An Adaptive Multi‐Grid Solver for Applications in Computer Graphics
A key processing step in numerous computer graphics applications is the solution of a linear system discretized over a spatial domain. Often, the linear system can be represented using an adaptive domain tessellation, either because the solution will only be sampled sparsely, or because the solution...
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| Veröffentlicht in: | Computer graphics forum 2019-02, Vol.38 (1), p.138-150 |
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| creator | Kazhdan, Misha Hoppe, Hugues |
| description | A key processing step in numerous computer graphics applications is the solution of a linear system discretized over a spatial domain. Often, the linear system can be represented using an adaptive domain tessellation, either because the solution will only be sampled sparsely, or because the solution is known to be ‘interesting’ (e.g. high frequency) only in localized regions. In this work, we propose an adaptive, finite elements, multi‐grid solver capable of efficiently solving such linear systems. Our solver is designed to be general‐purpose, supporting finite elements of different degrees, across different dimensions and supporting both integrated and pointwise constraints. We demonstrate the efficacy of our solver in applications including surface reconstruction, image stitching and Euclidean Distance Transform calculation.
A key processing step in numerous computer graphics applications is the solution of a linear system discretized over a spatial domain. Often, the linear system can be represented using an adaptive domain tessellation, either because the solution will only be sampled sparsely, or because the solution is known to be ‘interesting’ (e.g. high frequency) only in localized regions. In this work, we propose an adaptive, finite elements, multi‐grid solver capable of efficiently solving such linear systems. Our solver is designed to be general‐purpose, supporting finite elements of different degrees, across different dimensions and supporting both integrated and pointwise constraints. |
| doi_str_mv | 10.1111/cgf.13449 |
| format | Article |
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A key processing step in numerous computer graphics applications is the solution of a linear system discretized over a spatial domain. Often, the linear system can be represented using an adaptive domain tessellation, either because the solution will only be sampled sparsely, or because the solution is known to be ‘interesting’ (e.g. high frequency) only in localized regions. In this work, we propose an adaptive, finite elements, multi‐grid solver capable of efficiently solving such linear systems. Our solver is designed to be general‐purpose, supporting finite elements of different degrees, across different dimensions and supporting both integrated and pointwise constraints.</description><identifier>ISSN: 0167-7055</identifier><identifier>EISSN: 1467-8659</identifier><identifier>DOI: 10.1111/cgf.13449</identifier><language>eng</language><publisher>Oxford: Blackwell Publishing Ltd</publisher><subject>Adaptive systems ; Computer graphics ; Euclidean geometry ; I.3 Computing methodologies → Computer graphics ; Image reconstruction ; Linear systems ; matting & compositing ; numerical analysis ; Stitching ; surface reconstruction ; Tessellation</subject><ispartof>Computer graphics forum, 2019-02, Vol.38 (1), p.138-150</ispartof><rights>2018 The Authors Computer Graphics Forum © 2018 The Eurographics Association and John Wiley & Sons Ltd.</rights><rights>2019 The Eurographics Association and John Wiley & Sons Ltd.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3329-1e2e245ff38998cc3ca54662056af82264e5d77e48d4e07f891e6182d2ef9a4c3</citedby><cites>FETCH-LOGICAL-c3329-1e2e245ff38998cc3ca54662056af82264e5d77e48d4e07f891e6182d2ef9a4c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1111%2Fcgf.13449$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1111%2Fcgf.13449$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27901,27902,45550,45551</link.rule.ids></links><search><creatorcontrib>Kazhdan, Misha</creatorcontrib><creatorcontrib>Hoppe, Hugues</creatorcontrib><title>An Adaptive Multi‐Grid Solver for Applications in Computer Graphics</title><title>Computer graphics forum</title><description>A key processing step in numerous computer graphics applications is the solution of a linear system discretized over a spatial domain. Often, the linear system can be represented using an adaptive domain tessellation, either because the solution will only be sampled sparsely, or because the solution is known to be ‘interesting’ (e.g. high frequency) only in localized regions. In this work, we propose an adaptive, finite elements, multi‐grid solver capable of efficiently solving such linear systems. Our solver is designed to be general‐purpose, supporting finite elements of different degrees, across different dimensions and supporting both integrated and pointwise constraints. We demonstrate the efficacy of our solver in applications including surface reconstruction, image stitching and Euclidean Distance Transform calculation.
A key processing step in numerous computer graphics applications is the solution of a linear system discretized over a spatial domain. Often, the linear system can be represented using an adaptive domain tessellation, either because the solution will only be sampled sparsely, or because the solution is known to be ‘interesting’ (e.g. high frequency) only in localized regions. In this work, we propose an adaptive, finite elements, multi‐grid solver capable of efficiently solving such linear systems. Our solver is designed to be general‐purpose, supporting finite elements of different degrees, across different dimensions and supporting both integrated and pointwise constraints.</description><subject>Adaptive systems</subject><subject>Computer graphics</subject><subject>Euclidean geometry</subject><subject>I.3 Computing methodologies → Computer graphics</subject><subject>Image reconstruction</subject><subject>Linear systems</subject><subject>matting & compositing</subject><subject>numerical analysis</subject><subject>Stitching</subject><subject>surface reconstruction</subject><subject>Tessellation</subject><issn>0167-7055</issn><issn>1467-8659</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kLFOwzAQhi0EEqUw8AaRmBjS2o7t2GMUtQGpiAGYLcuxwVWaBDsp6sYj9Bl5Egxh5ZY76f_uTvoAuEZwgWIt9atdoIwQcQJmiLA85YyKUzCDKM45pPQcXISwhRCSnNEZWBVtUtSqH9zeJA9jM7ivz2PlXZ08dc3e-MR2Pin6vnFaDa5rQ-LapOx2_TjEsPKqf3M6XIIzq5pgrv76HLysV8_lXbp5rO7LYpPqLMMiRQYbTKi1GReCa51pRQljGFKmLMeYEUPrPDeE18TA3HKBDEMc19hYoYjO5uBmutv77n00YZDbbvRtfCkxEijjkHMSqduJ0r4LwRsre-92yh8kgvLHkoyW5K-lyC4n9sM15vA_KMtqPW18AxeEaEo</recordid><startdate>201902</startdate><enddate>201902</enddate><creator>Kazhdan, Misha</creator><creator>Hoppe, Hugues</creator><general>Blackwell Publishing Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>201902</creationdate><title>An Adaptive Multi‐Grid Solver for Applications in Computer Graphics</title><author>Kazhdan, Misha ; Hoppe, Hugues</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3329-1e2e245ff38998cc3ca54662056af82264e5d77e48d4e07f891e6182d2ef9a4c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Adaptive systems</topic><topic>Computer graphics</topic><topic>Euclidean geometry</topic><topic>I.3 Computing methodologies → Computer graphics</topic><topic>Image reconstruction</topic><topic>Linear systems</topic><topic>matting & compositing</topic><topic>numerical analysis</topic><topic>Stitching</topic><topic>surface reconstruction</topic><topic>Tessellation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kazhdan, Misha</creatorcontrib><creatorcontrib>Hoppe, Hugues</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computer graphics forum</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kazhdan, Misha</au><au>Hoppe, Hugues</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An Adaptive Multi‐Grid Solver for Applications in Computer Graphics</atitle><jtitle>Computer graphics forum</jtitle><date>2019-02</date><risdate>2019</risdate><volume>38</volume><issue>1</issue><spage>138</spage><epage>150</epage><pages>138-150</pages><issn>0167-7055</issn><eissn>1467-8659</eissn><abstract>A key processing step in numerous computer graphics applications is the solution of a linear system discretized over a spatial domain. Often, the linear system can be represented using an adaptive domain tessellation, either because the solution will only be sampled sparsely, or because the solution is known to be ‘interesting’ (e.g. high frequency) only in localized regions. In this work, we propose an adaptive, finite elements, multi‐grid solver capable of efficiently solving such linear systems. Our solver is designed to be general‐purpose, supporting finite elements of different degrees, across different dimensions and supporting both integrated and pointwise constraints. We demonstrate the efficacy of our solver in applications including surface reconstruction, image stitching and Euclidean Distance Transform calculation.
A key processing step in numerous computer graphics applications is the solution of a linear system discretized over a spatial domain. Often, the linear system can be represented using an adaptive domain tessellation, either because the solution will only be sampled sparsely, or because the solution is known to be ‘interesting’ (e.g. high frequency) only in localized regions. In this work, we propose an adaptive, finite elements, multi‐grid solver capable of efficiently solving such linear systems. Our solver is designed to be general‐purpose, supporting finite elements of different degrees, across different dimensions and supporting both integrated and pointwise constraints.</abstract><cop>Oxford</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1111/cgf.13449</doi><tpages>13</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Computer graphics forum, 2019-02, Vol.38 (1), p.138-150 |
| issn | 0167-7055 1467-8659 |
| language | eng |
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| source | Wiley Online Library Journals Frontfile Complete; EBSCOhost Business Source Complete |
| subjects | Adaptive systems Computer graphics Euclidean geometry I.3 Computing methodologies → Computer graphics Image reconstruction Linear systems matting & compositing numerical analysis Stitching surface reconstruction Tessellation |
| title | An Adaptive Multi‐Grid Solver for Applications in Computer Graphics |
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