General models for rational cameras and the case of two-slit projections
Identifieur interne : 000009 ( France/Analysis ); précédent : 000008; suivant : 000010General models for rational cameras and the case of two-slit projections
Auteurs : Matthew Trager [France] ; Bernd Sturmfels [États-Unis] ; John Canny [États-Unis] ; Martial Hebert [États-Unis] ; Jean Ponce [France]Source :
Abstract
The rational camera model recently introduced in [19] provides a general methodology for studying abstract nonlinear imaging systems and their multi-view geometry. This paper builds on this framework to study "physical realizations" of rational cameras. More precisely, we give an explicit account of the mapping between between physical visual rays and image points (missing in the original description), which allows us to give simple analytical expressions for direct and inverse projections. We also consider "primitive" camera models, that are orbits under the action of various projective transformations, and lead to a general notion of intrinsic parameters. The methodology is general, but it is illustrated concretely by an in-depth study of two-slit cameras, that we model using pairs of linear projections. This simple analytical form allows us to describe models for the corresponding primitive cameras, to introduce intrinsic parameters with a clear geometric meaning, and to define an epipolar tensor characterizing two-view correspondences. In turn, this leads to new algorithms for structure from motion and self-calibration.
Url:
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Hal, to step Corpus: 000300
- to stream Hal, to step Curation: 000300
- to stream Hal, to step Checkpoint: 000010
- to stream Main, to step Merge: 000010
- to stream Main, to step Curation: 000010
- to stream Main, to step Exploration: 000010
- to stream France, to step Extraction: 000009
Links to Exploration step
Hal:hal-01506996Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">General models for rational cameras and the case of two-slit projections</title>
<author><name sortKey="Trager, Matthew" sort="Trager, Matthew" uniqKey="Trager M" first="Matthew" last="Trager">Matthew Trager</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-454692" status="VALID"> <idno type="RNSR">200718311C</idno>
<orgName>Models of visual object recognition and scene understanding</orgName>
<orgName type="acronym">WILLOW</orgName>
<date type="start">2016-01-01</date>
<desc> <address> <country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/willow</ref>
</desc>
<listRelation> <relation active="#struct-25027" type="direct"></relation>
<relation active="#struct-59704" type="indirect"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation name="UMR8548" active="#struct-441569" type="indirect"></relation>
<relation active="#struct-454310" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-25027" type="direct"><org type="laboratory" xml:id="struct-25027" status="VALID"> <orgName>Département d'informatique de l'École normale supérieure</orgName>
<orgName type="acronym">DI-ENS</orgName>
<desc> <address> <addrLine>École normale supérieure 45 rue d'Ulm F-75230 Paris Cedex 05</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.di.ens.fr/</ref>
</desc>
<listRelation> <relation active="#struct-59704" type="direct"></relation>
<relation active="#struct-300009" type="direct"></relation>
<relation name="UMR8548" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-59704" type="indirect"><org type="institution" xml:id="struct-59704" status="VALID"> <orgName>École normale supérieure - Paris</orgName>
<orgName type="acronym">ENS Paris</orgName>
<desc> <address> <addrLine>45, Rue d'Ulm - 75230 Paris cedex 05</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.ens.fr</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR8548" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"> <idno type="IdRef">02636817X</idno>
<idno type="ISNI">0000000122597504</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc> <address> <country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-454310" type="direct"><org type="laboratory" xml:id="struct-454310" status="VALID"><orgName>Inria de Paris</orgName>
<desc><address><addrLine>2 rue Simone Iff -CS 42112 -75589 Paris Cedex 12</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/centre/paris</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
</affiliation>
</author>
<author><name sortKey="Sturmfels, Bernd" sort="Sturmfels, Bernd" uniqKey="Sturmfels B" first="Bernd" last="Sturmfels">Bernd Sturmfels</name>
<affiliation wicri:level="1"><hal:affiliation type="institution" xml:id="struct-300674" status="VALID"> <orgName>University of California [Berkeley]</orgName>
<desc> <address> <addrLine>Berkeley, CA</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.berkeley.edu/</ref>
</desc>
</hal:affiliation>
<country>États-Unis</country>
</affiliation>
</author>
<author><name sortKey="Canny, John" sort="Canny, John" uniqKey="Canny J" first="John" last="Canny">John Canny</name>
<affiliation wicri:level="1"><hal:affiliation type="institution" xml:id="struct-300674" status="VALID"> <orgName>University of California [Berkeley]</orgName>
<desc> <address> <addrLine>Berkeley, CA</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.berkeley.edu/</ref>
</desc>
</hal:affiliation>
<country>États-Unis</country>
</affiliation>
</author>
<author><name sortKey="Hebert, Martial" sort="Hebert, Martial" uniqKey="Hebert M" first="Martial" last="Hebert">Martial Hebert</name>
<affiliation wicri:level="1"><hal:affiliation type="institution" xml:id="struct-67135" status="VALID"> <orgName>Carnegie Mellon University [Pittsburgh]</orgName>
<orgName type="acronym">CMU</orgName>
<desc> <address> <addrLine>5000 Forbes Ave, Pittsburgh, PA 15213</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.cmu.edu/</ref>
</desc>
</hal:affiliation>
<country>États-Unis</country>
</affiliation>
</author>
<author><name sortKey="Ponce, Jean" sort="Ponce, Jean" uniqKey="Ponce J" first="Jean" last="Ponce">Jean Ponce</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-454692" status="VALID"> <idno type="RNSR">200718311C</idno>
<orgName>Models of visual object recognition and scene understanding</orgName>
<orgName type="acronym">WILLOW</orgName>
<date type="start">2016-01-01</date>
<desc> <address> <country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/willow</ref>
</desc>
<listRelation> <relation active="#struct-25027" type="direct"></relation>
<relation active="#struct-59704" type="indirect"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation name="UMR8548" active="#struct-441569" type="indirect"></relation>
<relation active="#struct-454310" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-25027" type="direct"><org type="laboratory" xml:id="struct-25027" status="VALID"> <orgName>Département d'informatique de l'École normale supérieure</orgName>
<orgName type="acronym">DI-ENS</orgName>
<desc> <address> <addrLine>École normale supérieure 45 rue d'Ulm F-75230 Paris Cedex 05</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.di.ens.fr/</ref>
</desc>
<listRelation> <relation active="#struct-59704" type="direct"></relation>
<relation active="#struct-300009" type="direct"></relation>
<relation name="UMR8548" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-59704" type="indirect"><org type="institution" xml:id="struct-59704" status="VALID"> <orgName>École normale supérieure - Paris</orgName>
<orgName type="acronym">ENS Paris</orgName>
<desc> <address> <addrLine>45, Rue d'Ulm - 75230 Paris cedex 05</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.ens.fr</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR8548" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"> <idno type="IdRef">02636817X</idno>
<idno type="ISNI">0000000122597504</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc> <address> <country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-454310" type="direct"><org type="laboratory" xml:id="struct-454310" status="VALID"><orgName>Inria de Paris</orgName>
<desc><address><addrLine>2 rue Simone Iff -CS 42112 -75589 Paris Cedex 12</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/centre/paris</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">HAL</idno>
<idno type="RBID">Hal:hal-01506996</idno>
<idno type="halId">hal-01506996</idno>
<idno type="halUri">https://hal.archives-ouvertes.fr/hal-01506996</idno>
<idno type="url">https://hal.archives-ouvertes.fr/hal-01506996</idno>
<date when="2017-07-21">2017-07-21</date>
<idno type="wicri:Area/Hal/Corpus">000300</idno>
<idno type="wicri:Area/Hal/Curation">000300</idno>
<idno type="wicri:Area/Hal/Checkpoint">000010</idno>
<idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">000010</idno>
<idno type="wicri:Area/Main/Merge">000010</idno>
<idno type="wicri:Area/Main/Curation">000010</idno>
<idno type="wicri:Area/Main/Exploration">000010</idno>
<idno type="wicri:Area/France/Extraction">000009</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en">General models for rational cameras and the case of two-slit projections</title>
<author><name sortKey="Trager, Matthew" sort="Trager, Matthew" uniqKey="Trager M" first="Matthew" last="Trager">Matthew Trager</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-454692" status="VALID"> <idno type="RNSR">200718311C</idno>
<orgName>Models of visual object recognition and scene understanding</orgName>
<orgName type="acronym">WILLOW</orgName>
<date type="start">2016-01-01</date>
<desc> <address> <country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/willow</ref>
</desc>
<listRelation> <relation active="#struct-25027" type="direct"></relation>
<relation active="#struct-59704" type="indirect"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation name="UMR8548" active="#struct-441569" type="indirect"></relation>
<relation active="#struct-454310" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-25027" type="direct"><org type="laboratory" xml:id="struct-25027" status="VALID"> <orgName>Département d'informatique de l'École normale supérieure</orgName>
<orgName type="acronym">DI-ENS</orgName>
<desc> <address> <addrLine>École normale supérieure 45 rue d'Ulm F-75230 Paris Cedex 05</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.di.ens.fr/</ref>
</desc>
<listRelation> <relation active="#struct-59704" type="direct"></relation>
<relation active="#struct-300009" type="direct"></relation>
<relation name="UMR8548" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-59704" type="indirect"><org type="institution" xml:id="struct-59704" status="VALID"> <orgName>École normale supérieure - Paris</orgName>
<orgName type="acronym">ENS Paris</orgName>
<desc> <address> <addrLine>45, Rue d'Ulm - 75230 Paris cedex 05</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.ens.fr</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR8548" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"> <idno type="IdRef">02636817X</idno>
<idno type="ISNI">0000000122597504</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc> <address> <country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-454310" type="direct"><org type="laboratory" xml:id="struct-454310" status="VALID"><orgName>Inria de Paris</orgName>
<desc><address><addrLine>2 rue Simone Iff -CS 42112 -75589 Paris Cedex 12</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/centre/paris</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
</affiliation>
</author>
<author><name sortKey="Sturmfels, Bernd" sort="Sturmfels, Bernd" uniqKey="Sturmfels B" first="Bernd" last="Sturmfels">Bernd Sturmfels</name>
<affiliation wicri:level="1"><hal:affiliation type="institution" xml:id="struct-300674" status="VALID"> <orgName>University of California [Berkeley]</orgName>
<desc> <address> <addrLine>Berkeley, CA</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.berkeley.edu/</ref>
</desc>
</hal:affiliation>
<country>États-Unis</country>
</affiliation>
</author>
<author><name sortKey="Canny, John" sort="Canny, John" uniqKey="Canny J" first="John" last="Canny">John Canny</name>
<affiliation wicri:level="1"><hal:affiliation type="institution" xml:id="struct-300674" status="VALID"> <orgName>University of California [Berkeley]</orgName>
<desc> <address> <addrLine>Berkeley, CA</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.berkeley.edu/</ref>
</desc>
</hal:affiliation>
<country>États-Unis</country>
</affiliation>
</author>
<author><name sortKey="Hebert, Martial" sort="Hebert, Martial" uniqKey="Hebert M" first="Martial" last="Hebert">Martial Hebert</name>
<affiliation wicri:level="1"><hal:affiliation type="institution" xml:id="struct-67135" status="VALID"> <orgName>Carnegie Mellon University [Pittsburgh]</orgName>
<orgName type="acronym">CMU</orgName>
<desc> <address> <addrLine>5000 Forbes Ave, Pittsburgh, PA 15213</addrLine>
<country key="US"></country>
</address>
<ref type="url">http://www.cmu.edu/</ref>
</desc>
</hal:affiliation>
<country>États-Unis</country>
</affiliation>
</author>
<author><name sortKey="Ponce, Jean" sort="Ponce, Jean" uniqKey="Ponce J" first="Jean" last="Ponce">Jean Ponce</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-454692" status="VALID"> <idno type="RNSR">200718311C</idno>
<orgName>Models of visual object recognition and scene understanding</orgName>
<orgName type="acronym">WILLOW</orgName>
<date type="start">2016-01-01</date>
<desc> <address> <country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/willow</ref>
</desc>
<listRelation> <relation active="#struct-25027" type="direct"></relation>
<relation active="#struct-59704" type="indirect"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation name="UMR8548" active="#struct-441569" type="indirect"></relation>
<relation active="#struct-454310" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-25027" type="direct"><org type="laboratory" xml:id="struct-25027" status="VALID"> <orgName>Département d'informatique de l'École normale supérieure</orgName>
<orgName type="acronym">DI-ENS</orgName>
<desc> <address> <addrLine>École normale supérieure 45 rue d'Ulm F-75230 Paris Cedex 05</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.di.ens.fr/</ref>
</desc>
<listRelation> <relation active="#struct-59704" type="direct"></relation>
<relation active="#struct-300009" type="direct"></relation>
<relation name="UMR8548" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-59704" type="indirect"><org type="institution" xml:id="struct-59704" status="VALID"> <orgName>École normale supérieure - Paris</orgName>
<orgName type="acronym">ENS Paris</orgName>
<desc> <address> <addrLine>45, Rue d'Ulm - 75230 Paris cedex 05</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.ens.fr</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR8548" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"> <idno type="IdRef">02636817X</idno>
<idno type="ISNI">0000000122597504</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc> <address> <country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-454310" type="direct"><org type="laboratory" xml:id="struct-454310" status="VALID"><orgName>Inria de Paris</orgName>
<desc><address><addrLine>2 rue Simone Iff -CS 42112 -75589 Paris Cedex 12</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/centre/paris</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
</affiliation>
</author>
</analytic>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass></textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">The rational camera model recently introduced in [19] provides a general methodology for studying abstract nonlinear imaging systems and their multi-view geometry. This paper builds on this framework to study "physical realizations" of rational cameras. More precisely, we give an explicit account of the mapping between between physical visual rays and image points (missing in the original description), which allows us to give simple analytical expressions for direct and inverse projections. We also consider "primitive" camera models, that are orbits under the action of various projective transformations, and lead to a general notion of intrinsic parameters. The methodology is general, but it is illustrated concretely by an in-depth study of two-slit cameras, that we model using pairs of linear projections. This simple analytical form allows us to describe models for the corresponding primitive cameras, to introduce intrinsic parameters with a clear geometric meaning, and to define an epipolar tensor characterizing two-view correspondences. In turn, this leads to new algorithms for structure from motion and self-calibration.</div>
</front>
</TEI>
<affiliations><list><country><li>France</li>
<li>États-Unis</li>
</country>
</list>
<tree><country name="France"><noRegion><name sortKey="Trager, Matthew" sort="Trager, Matthew" uniqKey="Trager M" first="Matthew" last="Trager">Matthew Trager</name>
</noRegion>
<name sortKey="Ponce, Jean" sort="Ponce, Jean" uniqKey="Ponce J" first="Jean" last="Ponce">Jean Ponce</name>
</country>
<country name="États-Unis"><noRegion><name sortKey="Sturmfels, Bernd" sort="Sturmfels, Bernd" uniqKey="Sturmfels B" first="Bernd" last="Sturmfels">Bernd Sturmfels</name>
</noRegion>
<name sortKey="Canny, John" sort="Canny, John" uniqKey="Canny J" first="John" last="Canny">John Canny</name>
<name sortKey="Hebert, Martial" sort="Hebert, Martial" uniqKey="Hebert M" first="Martial" last="Hebert">Martial Hebert</name>
</country>
</tree>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Amérique/explor/PittsburghV1/Data/France/Analysis
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000009 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/France/Analysis/biblio.hfd -nk 000009 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Amérique |area= PittsburghV1 |flux= France |étape= Analysis |type= RBID |clé= Hal:hal-01506996 |texte= General models for rational cameras and the case of two-slit projections }}
This area was generated with Dilib version V0.6.38. |