Publication Type

Journal Article

Version

publishedVersion

Publication Date

1-2010

Abstract

We provide a theoretical proof showing that under a proportional noise model, the discrete eight point algorithm behaves similarly to the differential eight point algorithm when the motion is small. This implies that the discrete algorithm can handle arbitrarily small motion for a general scene, as long as the noise decreases proportionally with the amount of image motion and the proportionality constant is small enough. This stability result extends to all normalized variants of the eight point algorithm. Using simulations, we show that given arbitrarily small motions and proportional noise regime, the normalized eight point algorithms outperform their differential counterparts by a large margin. Using real data, we show that in practical small motion problems involving optical flow, these discrete structure from motion (SFM) algorithms also provide better estimates than their differential counterparts, even when the motion magnitudes reach sub-pixel level. The better performance of these normalized discrete variants means that there is much to recommend them as differential SFM algorithms that are linear and normalized.

Keywords

Structure from motion;Perturbation analysis

Discipline

Computer and Systems Architecture

Research Areas

Data Science and Engineering

Publication

International Journal of Computer Vision

Volume

86

Issue

1

First Page

87

Last Page

110

ISSN

0920-5691

Identifier

10.1007/s11263-009-0260-y

Publisher

Springer Verlag (Germany)

Additional URL

https://doi.org/10.1007/s11263-009-0260-y

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