Total roto-translational variation View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03-16

AUTHORS

Antonin Chambolle, Thomas Pock

ABSTRACT

We consider curvature depending variational models for image regularization, such as Euler’s elastica. These models are known to provide strong priors for the continuity of edges and hence have important applications in shape- and image processing. We consider a lifted convex representation of these models in the roto-translation space: in this space, curvature depending variational energies are represented by means of a convex functional defined on divergence free vector fields. The line energies are then easily extended to any scalar function. It yields a natural generalization of the total variation to curvature-dependent energies. As our main result, we show that the proposed convex representation is tight for characteristic functions of smooth shapes. We also discuss cases where this representation fails. For numerical solution, we propose a staggered grid discretization based on an averaged Raviart–Thomas finite elements approximation. This discretization is consistent, up to minor details, with the underlying continuous model. The resulting non-smooth convex optimization problem is solved using a first-order primal-dual algorithm. We illustrate the results of our numerical algorithm on various problems from shape- and image processing. More... »

PAGES

1-56

References to SciGraph publications

  • 2017-05. Global Minimum for a Finsler Elastica Minimal Path Approach in INTERNATIONAL JOURNAL OF COMPUTER VISION
  • 2007. Asymptotic Properties of the Nitzberg-Mumford Variational Model for Segmentation with Depth in FREE BOUNDARY PROBLEMS
  • 2014-07. Understanding, Optimising, and Extending Data Compression with Anisotropic Diffusion in INTERNATIONAL JOURNAL OF COMPUTER VISION
  • 2015. Image Processing in the Semidiscrete Group of Rototranslations in GEOMETRIC SCIENCE OF INFORMATION
  • 2014-06. Association Fields via Cuspless Sub-Riemannian Geodesics in SE(2) in JOURNAL OF MATHEMATICAL IMAGING AND VISION
  • 1993. Filtering, Segmentation and Depth in NONE
  • 2016-09. On the ergodic convergence rates of a first-order primal–dual algorithm in MATHEMATICAL PROGRAMMING
  • 2005-09. On the approximation of the elastica functional in radial symmetry in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 2015. Alternating Direction Method of Multiplier for Euler’s Elastica-Based Denoising in SCALE SPACE AND VARIATIONAL METHODS IN COMPUTER VISION
  • 2011-05. A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging in JOURNAL OF MATHEMATICAL IMAGING AND VISION
  • 1987-03. Representation of local geometry in the visual system in BIOLOGICAL CYBERNETICS
  • 2009-12. Crossing-Preserving Coherence-Enhancing Diffusion on Invertible Orientation Scores in INTERNATIONAL JOURNAL OF COMPUTER VISION
  • 2016. Some Facts About Operator-Splitting and Alternating Direction Methods in SPLITTING METHODS IN COMMUNICATION, IMAGING, SCIENCE, AND ENGINEERING
  • 2017-06. Curvature-dependent Energies in MILAN JOURNAL OF MATHEMATICS
  • 2008-01. The symplectic structure of the primary visual cortex in BIOLOGICAL CYBERNETICS
  • 2003-01. Segmentation with Depth but Without Detecting Junctions in JOURNAL OF MATHEMATICAL IMAGING AND VISION
  • 2016. ADMM and Non-convex Variational Problems in SPLITTING METHODS IN COMMUNICATION, IMAGING, SCIENCE, AND ENGINEERING
  • 2013-11. Convex Relaxation of a Class of Vertex Penalizing Functionals in JOURNAL OF MATHEMATICAL IMAGING AND VISION
  • 2012-08. A Linear Framework for Region-Based Image Segmentation and Inpainting Involving Curvature Penalization in INTERNATIONAL JOURNAL OF COMPUTER VISION
  • 2012. On a Linear Programming Approach to the Discrete Willmore Boundary Value Problem and Generalizations in CURVES AND SURFACES
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00211-019-01026-w

    DOI

    http://dx.doi.org/10.1007/s00211-019-01026-w

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1112829522


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0103", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Numerical and Computational Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Centre de Math\u00e9matiques Appliqu\u00e9es", 
              "id": "https://www.grid.ac/institutes/grid.462265.1", 
              "name": [
                "CMAP, Ecole Polytechnique, CNRS, 91128, Palaiseau, France"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Chambolle", 
            "givenName": "Antonin", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Austrian Institute of Technology", 
              "id": "https://www.grid.ac/institutes/grid.4332.6", 
              "name": [
                "Institute for Computer Graphics and Vision, Graz University of Technology, 8010, Graz, Austria", 
                "Center for Vision, Automation and Control, AIT Austrian Institute of Technology GmbH, 1220, Vienna, Austria"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Pock", 
            "givenName": "Thomas", 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf00318371", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003867987", 
              "https://doi.org/10.1007/bf00318371"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00318371", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003867987", 
              "https://doi.org/10.1007/bf00318371"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11263-012-0518-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009460524", 
              "https://doi.org/10.1007/s11263-012-0518-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10851-010-0251-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010318529", 
              "https://doi.org/10.1007/s10851-010-0251-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-319-41589-5_2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010360211", 
              "https://doi.org/10.1007/978-3-319-41589-5_2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-27413-8_42", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011783284", 
              "https://doi.org/10.1007/978-3-642-27413-8_42"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10107-015-0957-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012909932", 
              "https://doi.org/10.1007/s10107-015-0957-3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10851-012-0347-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014012209", 
              "https://doi.org/10.1007/s10851-012-0347-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11263-014-0702-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014506349", 
              "https://doi.org/10.1007/s11263-014-0702-z"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1145/344779.344972", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017343760"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1515/dmvm-2012-0040", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017661175"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.na.2016.05.012", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018692034"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-319-41589-5_8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023565639", 
              "https://doi.org/10.1007/978-3-319-41589-5_8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00422-007-0194-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031206987", 
              "https://doi.org/10.1007/s00422-007-0194-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00422-007-0194-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031206987", 
              "https://doi.org/10.1007/s00422-007-0194-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00526-004-0312-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032338719", 
              "https://doi.org/10.1007/s00526-004-0312-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1021837026373", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033174574", 
              "https://doi.org/10.1023/a:1021837026373"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-319-25040-3_67", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033318547", 
              "https://doi.org/10.1007/978-3-319-25040-3_67"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11263-009-0213-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1037514354", 
              "https://doi.org/10.1007/s11263-009-0213-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0022-1236(88)90009-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038059297"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.anihpc.2004.01.001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040363104"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-7643-7719-9_8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044419344", 
              "https://doi.org/10.1007/978-3-7643-7719-9_8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.acha.2014.09.001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047169717"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10851-013-0475-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047615142", 
              "https://doi.org/10.1007/s10851-013-0475-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10851-013-0475-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047615142", 
              "https://doi.org/10.1007/s10851-013-0475-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1113/jphysiol.1959.sp006308", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047763294"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11263-016-0975-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051848059", 
              "https://doi.org/10.1007/s11263-016-0975-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11263-016-0975-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051848059", 
              "https://doi.org/10.1007/s11263-016-0975-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-319-18461-6_55", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052872562", 
              "https://doi.org/10.1007/978-3-319-18461-6_55"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1515/crll.1997.486.17", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053432615"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1017/s0956792502004904", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1054001663"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1051/cocv/2009004", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1056951756"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1051/cocv/2013082", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1056951983"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1051/cocv/2016073", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1056952185"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/83.935036", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1061240356"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/tip.2011.2118225", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1061642780"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/tip.2016.2545244", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1061644924"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/100803730", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062859201"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/120861667", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062868980"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/130924731", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062870906"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/130939493", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062871343"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/15m1013572", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062873489"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/15m1018460", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062873611"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/16m1063757", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062874517"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/s0036139901390088", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062874745"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/s1540345903422458", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062884844"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0218202504003143", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062962700"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2140/pjm.1971.39.439", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1069065133"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2140/pjm.1997.179.301", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1069070479"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2140/pjm.1997.179.301", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1069070479"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.3934/ipi.2013.7.1409", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1071739154"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4000/msh.2809", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1071850787"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4171/ifb/72", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072317634"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/jdg/1214458533", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1084460111"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00032-017-0265-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1084990180", 
              "https://doi.org/10.1007/s00032-017-0265-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00032-017-0265-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1084990180", 
              "https://doi.org/10.1007/s00032-017-0265-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.3934/ipi.2017001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1087287249"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.3934/ipi.2017001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1087287249"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/cvpr.2010.5540057", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1093517658"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/iccv.2007.4408973", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1094197282"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/iccv.2011.6126441", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1094870509"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/icip.1998.999016", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1095826280"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/1.9781611971088", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1098555842"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1512/iumj.2018.67.7393", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1106444640"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1109702577", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-56484-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1109702577", 
              "https://doi.org/10.1007/3-540-56484-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-56484-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1109702577", 
              "https://doi.org/10.1007/3-540-56484-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-56484-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1109702577", 
              "https://doi.org/10.1007/3-540-56484-5"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2019-03-16", 
        "datePublishedReg": "2019-03-16", 
        "description": "We consider curvature depending variational models for image regularization, such as Euler\u2019s elastica. These models are known to provide strong priors for the continuity of edges and hence have important applications in shape- and image processing. We consider a lifted convex representation of these models in the roto-translation space: in this space, curvature depending variational energies are represented by means of a convex functional defined on divergence free vector fields. The line energies are then easily extended to any scalar function. It yields a natural generalization of the total variation to curvature-dependent energies. As our main result, we show that the proposed convex representation is tight for characteristic functions of smooth shapes. We also discuss cases where this representation fails. For numerical solution, we propose a staggered grid discretization based on an averaged Raviart\u2013Thomas finite elements approximation. This discretization is consistent, up to minor details, with the underlying continuous model. The resulting non-smooth convex optimization problem is solved using a first-order primal-dual algorithm. We illustrate the results of our numerical algorithm on various problems from shape- and image processing.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s00211-019-01026-w", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isFundedItemOf": [
          {
            "id": "sg:grant.6208924", 
            "type": "MonetaryGrant"
          }, 
          {
            "id": "sg:grant.3861913", 
            "type": "MonetaryGrant"
          }, 
          {
            "id": "sg:grant.4056990", 
            "type": "MonetaryGrant"
          }
        ], 
        "isPartOf": [
          {
            "id": "sg:journal.1136759", 
            "issn": [
              "0029-599X", 
              "0945-3245"
            ], 
            "name": "Numerische Mathematik", 
            "type": "Periodical"
          }
        ], 
        "name": "Total roto-translational variation", 
        "pagination": "1-56", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "497f19ce3617b00a8b950c5ac4eae087a064d8d6ad9d81151003f2766ec9e28e"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00211-019-01026-w"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1112829522"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00211-019-01026-w", 
          "https://app.dimensions.ai/details/publication/pub.1112829522"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T12:05", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000360_0000000360/records_118321_00000001.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs00211-019-01026-w"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00211-019-01026-w'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00211-019-01026-w'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00211-019-01026-w'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00211-019-01026-w'


     

    This table displays all metadata directly associated to this object as RDF triples.

    266 TRIPLES      21 PREDICATES      83 URIs      16 LITERALS      5 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00211-019-01026-w schema:about anzsrc-for:01
    2 anzsrc-for:0103
    3 schema:author Nc10cc90c5d704edb955a4c5d2c6e4942
    4 schema:citation sg:pub.10.1007/3-540-56484-5
    5 sg:pub.10.1007/978-3-319-18461-6_55
    6 sg:pub.10.1007/978-3-319-25040-3_67
    7 sg:pub.10.1007/978-3-319-41589-5_2
    8 sg:pub.10.1007/978-3-319-41589-5_8
    9 sg:pub.10.1007/978-3-642-27413-8_42
    10 sg:pub.10.1007/978-3-7643-7719-9_8
    11 sg:pub.10.1007/bf00318371
    12 sg:pub.10.1007/s00032-017-0265-x
    13 sg:pub.10.1007/s00422-007-0194-9
    14 sg:pub.10.1007/s00526-004-0312-7
    15 sg:pub.10.1007/s10107-015-0957-3
    16 sg:pub.10.1007/s10851-010-0251-1
    17 sg:pub.10.1007/s10851-012-0347-x
    18 sg:pub.10.1007/s10851-013-0475-y
    19 sg:pub.10.1007/s11263-009-0213-5
    20 sg:pub.10.1007/s11263-012-0518-7
    21 sg:pub.10.1007/s11263-014-0702-z
    22 sg:pub.10.1007/s11263-016-0975-5
    23 sg:pub.10.1023/a:1021837026373
    24 https://app.dimensions.ai/details/publication/pub.1109702577
    25 https://doi.org/10.1016/0022-1236(88)90009-2
    26 https://doi.org/10.1016/j.acha.2014.09.001
    27 https://doi.org/10.1016/j.anihpc.2004.01.001
    28 https://doi.org/10.1016/j.na.2016.05.012
    29 https://doi.org/10.1017/s0956792502004904
    30 https://doi.org/10.1051/cocv/2009004
    31 https://doi.org/10.1051/cocv/2013082
    32 https://doi.org/10.1051/cocv/2016073
    33 https://doi.org/10.1109/83.935036
    34 https://doi.org/10.1109/cvpr.2010.5540057
    35 https://doi.org/10.1109/iccv.2007.4408973
    36 https://doi.org/10.1109/iccv.2011.6126441
    37 https://doi.org/10.1109/icip.1998.999016
    38 https://doi.org/10.1109/tip.2011.2118225
    39 https://doi.org/10.1109/tip.2016.2545244
    40 https://doi.org/10.1113/jphysiol.1959.sp006308
    41 https://doi.org/10.1137/1.9781611971088
    42 https://doi.org/10.1137/100803730
    43 https://doi.org/10.1137/120861667
    44 https://doi.org/10.1137/130924731
    45 https://doi.org/10.1137/130939493
    46 https://doi.org/10.1137/15m1013572
    47 https://doi.org/10.1137/15m1018460
    48 https://doi.org/10.1137/16m1063757
    49 https://doi.org/10.1137/s0036139901390088
    50 https://doi.org/10.1137/s1540345903422458
    51 https://doi.org/10.1142/s0218202504003143
    52 https://doi.org/10.1145/344779.344972
    53 https://doi.org/10.1512/iumj.2018.67.7393
    54 https://doi.org/10.1515/crll.1997.486.17
    55 https://doi.org/10.1515/dmvm-2012-0040
    56 https://doi.org/10.2140/pjm.1971.39.439
    57 https://doi.org/10.2140/pjm.1997.179.301
    58 https://doi.org/10.3934/ipi.2013.7.1409
    59 https://doi.org/10.3934/ipi.2017001
    60 https://doi.org/10.4000/msh.2809
    61 https://doi.org/10.4171/ifb/72
    62 https://doi.org/10.4310/jdg/1214458533
    63 schema:datePublished 2019-03-16
    64 schema:datePublishedReg 2019-03-16
    65 schema:description We consider curvature depending variational models for image regularization, such as Euler’s elastica. These models are known to provide strong priors for the continuity of edges and hence have important applications in shape- and image processing. We consider a lifted convex representation of these models in the roto-translation space: in this space, curvature depending variational energies are represented by means of a convex functional defined on divergence free vector fields. The line energies are then easily extended to any scalar function. It yields a natural generalization of the total variation to curvature-dependent energies. As our main result, we show that the proposed convex representation is tight for characteristic functions of smooth shapes. We also discuss cases where this representation fails. For numerical solution, we propose a staggered grid discretization based on an averaged Raviart–Thomas finite elements approximation. This discretization is consistent, up to minor details, with the underlying continuous model. The resulting non-smooth convex optimization problem is solved using a first-order primal-dual algorithm. We illustrate the results of our numerical algorithm on various problems from shape- and image processing.
    66 schema:genre research_article
    67 schema:inLanguage en
    68 schema:isAccessibleForFree false
    69 schema:isPartOf sg:journal.1136759
    70 schema:name Total roto-translational variation
    71 schema:pagination 1-56
    72 schema:productId N571a4d902421454bbb059c846aac0e6f
    73 N91a566ecee36486a8c3a035ac672a57d
    74 Ncaf22b13b85c4761a5f79e8fe1f670d1
    75 schema:sameAs https://app.dimensions.ai/details/publication/pub.1112829522
    76 https://doi.org/10.1007/s00211-019-01026-w
    77 schema:sdDatePublished 2019-04-11T12:05
    78 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    79 schema:sdPublisher N9fa6138d83e84c3a8df115668daa3073
    80 schema:url https://link.springer.com/10.1007%2Fs00211-019-01026-w
    81 sgo:license sg:explorer/license/
    82 sgo:sdDataset articles
    83 rdf:type schema:ScholarlyArticle
    84 N00068051d94f4d43add23453d0d60125 schema:affiliation https://www.grid.ac/institutes/grid.4332.6
    85 schema:familyName Pock
    86 schema:givenName Thomas
    87 rdf:type schema:Person
    88 N571a4d902421454bbb059c846aac0e6f schema:name readcube_id
    89 schema:value 497f19ce3617b00a8b950c5ac4eae087a064d8d6ad9d81151003f2766ec9e28e
    90 rdf:type schema:PropertyValue
    91 N91a566ecee36486a8c3a035ac672a57d schema:name dimensions_id
    92 schema:value pub.1112829522
    93 rdf:type schema:PropertyValue
    94 N96f501efec0e415d93bf5c60d3ea06af schema:affiliation https://www.grid.ac/institutes/grid.462265.1
    95 schema:familyName Chambolle
    96 schema:givenName Antonin
    97 rdf:type schema:Person
    98 N9fa6138d83e84c3a8df115668daa3073 schema:name Springer Nature - SN SciGraph project
    99 rdf:type schema:Organization
    100 Nc10cc90c5d704edb955a4c5d2c6e4942 rdf:first N96f501efec0e415d93bf5c60d3ea06af
    101 rdf:rest Nd0318c41125e4e71bc4db37624e5b5d4
    102 Ncaf22b13b85c4761a5f79e8fe1f670d1 schema:name doi
    103 schema:value 10.1007/s00211-019-01026-w
    104 rdf:type schema:PropertyValue
    105 Nd0318c41125e4e71bc4db37624e5b5d4 rdf:first N00068051d94f4d43add23453d0d60125
    106 rdf:rest rdf:nil
    107 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    108 schema:name Mathematical Sciences
    109 rdf:type schema:DefinedTerm
    110 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
    111 schema:name Numerical and Computational Mathematics
    112 rdf:type schema:DefinedTerm
    113 sg:grant.3861913 http://pending.schema.org/fundedItem sg:pub.10.1007/s00211-019-01026-w
    114 rdf:type schema:MonetaryGrant
    115 sg:grant.4056990 http://pending.schema.org/fundedItem sg:pub.10.1007/s00211-019-01026-w
    116 rdf:type schema:MonetaryGrant
    117 sg:grant.6208924 http://pending.schema.org/fundedItem sg:pub.10.1007/s00211-019-01026-w
    118 rdf:type schema:MonetaryGrant
    119 sg:journal.1136759 schema:issn 0029-599X
    120 0945-3245
    121 schema:name Numerische Mathematik
    122 rdf:type schema:Periodical
    123 sg:pub.10.1007/3-540-56484-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1109702577
    124 https://doi.org/10.1007/3-540-56484-5
    125 rdf:type schema:CreativeWork
    126 sg:pub.10.1007/978-3-319-18461-6_55 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052872562
    127 https://doi.org/10.1007/978-3-319-18461-6_55
    128 rdf:type schema:CreativeWork
    129 sg:pub.10.1007/978-3-319-25040-3_67 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033318547
    130 https://doi.org/10.1007/978-3-319-25040-3_67
    131 rdf:type schema:CreativeWork
    132 sg:pub.10.1007/978-3-319-41589-5_2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010360211
    133 https://doi.org/10.1007/978-3-319-41589-5_2
    134 rdf:type schema:CreativeWork
    135 sg:pub.10.1007/978-3-319-41589-5_8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023565639
    136 https://doi.org/10.1007/978-3-319-41589-5_8
    137 rdf:type schema:CreativeWork
    138 sg:pub.10.1007/978-3-642-27413-8_42 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011783284
    139 https://doi.org/10.1007/978-3-642-27413-8_42
    140 rdf:type schema:CreativeWork
    141 sg:pub.10.1007/978-3-7643-7719-9_8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044419344
    142 https://doi.org/10.1007/978-3-7643-7719-9_8
    143 rdf:type schema:CreativeWork
    144 sg:pub.10.1007/bf00318371 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003867987
    145 https://doi.org/10.1007/bf00318371
    146 rdf:type schema:CreativeWork
    147 sg:pub.10.1007/s00032-017-0265-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1084990180
    148 https://doi.org/10.1007/s00032-017-0265-x
    149 rdf:type schema:CreativeWork
    150 sg:pub.10.1007/s00422-007-0194-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031206987
    151 https://doi.org/10.1007/s00422-007-0194-9
    152 rdf:type schema:CreativeWork
    153 sg:pub.10.1007/s00526-004-0312-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032338719
    154 https://doi.org/10.1007/s00526-004-0312-7
    155 rdf:type schema:CreativeWork
    156 sg:pub.10.1007/s10107-015-0957-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012909932
    157 https://doi.org/10.1007/s10107-015-0957-3
    158 rdf:type schema:CreativeWork
    159 sg:pub.10.1007/s10851-010-0251-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010318529
    160 https://doi.org/10.1007/s10851-010-0251-1
    161 rdf:type schema:CreativeWork
    162 sg:pub.10.1007/s10851-012-0347-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1014012209
    163 https://doi.org/10.1007/s10851-012-0347-x
    164 rdf:type schema:CreativeWork
    165 sg:pub.10.1007/s10851-013-0475-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1047615142
    166 https://doi.org/10.1007/s10851-013-0475-y
    167 rdf:type schema:CreativeWork
    168 sg:pub.10.1007/s11263-009-0213-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037514354
    169 https://doi.org/10.1007/s11263-009-0213-5
    170 rdf:type schema:CreativeWork
    171 sg:pub.10.1007/s11263-012-0518-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009460524
    172 https://doi.org/10.1007/s11263-012-0518-7
    173 rdf:type schema:CreativeWork
    174 sg:pub.10.1007/s11263-014-0702-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1014506349
    175 https://doi.org/10.1007/s11263-014-0702-z
    176 rdf:type schema:CreativeWork
    177 sg:pub.10.1007/s11263-016-0975-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051848059
    178 https://doi.org/10.1007/s11263-016-0975-5
    179 rdf:type schema:CreativeWork
    180 sg:pub.10.1023/a:1021837026373 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033174574
    181 https://doi.org/10.1023/a:1021837026373
    182 rdf:type schema:CreativeWork
    183 https://app.dimensions.ai/details/publication/pub.1109702577 schema:CreativeWork
    184 https://doi.org/10.1016/0022-1236(88)90009-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038059297
    185 rdf:type schema:CreativeWork
    186 https://doi.org/10.1016/j.acha.2014.09.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047169717
    187 rdf:type schema:CreativeWork
    188 https://doi.org/10.1016/j.anihpc.2004.01.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040363104
    189 rdf:type schema:CreativeWork
    190 https://doi.org/10.1016/j.na.2016.05.012 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018692034
    191 rdf:type schema:CreativeWork
    192 https://doi.org/10.1017/s0956792502004904 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054001663
    193 rdf:type schema:CreativeWork
    194 https://doi.org/10.1051/cocv/2009004 schema:sameAs https://app.dimensions.ai/details/publication/pub.1056951756
    195 rdf:type schema:CreativeWork
    196 https://doi.org/10.1051/cocv/2013082 schema:sameAs https://app.dimensions.ai/details/publication/pub.1056951983
    197 rdf:type schema:CreativeWork
    198 https://doi.org/10.1051/cocv/2016073 schema:sameAs https://app.dimensions.ai/details/publication/pub.1056952185
    199 rdf:type schema:CreativeWork
    200 https://doi.org/10.1109/83.935036 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061240356
    201 rdf:type schema:CreativeWork
    202 https://doi.org/10.1109/cvpr.2010.5540057 schema:sameAs https://app.dimensions.ai/details/publication/pub.1093517658
    203 rdf:type schema:CreativeWork
    204 https://doi.org/10.1109/iccv.2007.4408973 schema:sameAs https://app.dimensions.ai/details/publication/pub.1094197282
    205 rdf:type schema:CreativeWork
    206 https://doi.org/10.1109/iccv.2011.6126441 schema:sameAs https://app.dimensions.ai/details/publication/pub.1094870509
    207 rdf:type schema:CreativeWork
    208 https://doi.org/10.1109/icip.1998.999016 schema:sameAs https://app.dimensions.ai/details/publication/pub.1095826280
    209 rdf:type schema:CreativeWork
    210 https://doi.org/10.1109/tip.2011.2118225 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061642780
    211 rdf:type schema:CreativeWork
    212 https://doi.org/10.1109/tip.2016.2545244 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061644924
    213 rdf:type schema:CreativeWork
    214 https://doi.org/10.1113/jphysiol.1959.sp006308 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047763294
    215 rdf:type schema:CreativeWork
    216 https://doi.org/10.1137/1.9781611971088 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098555842
    217 rdf:type schema:CreativeWork
    218 https://doi.org/10.1137/100803730 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062859201
    219 rdf:type schema:CreativeWork
    220 https://doi.org/10.1137/120861667 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062868980
    221 rdf:type schema:CreativeWork
    222 https://doi.org/10.1137/130924731 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062870906
    223 rdf:type schema:CreativeWork
    224 https://doi.org/10.1137/130939493 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062871343
    225 rdf:type schema:CreativeWork
    226 https://doi.org/10.1137/15m1013572 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062873489
    227 rdf:type schema:CreativeWork
    228 https://doi.org/10.1137/15m1018460 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062873611
    229 rdf:type schema:CreativeWork
    230 https://doi.org/10.1137/16m1063757 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062874517
    231 rdf:type schema:CreativeWork
    232 https://doi.org/10.1137/s0036139901390088 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062874745
    233 rdf:type schema:CreativeWork
    234 https://doi.org/10.1137/s1540345903422458 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062884844
    235 rdf:type schema:CreativeWork
    236 https://doi.org/10.1142/s0218202504003143 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062962700
    237 rdf:type schema:CreativeWork
    238 https://doi.org/10.1145/344779.344972 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017343760
    239 rdf:type schema:CreativeWork
    240 https://doi.org/10.1512/iumj.2018.67.7393 schema:sameAs https://app.dimensions.ai/details/publication/pub.1106444640
    241 rdf:type schema:CreativeWork
    242 https://doi.org/10.1515/crll.1997.486.17 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053432615
    243 rdf:type schema:CreativeWork
    244 https://doi.org/10.1515/dmvm-2012-0040 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017661175
    245 rdf:type schema:CreativeWork
    246 https://doi.org/10.2140/pjm.1971.39.439 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069065133
    247 rdf:type schema:CreativeWork
    248 https://doi.org/10.2140/pjm.1997.179.301 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069070479
    249 rdf:type schema:CreativeWork
    250 https://doi.org/10.3934/ipi.2013.7.1409 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071739154
    251 rdf:type schema:CreativeWork
    252 https://doi.org/10.3934/ipi.2017001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1087287249
    253 rdf:type schema:CreativeWork
    254 https://doi.org/10.4000/msh.2809 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071850787
    255 rdf:type schema:CreativeWork
    256 https://doi.org/10.4171/ifb/72 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072317634
    257 rdf:type schema:CreativeWork
    258 https://doi.org/10.4310/jdg/1214458533 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084460111
    259 rdf:type schema:CreativeWork
    260 https://www.grid.ac/institutes/grid.4332.6 schema:alternateName Austrian Institute of Technology
    261 schema:name Center for Vision, Automation and Control, AIT Austrian Institute of Technology GmbH, 1220, Vienna, Austria
    262 Institute for Computer Graphics and Vision, Graz University of Technology, 8010, Graz, Austria
    263 rdf:type schema:Organization
    264 https://www.grid.ac/institutes/grid.462265.1 schema:alternateName Centre de Mathématiques Appliquées
    265 schema:name CMAP, Ecole Polytechnique, CNRS, 91128, Palaiseau, France
    266 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...