Combining Contrast Invariant L1 Data Fidelities with Nonlinear Spectral Image Decomposition

This paper focuses on multi-scale approaches for variational methods and corresponding gradient flows. Recently, for convex regularization functionals such as total variation, new theory and algorithms for nonlinear eigenvalue problems via nonlinear spectral decompositions have been developed. Those methods open new directions for advanced image filtering. However, for an effective use in image segmentation and shape decomposition, a clear interpretation of the spectral response regarding size and intensity scales is needed but lacking in current approaches. In this context, $L^1$ data fidelities are particularly helpful due to their interesting multi-scale properties such as contrast invariance. Hence, the novelty of this work is the combination of $L^1$-based multi-scale methods with nonlinear spectral decompositions. We compare $L^1$ with $L^2$ scale-space methods in view of spectral image representation and decomposition. We show that the contrast invariant multi-scale behavior of $L^1-TV$ promotes sparsity in the spectral response providing more informative decompositions. We provide a numerical method and analyze synthetic and biomedical images at which decomposition leads to improved segmentation.Comment: 13 pages, 7 figures, conference SSVM 201

A subdivision scheme for continuous-scale B-splines and affine invariant progressive

Caption title.Includes bibliographical references (p. 19-22).Partially supported by the Rothschild Foundation-Yad Hanadiv. Partially supported by the Army Research Office. DAAL03-92-G-0115Guillermo Sapiro, Albert Cohen, Alfred M. Bruckstein

Polarized wavelets and curvelets on the sphere

The statistics of the temperature anisotropies in the primordial cosmic microwave background radiation field provide a wealth of information for cosmology and for estimating cosmological parameters. An even more acute inference should stem from the study of maps of the polarization state of the CMB radiation. Measuring the extremely weak CMB polarization signal requires very sensitive instruments. The full-sky maps of both temperature and polarization anisotropies of the CMB to be delivered by the upcoming Planck Surveyor satellite experiment are hence being awaited with excitement. Multiscale methods, such as isotropic wavelets, steerable wavelets, or curvelets, have been proposed in the past to analyze the CMB temperature map. In this paper, we contribute to enlarging the set of available transforms for polarized data on the sphere. We describe a set of new multiscale decompositions for polarized data on the sphere, including decimated and undecimated Q-U or E-B wavelet transforms and Q-U or E-B curvelets. The proposed transforms are invertible and so allow for applications in data restoration and denoising.Comment: Accepted. Full paper will figures available at http://jstarck.free.fr/aa08_pola.pd

Advances in Hyperspectral Image Classification: Earth monitoring with statistical learning methods

Hyperspectral images show similar statistical properties to natural grayscale or color photographic images. However, the classification of hyperspectral images is more challenging because of the very high dimensionality of the pixels and the small number of labeled examples typically available for learning. These peculiarities lead to particular signal processing problems, mainly characterized by indetermination and complex manifolds. The framework of statistical learning has gained popularity in the last decade. New methods have been presented to account for the spatial homogeneity of images, to include user's interaction via active learning, to take advantage of the manifold structure with semisupervised learning, to extract and encode invariances, or to adapt classifiers and image representations to unseen yet similar scenes. This tutuorial reviews the main advances for hyperspectral remote sensing image classification through illustrative examples.Comment: IEEE Signal Processing Magazine, 201

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference