Guest Editorial: Scale-Space and Variational Methods

Journal of Mathematical Imaging and Vision, Aug 2016

Jean-Francois Aujol, Mila Nikolova, Nicolas Papadakis

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Guest Editorial: Scale-Space and Variational Methods

Guest Editorial: Scale-Space and Variational Methods Jean-Francois Aujol 0 1 Mila Nikolova 0 1 Nicolas Papadakis 0 1 Mila Nikolova 0 1 0 CMLA, ENS Cachan, CNRS, Université Paris-Saclay , 94235 Cachan , France 1 Nicolas Papadakis - 1 Institut Universitaire de France, Institut de Mathématiques de Bordeaux, Université de Bordeaux, Talence Cedex, France 3 Institut de Mathématiques de Bordeaux, CNRS, Université de Bordeaux, Talence Cedex, France algorithm to solve regularization problems involving parameterized non-convex regularizers by turning them into convex one. Looking at continuous optimization problems from a discrete point of view is a natural consideration when dealing with images that are essentially discrete data. This makes possible the use of tools devoted to discrete objects, as proposed in “Multicuts and Perturb & MAP for Probabilistic Graph Clustering” (doi:10.1007/s10851-016-0659-3) by J. H. Kappes, P. Swoboda, B. Savchynskyy, T. Hazan and C. Schnörr, where a graph clustering algorithm is proposed using globally optimal MAP inference by integer programming and perturbation-based approximations of the log-partition function. A famous hot topic in image processing these last years is the use of optimal transport to deal with images (in particular with image histograms). In “A Sparse Multiscale Algorithm for Dense Optimal Transport” (doi:10.1007/ s10851-016-0653-9), B. Schmitzer proposes a novel method to deal with large-scale dense optimal transport with a sparse and fast multiscale strategy that exploits the geometric structure of the cost function. Image processing research also shares strong links with movie industries that keep calling for new methods to analyze and or synthesize images and videos with fast and efficient approaches. In this context, L. Raad, A. Desolneux, and J.-M. Morel propose in “A Conditional Multiscale Locally Gaussian Texture Synthesis Algorithm” (doi:10. 1007/s10851-016-0656-6) a method for the synthesis of locally Gaussian textures using a multiscale approach. Relying on the modeling of texture self-similarity with conditional Gaussian distributions in the patch space, this new approach is able to extend the use of stitching techniques. In the work “A Variational Aggregation Framework for Patch-Based Optical Flow Estimation” (doi:10.1007/ J Math Imaging Vis s10851-016-0664-6 ) by D. Fortun , P. Bouthemy , and C. Kervrann , an original variational approach merging parametric motion models and patch-based motion candidates is designed to capture large displacements without requiring any coarse-to-fine strategy . A natural counter-part to variational approaches is PDEs ones . In “ Nonlinear Spectral Analysis via One-Homogeneous Functionals-Overview and Future Prospects” (doi:10.1007/ s10851-016-0665-5), G. Gilboa, M. Moeller , and M. Burger introduce new ideas as well as new scale-space concepts to realize nonlinear spectral analysis of images, via PDEs derived from one-homogeneous functionals . The focus in “Multivariate Median Filters and Partial Differential Equations” (doi:10.1007/s10851-016-0645-9) by M. Welk is to approximate the mean curvature motion PDE for multichannel images using filtering. The author explores the affine equivariants Oja and transformationretransformation L1 medians. He derives the corresponding PDEs and gives their geometric interpretation . In “Morphological Counterparts of Linear Shift-Invariant Scale-Spaces” (doi:10.1007/s10851-016-0646-8), M. Schmidt and J. Weickert establish a formal connection between linear shift-invariant and morphological systems, which finally closes the gap between them. Thus, any evolution equation from the first system can be translated to its counterpart in the second system, and vice versa. Their approach is based on the symbols of the (pseudo)differential operators corresponding to scale-space representations .

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Jean-Francois Aujol, Mila Nikolova, Nicolas Papadakis. Guest Editorial: Scale-Space and Variational Methods, Journal of Mathematical Imaging and Vision, 2016, 173-174, DOI: 10.1007/s10851-016-0679-z