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A Brief Survey on Semi-Lagrangian Schemes for Image Processing

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Innovations for Shape Analysis

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

In this survey we present some semi-Lagrangian schemes for the approximation of weak solutions of first and second order differential problems related to image processing and computer vision. The general framework is given by the theory of viscosity solutions and, in some cases, of calculus of variations. The schemes proposed here have interesting stability properties for evolutive problems since they allow for large time steps, can deal with degenerate problems and are more accurate if compared to standard finite difference/element methods of the same order. Several examples on classical problems will illustrate these properties.

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Authors and Affiliations

  1. Dipartimento di Matematica “G. Castelnuovo”, Sapienza – Università di Roma, P. Aldo Moro, 2, 00185, Roma, Italy

    Elisabetta Carlini, Maurizio Falcone & Adriano Festa

Authors
  1. Elisabetta Carlini
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  2. Maurizio Falcone
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  3. Adriano Festa
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Correspondence to Elisabetta Carlini .

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Editors and Affiliations

  1. , Inst. for Appl. Math.&Scient.Comp., Brandenburg Technical University, Platz der Deutschen Einheit 1, Cottbus, 03046, Germany

    Michael Breuß

  2. Department of Computer Science, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Alfred Bruckstein

  3. School of Electrical &, Computer Engineering, National Technical University of Athens, Athens, 15773, Greece

    Petros Maragos

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Carlini, E., Falcone, M., Festa, A. (2013). A Brief Survey on Semi-Lagrangian Schemes for Image Processing. In: Breuß, M., Bruckstein, A., Maragos, P. (eds) Innovations for Shape Analysis. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34141-0_9

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