Algebraic Functions For Recognition

Amnon Shashua

doi:10.1109/34.400567

Algebraic Functions For Recognition

Amnon Shashua^*

^*Corresponding author for this work

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

184 Scopus citations

Abstract

In the general case, a trilinear relationship between three perspective views is shown to exist. The trilinearity result is shown to be of much practical use in visual recognition by alignment—yielding a direct reprojection method that cuts through the computations of camera transformation, scene structure and epipolar geometry. Moreover, the direct method is linear and sets a new lower theoretical bound on the minimal number of points that are required for a linear solution for the task of reprojection. The proof of the central result may be of further interest as it demonstrates certain regularities across homographies of the plane and introduces new view invariants. Experiments on simulated and real image data were conducted, including a comparative analysis with epipolar intersection and the linear combination methods, with results indicating a greater degree of robustness in practice and a higher level of performance in reprojection tasks.

Original language	English
Pages (from-to)	779-789
Number of pages	11
Journal	IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume	17
Issue number	8
DOIs	https://doi.org/10.1109/34.400567
State	Published - Aug 1995
Externally published	Yes

Bibliographical note

Funding Information:
I acknowledge Office of Naval Research grants N00014-92-5-1879 and N00014-93-1-0385, National Science Foundation grant ASC-9217041, and ARPA grant NOOO14-91-J-4038 as sources of funding for the Artificial Intelligence Laboratory and for the Center for Biological Computational Learning. Also acknowledged is the McDonnell-Pew postdoctoral fellowship that has been my direct source of funding for the duration of this work. I thank T. Luong and L. Quan for providing their implementation for recovering fundamental matrices and epipoles. Thanks to N. Navab and A. Azarbayejani for assistance in capturing the image sequence (equipment courtesy of MIT Media Laboratory).

Keywords

Visual recognition
algebraic and geometric invariants
alignment
projective geometry
reprojection

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10.1109/34.400567

Cite this

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title = "Algebraic Functions For Recognition",

abstract = "In the general case, a trilinear relationship between three perspective views is shown to exist. The trilinearity result is shown to be of much practical use in visual recognition by alignment—yielding a direct reprojection method that cuts through the computations of camera transformation, scene structure and epipolar geometry. Moreover, the direct method is linear and sets a new lower theoretical bound on the minimal number of points that are required for a linear solution for the task of reprojection. The proof of the central result may be of further interest as it demonstrates certain regularities across homographies of the plane and introduces new view invariants. Experiments on simulated and real image data were conducted, including a comparative analysis with epipolar intersection and the linear combination methods, with results indicating a greater degree of robustness in practice and a higher level of performance in reprojection tasks.",

keywords = "Visual recognition, algebraic and geometric invariants, alignment, projective geometry, reprojection",

author = "Amnon Shashua",

note = "Funding Information: I acknowledge Office of Naval Research grants N00014-92-5-1879 and N00014-93-1-0385, National Science Foundation grant ASC-9217041, and ARPA grant NOOO14-91-J-4038 as sources of funding for the Artificial Intelligence Laboratory and for the Center for Biological Computational Learning. Also acknowledged is the McDonnell-Pew postdoctoral fellowship that has been my direct source of funding for the duration of this work. I thank T. Luong and L. Quan for providing their implementation for recovering fundamental matrices and epipoles. Thanks to N. Navab and A. Azarbayejani for assistance in capturing the image sequence (equipment courtesy of MIT Media Laboratory).",

year = "1995",

month = aug,

doi = "10.1109/34.400567",

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AB - In the general case, a trilinear relationship between three perspective views is shown to exist. The trilinearity result is shown to be of much practical use in visual recognition by alignment—yielding a direct reprojection method that cuts through the computations of camera transformation, scene structure and epipolar geometry. Moreover, the direct method is linear and sets a new lower theoretical bound on the minimal number of points that are required for a linear solution for the task of reprojection. The proof of the central result may be of further interest as it demonstrates certain regularities across homographies of the plane and introduces new view invariants. Experiments on simulated and real image data were conducted, including a comparative analysis with epipolar intersection and the linear combination methods, with results indicating a greater degree of robustness in practice and a higher level of performance in reprojection tasks.

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KW - algebraic and geometric invariants

KW - alignment

KW - projective geometry

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Algebraic Functions For Recognition

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Keywords

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