# In Defense of Relative Multi-View Geometry

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.
Keywords :
Document type :
Preprints, Working Papers, ...

Cited literature [7 references]

https://hal.inria.fr/hal-01676732
Contributor : Matthew Trager <>
Submitted on : Friday, August 10, 2018 - 5:16:45 PM
Last modification on : Tuesday, April 9, 2019 - 1:22:16 AM
Document(s) archivé(s) le : Sunday, November 11, 2018 - 12:22:23 PM

### Files

draft-signed-new.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-01676732, version 2

### Citation

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

Record views