Fractal descriptors based on Fourier spectrum applied to texture analysis

This work proposes the development and study of a novel technique lot the generation of fractal descriptors used in texture analysis. The novel descriptors are obtained from a multiscale transform applied to the Fourier technique of fractal dimension calculus. The power spectrum of the Fourier transform of the image is plotted against the frequency in a log-log scale and a multiscale transform is applied to this curve. The obtained values are taken as the fractal descriptors of the image. The validation of the proposal is performed by the use of the descriptors for the classification of a dataset of texture images whose real classes are previously known. The classification precision is compared to other fractal descriptors known in the literature. The results confirm the efficiency of the proposed method. (C) 2012 Elsevier B.V. All rights reserved.

Analytic perturbation theory for bound states in the transfer matrix spectrum of weakly correlated lattice ferromagnetic spin systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region ('beta' << 1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter 'alfa' = ('S POT.4') - 3 '(S POT.2') POT.2' > 0, i.e. in the region which we call Gaussian subjugation, where ('S POT.K') denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass -ln 'beta' and a bound state below the two-particle threshold. We develop a 'beta' analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in 'beta'.

Quantification of Retinal Neural Loss in Patients with Neuromyelitis Optica and Multiple Sclerosis with or without Optic Neuritis Using Fourier-Domain Optical Coherence Tomography

PURPOSE. We compared retinal nerve fiber layer (RNFL) and macular thickness measurements in patients with multiple sclerosis (MS) and neuromyelitis optica (NMO) with or without a history of optic neuritis, and in controls using Fourier-domain (FD) optical coherence tomography (OCT). METHODS. Patients with MS (n = 60), NMO (n = 33), longitudinal extensive transverse myelitis (LETM, n = 28) and healthy controls (n = 41) underwent ophthalmic examination, including automated perimetry, and FD-OCT RNFL and macular thickness measurements. Five groups of eyes were compared: MS with or without previous optic neuritis, NMO, LETM, and controls. Correlation between OCT and visual field (VF) findings was investigated. RESULTS. With regard to most parameters, RNFL and macular thickness measurements were significantly smaller in eyes of each group of patients compared to controls. MS eyes with optic neuritis did not differ significantly from MS eyes without optic neuritis, but measurements were smaller in NMO eyes than in all other groups. RNFL (but not macular thickness) measurements were significantly smaller in LETM eyes than in controls. While OCT abnormalities were correlated significantly with VF loss in NMO/LETM and MS, the correlation was much stronger in the former. CONCLUSIONS. Although FD-OCT RNFL and macular thickness measurements can reveal subclinical or optic neuritis-related abnormalities in NMO-spectrum and MS patients, abnormalities are predominant in the macula of MS patients and in RFNL measurements in NMO patients. The correlation between OCT and VF abnormalities was stronger in NMO than in MS, suggesting the two conditions differ regarding structural and functional damage. (ClinicalTrials.gov number, NCT01024985.) Invest Ophthalmol Vis Sci. 2012;53:3959-3966) DOI:10.1167/iovs.11-9324