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In Defense of Relative Multi-View Geometry

Matthew Trager 1 Jean Ponce 1
1 WILLOW - Models of visual object recognition and scene understanding
DI-ENS - Département d'informatique de l'École normale supérieure, Inria de Paris
Abstract : The idea of studying multi-view geometry and structure-from-motion problems {\em relative} to the scene and camera configurations, without appeal to external coordinate systems, dates back to the early days of modern geometric computer vision. Yet, it has a bad rap, the scene reconstructions obtained often being deemed as inaccurate despite careful implementations. The aim of this article is to correct this perception with a series of new results. In particular, we show that using a small subset of scene and image points to parameterize their relative configurations offers a natural coordinate-free formulation of Carlsson-Weinshall duality for arbitrary numbers of images. For three views, this approach also yields novel purely- and quasi-linear formulations of structure from motion using {\em reduced trilinearities}, without the complex polynomial constraints associated with trifocal tensors, revealing in passing the strong link between ``3D''($\mathbb P^3\rightarrow\mathbb P^2$) and ``2D'' ($\mathbb P^2\rightarrow\mathbb P^1$) models of trinocular vision. Finally, we demonstrate through preliminary experiments that the proposed relative reconstruction methods gives good results on real data.
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https://hal.inria.fr/hal-01676732
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Submitted on : Friday, August 10, 2018 - 5:16:45 PM
Last modification on : Tuesday, April 9, 2019 - 1:22:16 AM
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  • HAL Id : hal-01676732, version 2

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Matthew Trager, Jean Ponce. In Defense of Relative Multi-View Geometry. 2018. ⟨hal-01676732v2⟩

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