@inbook {IOPORT.05935874,
    author       = {Tschumperl\'e, David and Brun, Luc},
    title        = {Non-local regularization and registration of multi-valued images by PDE's and variational methods on higher dimensional spaces.},
    year         = {2011},
    booktitle    = {Computational optimization, methods and algorithms.},
    isbn         = {978-3-642-20858-4},
    pages        = {181-197},
    publisher    = {Berlin: Springer},
    doi          = {10.1007/978-3-642-19604-1_10},
    abstract     = {Summary: We are interested in a simple transform that maps 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.},
    identifier   = {05935874},
}