next we show how to go from this reconstruction to a more constrained class of reconstructions, defined up to an unknown affine transformation (i.e. parameterized with 12 arbitrary parameters) by exploiting known geometric relations between features in the scene such as parallelism. Finally, we show how to go from this reconstruction to another class, defined up to an unknown similitude (i.e. parameterized with 7 arbitrary parameters). This means that in an Euclidean frame attached to the scene or to one of the cameras, the reconstruction depends only upon one parameter, the global scale. This parameter is easily fixed as soon as one absolute length measurement is known. We see this vision system as a building block, a vision server, of a CAD system that is used by a human to model a scene for such applications as simulation, virtual or augmented reality. We believe that such a system can save a lot of tedious work to the human observer as well as play a leading role in keeping the geometric data base accurate and coherent.
Stéphane Laveau is supported by a grant under DRET contract No 91–815/DRET/EAR. This work was also partially funded by the EEC under Esprit, project 6448, Viva and Esprit, project. 8878, Realise.
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Faugeras, O., Laveau, S., Robert, L., Csurka, G., Zeller, C. (1995). 3-D Reconstruction of Urban Scenes from Sequences of Images. In: Gruen, A., Kuebler, O., Agouris, P. (eds) Automatic Extraction of Man-Made Objects from Aerial and Space Images. Monte Verità. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9242-1_15
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DOI: https://doi.org/10.1007/978-3-0348-9242-1_15
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