On projection matrices Pk → P2, k = 3, ⋯, 6, and their applications in computer vision

Lior Wolf; Amnon Shashua

doi:10.1023/A:1014855311993

On projection matrices P^k → P², k = 3, ⋯, 6, and their applications in computer vision

Lior Wolf^*, Amnon Shashua

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

34 Scopus citations

Abstract

Projection matrices from projective spaces P³ to P² have long been used in multiple-view geometry to model the perspective projection created by the pin-hole camera. In this work we introduce higher-dimensional mappings P^k → P², k = 3, 4, 5, 6 for the representation of various applications in which the world we view is no longer rigid. We also describe the multi-view constraints from these new projection matrices (where k > 3) and methods for extracting the (non-rigid) structure and motion for each application.

Original language	American English
Pages (from-to)	53-67
Number of pages	15
Journal	International Journal of Computer Vision
Volume	48
Issue number	1
DOIs	https://doi.org/10.1023/A:1014855311993
State	Published - Jun 2002

Bibliographical note

Funding Information:
∗This work has been partly funded by the Israeli Science Ministry grant 1229 and by a grant of the Israeli Science Foundation (ISF).

Keywords

Dynamic structure from motion
Multi-linear constraints
Multiple view geometry

Access to Document

10.1023/A:1014855311993

Cite this

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abstract = "Projection matrices from projective spaces P3 to P2 have long been used in multiple-view geometry to model the perspective projection created by the pin-hole camera. In this work we introduce higher-dimensional mappings Pk → P2, k = 3, 4, 5, 6 for the representation of various applications in which the world we view is no longer rigid. We also describe the multi-view constraints from these new projection matrices (where k > 3) and methods for extracting the (non-rigid) structure and motion for each application.",

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