Bias–Variance Analysis for Controlling Adaptive Surface Meshes
Identifieur interne : 000298 ( UK/Analysis ); précédent : 000297; suivant : 000299Bias–Variance Analysis for Controlling Adaptive Surface Meshes
Auteurs : Richard C. Wilson [Royaume-Uni] ; Edwin R. Hancock [Royaume-Uni]Source :
- Computer Vision and Image Understanding [ 1077-3142 ] ; 1999.
Abstract
This paper presents a statistical methodology for exerting control over adaptive surface meshes. The goal is to develop an adaptive mesh which uses split and merge operations to control the distribution of planar or quadric surface patches. The novelty of the work reported in this paper is to focus on the variance–bias tradeoff that exists between the size of the fitted patches and their associated parameter variances. In particular, we provide an analysis which shows that there is an optimal patch area. This area offers the best compromise between the noise-variance, which decreases with increasing area, and the model-bias, which increases in a polynomial manner with area. The computed optimal areas of the local surface patches are used to exert control over the facets of the adaptive mesh. We use a series of split and merge operations to distribute the faces of the mesh so that each resembles as closely as possible its optimal area. In this way the mesh automatically selects its own density by adjusting the number of control-points or nodes. We provide experiments on both real and synthetic data. This experimentation demonstrates that our mesh is capable of efficiently representing high curvature surface detail.
Url:
DOI: 10.1006/cviu.1999.0810
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 000E78
- to stream Istex, to step Curation: 000C24
- to stream Istex, to step Checkpoint: 002285
- to stream Main, to step Merge: 002B22
- to stream Main, to step Curation: 002A53
- to stream Main, to step Exploration: 002A53
- to stream UK, to step Extraction: 000298
Links to Exploration step
ISTEX:DA03A21156ECACB73E5D52AE389DD2B41C96E4CALe document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Bias–Variance Analysis for Controlling Adaptive Surface Meshes</title><author><name sortKey="Wilson, Richard C" sort="Wilson, Richard C" uniqKey="Wilson R" first="Richard C." last="Wilson">Richard C. Wilson</name></author><author><name sortKey="Hancock, Edwin R" sort="Hancock, Edwin R" uniqKey="Hancock E" first="Edwin R." last="Hancock">Edwin R. Hancock</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:DA03A21156ECACB73E5D52AE389DD2B41C96E4CA</idno><date when="2000" year="2000">2000</date><idno type="doi">10.1006/cviu.1999.0810</idno><idno type="url">https://api.istex.fr/document/DA03A21156ECACB73E5D52AE389DD2B41C96E4CA/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000E78</idno><idno type="wicri:Area/Istex/Curation">000C24</idno><idno type="wicri:Area/Istex/Checkpoint">002285</idno><idno type="wicri:doubleKey">1077-3142:2000:Wilson R:bias:variance:analysis</idno><idno type="wicri:Area/Main/Merge">002B22</idno><idno type="wicri:Area/Main/Curation">002A53</idno><idno type="wicri:Area/Main/Exploration">002A53</idno><idno type="wicri:Area/UK/Extraction">000298</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Bias–Variance Analysis for Controlling Adaptive Surface Meshes</title><author><name sortKey="Wilson, Richard C" sort="Wilson, Richard C" uniqKey="Wilson R" first="Richard C." last="Wilson">Richard C. Wilson</name><affiliation wicri:level="1"><country xml:lang="fr">Royaume-Uni</country><wicri:regionArea>Department of Computer Science, University of York, York, Y01 5DD</wicri:regionArea><wicri:noRegion>Y01 5DD</wicri:noRegion></affiliation></author><author><name sortKey="Hancock, Edwin R" sort="Hancock, Edwin R" uniqKey="Hancock E" first="Edwin R." last="Hancock">Edwin R. Hancock</name><affiliation wicri:level="1"><country xml:lang="fr">Royaume-Uni</country><wicri:regionArea>Department of Computer Science, University of York, York, Y01 5DD</wicri:regionArea><wicri:noRegion>Y01 5DD</wicri:noRegion></affiliation></author></analytic><monogr></monogr><series><title level="j">Computer Vision and Image Understanding</title><title level="j" type="abbrev">YCVIU</title><idno type="ISSN">1077-3142</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1999">1999</date><biblScope unit="volume">77</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="25">25</biblScope><biblScope unit="page" to="47">47</biblScope></imprint><idno type="ISSN">1077-3142</idno></series><idno type="istex">DA03A21156ECACB73E5D52AE389DD2B41C96E4CA</idno><idno type="DOI">10.1006/cviu.1999.0810</idno><idno type="PII">S1077-3142(99)90810-X</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">1077-3142</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">This paper presents a statistical methodology for exerting control over adaptive surface meshes. The goal is to develop an adaptive mesh which uses split and merge operations to control the distribution of planar or quadric surface patches. The novelty of the work reported in this paper is to focus on the variance–bias tradeoff that exists between the size of the fitted patches and their associated parameter variances. In particular, we provide an analysis which shows that there is an optimal patch area. This area offers the best compromise between the noise-variance, which decreases with increasing area, and the model-bias, which increases in a polynomial manner with area. The computed optimal areas of the local surface patches are used to exert control over the facets of the adaptive mesh. We use a series of split and merge operations to distribute the faces of the mesh so that each resembles as closely as possible its optimal area. In this way the mesh automatically selects its own density by adjusting the number of control-points or nodes. We provide experiments on both real and synthetic data. This experimentation demonstrates that our mesh is capable of efficiently representing high curvature surface detail.</div></front></TEI><affiliations><list><country><li>Royaume-Uni</li></country></list><tree><country name="Royaume-Uni"><noRegion><name sortKey="Wilson, Richard C" sort="Wilson, Richard C" uniqKey="Wilson R" first="Richard C." last="Wilson">Richard C. Wilson</name></noRegion><name sortKey="Hancock, Edwin R" sort="Hancock, Edwin R" uniqKey="Hancock E" first="Edwin R." last="Hancock">Edwin R. Hancock</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Musique/explor/MozartV1/Data/UK/Analysis
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000298 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/UK/Analysis/biblio.hfd -nk 000298 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Musique
|area= MozartV1
|flux= UK
|étape= Analysis
|type= RBID
|clé= ISTEX:DA03A21156ECACB73E5D52AE389DD2B41C96E4CA
|texte= Bias–Variance Analysis for Controlling Adaptive Surface Meshes
}}
| This area was generated with Dilib version V0.6.20. |  |