Fractal structure in the color distribution of natural images

The colorimetric organization of RGB color images is investigated through the computation of the correlation integral of their three-dimensional histogram. For natural color images, as a common behavior, the correlation integral is found to follow a power law, with a noninteger exponent characteristic of a given image. This behavior identifies a fractal or multiscale self-similar distribution of the colors contained in typical natural images. This finding of a possible fractal structure in the colorimetric organization of natural images complement other fractal properties previously observed in their spatial organization. Such fractal colorimetric properties may be helpful to the characterization and modeling of natural images, and may contribute to progress in vision

Fractal capacity dimension of three-dimensional histogram from color images

To contribute to the important task of characterizing the complex multidimensional structure of natural images, a fractal characterization is proposed for the colorimetric organization of natural color images. This is realized from their three-dimensional RGB color histogram, by applying a box-counting procedure to assess the dimensionality of its support. Regular scaling emerges, almost linear over the whole range of accessible scales, and with non-integer slope in log-log allowing the definition of a capacity dimension for the histogram. This manifests a fractal colorimetric organization with a self-similar structure of the color palette typically composing natural images. Such a fractal characterization complements other previously known fractal properties of natural images, some reported recently in their colorimetric organization, and others reported more classically in their spatial organization. Such fractal multiscale features uncovered in natural images provide helpful clues relevant to image modeling, processing and visual perception

Multifractal analysis of three-dimensional histogram from color images

Natural images, especially color or multicomponent images, are complex information-carrying signals. To contribute to the characterization of this complexity, we investigate the possibility of multiscale organization in the colorimetric structure of natural images. This is realized by means of a multifractal analysis applied to the three-dimensional histogram from natural color images. The observed behaviors are confronted to those of reference models with known multifractal properties. We use for this purpose synthetic random images with trivial monofractal behavior, and multidimensional multiplicative cascades known for their actual multifractal behavior. The behaviors observed on natural images exhibit similarities with those of the multifractal multiplicative cascades and display the signature of elaborate multiscale organizations stemming from the histograms of natural color images. This type of characterization of colorimetric properties can be helpful to various tasks of digital image processing, as for instance modeling, classification, indexing

Fractal analysis tools for characterizing the colorimetric organization of digital image

The colorimetric organization of RGB color images is analyzed through the computation of algorithms which can characterize fractal organizations in the support and population of their three-dimensional color histogram. These algorithms have shown that complex organizations across scales exist in the colorimetric domain for natural images with often non-integer fractal dimension over a certain range of scale. In this paper, we applythis method of colorimetric characterization to synthetic images produced by rendering techniques of increasing sophistication. We show that the fractal or scale invariant signatures are more pronounced when the realism of the synthetic images increases. Such results could have interesting applications to improve the colorimetric realism of synthetic images. This also may contribute to progress in classification and vision, in using fractal colorimetric properties to differentiate natural and synthetic images

Interacting Multiple Try Algorithms with Different Proposal Distributions

We propose a new class of interacting Markov chain Monte Carlo (MCMC) algorithms designed for increasing the efficiency of a modified multiple-try Metropolis (MTM) algorithm. The extension with respect to the existing MCMC literature is twofold. The sampler proposed extends the basic MTM algorithm by allowing different proposal distributions in the multiple-try generation step. We exploit the structure of the MTM algorithm with different proposal distributions to naturally introduce an interacting MTM mechanism (IMTM) that expands the class of population Monte Carlo methods. We show the validity of the algorithm and discuss the choice of the selection weights and of the different proposals. We provide numerical studies which show that the new algorithm can perform better than the basic MTM algorithm and that the interaction mechanism allows the IMTM to efficiently explore the state space

Superfluid fraction in an interacting spatially modulated Bose-Einstein condensate

At zero temperature, a Galilean-invariant Bose fluid is expected to be fully superfluid. Here we investigate theoretically and experimentally the quenching of the superfluid density of a dilute Bose-Einstein condensate due to the breaking of translational (and thus Galilean) invariance by an external 1D periodic potential. Both Leggett's bound fixed by the knowledge of the total density and the anisotropy of the sound velocity provide a consistent determination of the superfluid fraction. The use of a large-period lattice emphasizes the important role of two-body interactions on superfluidity

Current paradigm of the 18-kDa translocator protein (TSPO) as a molecular target for PET imaging in neuroinflammation and neurodegenerative diseases

Neuroinflammation is a process characterised by drastic changes in microglial morphology and by marked upregulation of the 18-kDa translocator protein (TSPO) on the mitochondria. The continual increase in incidence of neuroinflammation and neurodegenerative diseases poses a major health issue in many countries, requiring more innovative diagnostic and monitoring tools. TSPO expression may constitute a biomarker for brain inflammation that could be monitored by using TSPO tracers as neuroimaging agents. From medical imaging perspectives, this review focuses on the current concepts related to the TSPO, and discusses briefly on the status of its PET imaging related to neuroinflammation and neurodegenerative diseases in humans