PittsburghV1, France, Analysis, bibRecord, 000182

On Image Contours of Projective Shapes

Identifieur interne : 000182 ( France/Analysis ); précédent : 000181; suivant : 000183

On Image Contours of Projective Shapes

Auteurs : Jean Ponce [France] ; Martial Hebert [États-Unis]

Source :

RBID : Hal:hal-01053677

Abstract

This paper revisits classical properties of the outlines of solid shapes bounded by smooth surfaces, and shows that they can be established in a purely projective setting, without appealing to Euclidean measurements such as normals or curvatures. In particular, we give new synthetic proofs of Koenderink's famous theorem on convexities and concavities of the image contour, and of the fact that the rim turns in the same direction as the viewpoint in the tangent plane at a convex point, and in the opposite direction at a hyperbolic point. This suggests that projective geometry should not be viewed merely as an analytical device for linearizing calculations (its main role in structure from motion), but as the proper framework for studying the relation between solid shape and its perspective projections. Unlike previous work in this area, the proposed approach does not require an oriented setting, nor does it rely on any choice of coordinate system or analytical considerations.

Url:

https://hal.inria.fr/hal-01053677

Affiliations:

France, États-Unis

Links toward previous steps (curation, corpus...)

to stream Hal, to step Corpus: 000428
to stream Hal, to step Curation: 000428
to stream Hal, to step Checkpoint: 000202
to stream Main, to step Merge: 000693
to stream Main, to step Curation: 000693
to stream Main, to step Exploration: 000693
to stream France, to step Extraction: 000182

Links to Exploration step

Hal:hal-01053677

Le document en format XML

<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">On Image Contours of Projective Shapes</title>
<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="laboratory" xml:id="struct-1315" status="VALID"><orgName>Laboratoire d'informatique de l'école normale supérieure</orgName>
<orgName type="acronym">LIENS</orgName>
<desc><address><addrLine>45 Rue d'Ulm 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 name="UMR8548" active="#struct-441569" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-59704" type="direct"><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 name="UMR8548" active="#struct-441569" type="direct"><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>
</tutelles>
</hal:affiliation>
<country>France</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="laboratory" xml:id="struct-50083" status="VALID">          <orgName>The Robotics Institute</orgName>
          <desc>            <address>              <addrLine>5000 Forbes Avenue Pittsburgh PA 15213-3890</addrLine>
              <country key="US"></country>
            </address>
            <ref type="url">http://www.ri.cmu.edu/</ref>
          </desc>
          <listRelation>            <relation active="#struct-67135" type="direct"></relation>
          </listRelation>
        <tutelles><tutelle active="#struct-67135" type="direct"><org 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>
        </org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>États-Unis</country>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">HAL</idno>
<idno type="RBID">Hal:hal-01053677</idno>
<idno type="halId">hal-01053677</idno>
<idno type="halUri">https://hal.inria.fr/hal-01053677</idno>
<idno type="url">https://hal.inria.fr/hal-01053677</idno>
<date when="2014-09-06">2014-09-06</date>
<idno type="wicri:Area/Hal/Corpus">000428</idno>
<idno type="wicri:Area/Hal/Curation">000428</idno>
<idno type="wicri:Area/Hal/Checkpoint">000202</idno>
<idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">000202</idno>
<idno type="wicri:Area/Main/Merge">000693</idno>
<idno type="wicri:Area/Main/Curation">000693</idno>
<idno type="wicri:Area/Main/Exploration">000693</idno>
<idno type="wicri:Area/France/Extraction">000182</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en">On Image Contours of Projective Shapes</title>
<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="laboratory" xml:id="struct-1315" status="VALID"><orgName>Laboratoire d'informatique de l'école normale supérieure</orgName>
<orgName type="acronym">LIENS</orgName>
<desc><address><addrLine>45 Rue d'Ulm 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 name="UMR8548" active="#struct-441569" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-59704" type="direct"><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 name="UMR8548" active="#struct-441569" type="direct"><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>
</tutelles>
</hal:affiliation>
<country>France</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="laboratory" xml:id="struct-50083" status="VALID">          <orgName>The Robotics Institute</orgName>
          <desc>            <address>              <addrLine>5000 Forbes Avenue Pittsburgh PA 15213-3890</addrLine>
              <country key="US"></country>
            </address>
            <ref type="url">http://www.ri.cmu.edu/</ref>
          </desc>
          <listRelation>            <relation active="#struct-67135" type="direct"></relation>
          </listRelation>
        <tutelles><tutelle active="#struct-67135" type="direct"><org 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>
        </org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>États-Unis</country>
</affiliation>
</author>
</analytic>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass></textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">This paper revisits classical properties of the outlines of solid shapes bounded by smooth surfaces, and shows that they can be established in a purely projective setting, without appealing to Euclidean measurements such as normals or curvatures. In particular, we give new synthetic proofs of Koenderink's famous theorem on convexities and concavities of the image contour, and of the fact that the rim turns in the same direction as the viewpoint in the tangent plane at a convex point, and in the opposite direction at a hyperbolic point. This suggests that projective geometry should not be viewed merely as an analytical device for linearizing calculations (its main role in structure from motion), but as the proper framework for studying the relation between solid shape and its perspective projections. Unlike previous work in this area, the proposed approach does not require an oriented setting, nor does it rely on any choice of coordinate system or analytical considerations.</div>
</front>
</TEI>
<affiliations><list><country><li>France</li>
<li>États-Unis</li>
</country>
</list>
<tree><country name="France"><noRegion><name sortKey="Ponce, Jean" sort="Ponce, Jean" uniqKey="Ponce J" first="Jean" last="Ponce">Jean Ponce</name>
</noRegion>
</country>
<country name="États-Unis"><noRegion><name sortKey="Hebert, Martial" sort="Hebert, Martial" uniqKey="Hebert M" first="Martial" last="Hebert">Martial Hebert</name>
</noRegion>
</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 000182 | SxmlIndent | more

HfdSelect -h $EXPLOR_AREA/Data/France/Analysis/biblio.hfd -nk 000182 | 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-01053677
   |texte=   On Image Contours of Projective Shapes
}}

This area was generated with Dilib version V0.6.38.
Data generation: Fri Jun 18 17:37:45 2021. Site generation: Fri Jun 18 18:15:47 2021

	Serveur d'exploration sur Pittsburgh
	Attention, ce site est en cours de développement ! Attention, site généré par des moyens informatiques à partir de corpus bruts. Les informations ne sont donc pas validées.

Serveur d'exploration sur Pittsburgh

On Image Contours of Projective Shapes

On Image Contours of Projective Shapes

Source :

Abstract

Links toward previous steps (curation, corpus...)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri