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Analysis of a New Nonlinear Subdivision Scheme. Applications in Image Processing

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Abstract

A nonlinear multiresolution scheme within Harten's framework is presented, based on a new nonlinear, centered piecewise polynomial interpolation technique. Analytical properties of the resulting subdivision scheme, such as convergence, smoothness, and stability, are studied. The stability and the compression properties of the associated multiresolution transform are demonstrated on several numerical experiments on images.

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Authors and Affiliations

  1. Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Spain

    Sergio Amat & J. Carlos Trillo

  2. Departament de Matematica Aplicada, Universitat de Valencia, Spain

    Rosa Donat

  3. Ecole Generaliste d'Ingenieurs de Marseille (EGIM), Laboratoire d'Analyse Topologie et Probabilites (LATP), France

    Jacques Liandrat

Authors
  1. Sergio Amat
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  2. Rosa Donat
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  3. Jacques Liandrat
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  4. J. Carlos Trillo
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Correspondence to Sergio Amat, Rosa Donat, Jacques Liandrat or J. Carlos Trillo.

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Amat, S., Donat, R., Liandrat, J. et al. Analysis of a New Nonlinear Subdivision Scheme. Applications in Image Processing. Found Comput Math 6, 193–225 (2006). https://doi.org/10.1007/s10208-004-0122-5

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  • DOI: https://doi.org/10.1007/s10208-004-0122-5

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