Algebraic derivations of relative affine structure and applications to 3D reconstruction from 2D views

Nassir Navab; Amnon Shashua

doi:10.1117/12.182821

17 August 1994 Algebraic derivations of relative affine structure and applications to 3D reconstruction from 2D views

Nassir Navab, Amnon Shashua

Proceedings Volume 2357, ISPRS Commission III Symposium: Spatial Information from Digital Photogrammetry and Computer Vision; (1994) https://doi.org/10.1117/12.182821
Event: Spatial Information from Digital Photogrammetry and Computer Vision: ISPRS Commission III Symposium, 1994, Munich, Germany

Abstract

We present an algebraic description of relative affine structure -- an invariant structure affinely related to the structure seen from one of the cameras. This algebraic description yields a simple canonical framework that unifies results in projective, affine, and Euclidean structure from motion. We then introduce a method for capturing the redundancy in recovering relative affine structure from a stream of perspective views. We propose a certain decomposition that on one hand involves an optimal projection of the contribution of each point at each frame onto a single bilinear equation; and on the other hand reveals a connection (bilinear) between the homography of an arbitrary plane and the translational component of motion. Given an estimation of the epipoles, which can be computed in a least squares manner for each frame separately, the decomposition equations yield a linear least squares method for solving for scene structure. The main results were applied to a real image sequence for the purpose of 3D reconstruction from 2D views, visual recognition by alignment, and image coding.

Citation Download Citation

Nassir Navab and Amnon Shashua "Algebraic derivations of relative affine structure and applications to 3D reconstruction from 2D views", Proc. SPIE 2357, ISPRS Commission III Symposium: Spatial Information from Digital Photogrammetry and Computer Vision, (17 August 1994); https://doi.org/10.1117/12.182821

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