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Non-Local Regularization and Registration of Multi-Valued Images By PDE’s and Variational Methods on Higher Dimensional Spaces

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Mathematical Image Processing

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 5))

Abstract

We are interested in a simple transform that map any regular 2D multi-valued image into a high-dimensional Euler space of patches, so that each initial image patch is mapped as a single high-dimensional point. We propose a way to study the local geometry of this patch-projected image and we consider variational formulations and PDE’s in this particular space. Hence, we define a way to find natural patch-based counterparts of some classical image processing techniques, including Lucas–Kanade registration, Tikhonov regularization and tensor-driven anisotropic diffusion PDE’s. As a result, we end up with noteworthy variants of already known (non-variational) patch-based algorithms, namely the Non Local Means and Block Matching techniques. The interest of considering such variational or PDE approaches on high dimensional patch spaces is discussed and illustrated by comparison results with corresponding non-variational or non-patch methods.

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Authors and Affiliations

  1. Image Team, Laboratoire GREYC, 6 Bd Maréchal Juin, 14050, Caen Cedex, France

    David Tschumperlé & Luc Brun

Authors
  1. David Tschumperlé
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  2. Luc Brun
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Correspondence to David Tschumperlé .

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Editors and Affiliations

  1. , UMR 6628-MAPMO, Université d'Orléans, Orléans Cedex 2, 45067, France

    Maïtine Bergounioux

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Tschumperlé, D., Brun, L. (2011). Non-Local Regularization and Registration of Multi-Valued Images By PDE’s and Variational Methods on Higher Dimensional Spaces. In: Bergounioux, M. (eds) Mathematical Image Processing. Springer Proceedings in Mathematics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19604-1_10

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