We propose here a class of restoration algorithms for color images, based upon the Mumford-Shah (MS) model and nonlocal image information. The Ambrosio-Tortorelli and Shah elliptic approximations are defined to work in a small local neighborhood, which are sufficient to denoise smooth regions with sharp boundaries. However, texture is nonlocal in nature and requires semilocal/non-local information for efficient image denoising and restoration. Inspired from recent works (nonlocal means of Buades, Coll, Morel, and nonlocal total variation of Gilboa, Osher), we extend the local Ambrosio-Tortorelli and Shah approximations to MS functional (MS) to novel nonlocal formulations, for better restoration of fine structures and texture. We present several applications of the proposed nonlocal MS regularizers in image processing such as color image denoising, color image deblurring in the presence of Gaussian or impulse noise, color image inpainting, color image super-resolution, and color filter array demosaicing. In all the applications, the proposed nonlocal regularizers produce superior results over the local ones, especially in image inpainting with large missing regions. We also prove several characterizations of minimizers based upon dual norm formulations.

Abstract. This article introduces a new image segmentation method that makes use of non-local comparisons between pairs of patches of features. A non-local energy is defined by summing the interactions between pairs of patches inside and outside the segmented domain. A maximum radius of interaction can be adapted to fit the amount of variation of the features inside and outside the region to segment. This non-local energy is minimized using a level set approach. The corresponding curve evolution defines a non-local active contour that converges to a local minimum of our energy. In contrast to previous segmentation methods, this approach only requires a local homogeneity of the features inside and outside the region to segment. This does not impose a global homogeneity as required by region-based segmentation methods. This comparison principle is also less sensitive to initialization than edge-based approaches. We instantiate this novel framework using patches of intensity or color values as well as Gabor features. This allows us to segment regions with smoothly varying intensity or colors as well as well as complicated textures with a spatially varying local orientation.

A Gram-positive, rod-shaped, endospore-forming organism, strain BL3-6(T), was isolated from tidal flat sediments of the Yellow Sea in the region of Tae-An. A 16S rRNA gene sequence analysis demonstrated that this isolate belongs to the Bacillus cereus group, and is closely related to Bacillus mycoides (99.0% similarity), Bacillus thuringiensis (99.0%), Bacillus weihenstephanensis (99.0%), Bacillus cereus (98.9%), Bacillus anthracis (98.8%), and Bacillus pseudomycoides (98.1%). The phylogenetic distance from any validly described Bacillus species outside the Bacillus cereus group was less than 95.6%. The DNA G+C content of the strain was 39.4 mol% and the major respiratory quinone was menaquinone-7. The major cellular fatty acids were iso-C(14:0) (17.8%), iso-C(16:0) (15.8%), and iso-C(12:0) (11.3%). The diagnostic amino acid of the cell wall was meso-diaminopimelic acid and the major cell wall sugar was galactose. The results of DNA-DNA hybridization (<55.6%) and physiological and biochemical tests allowed genotypic and phenotypic differentiation of strain BL3-6(T) from the published Bacillus species. BL3-6(T) therefore represents a new species, for which the name Bacillus gaemokensis sp. nov. is proposed, with the type strain BL3-6(T) (=KCTC 13318(T) =JCM 15801(T)).

This article introduces a variational color image decomposition and restoration model. The aim is to recover an image from its degraded version, while simultaneously decomposing the image into its cartoon and texture components. The energy involves adaptive higher-order regularizers, incorporated with an edge indicator function. This not only helps cartoon and texture decomposition, but also provides higher quality image restoration by ameliorating the staircasing effect that arises in total variation regularization methods. To realize the proposed models, we present fast and efficient iterative algorithms based on a variable splitting scheme and an augmented Lagrangian method. A convergence analysis of the proposed algorithms is also presented under certain conditions. Numerical results and comparisons demonstrate that the proposed model is more effective than state-of-the-art methods for both image decomposition and restoration.