Fractal temporal organisation of motricity is altered in major depression.

OBJECTIVE: Motor changes in major depression (MD) may represent potential markers of treatment response. Physiological rhythms (heart rate/gait cycle/hand movements) have been recently shown to be neither random nor regular but to display a fractal temporal organisation, possibly reflecting a unique central "internal clock" control. Sleep and mood circadian rhythm modifications observed in MD also suggest a role for this "internal clock". We set out to examine the fractal pattern of motor activity in MD. METHODS: Ten depressed patients (46±20 years) and ten age- and gender-matched healthy controls (48±21 years) underwent a 6-h ambulatory monitoring of spontaneous hand activity with a validated wireless device. Fractal scaling exponent (α) was analysed. An α value close to 1 means the pattern is fractal. RESULTS: Healthy controls displayed a fractal pattern of spontaneous motor hand activity (α: 1.0±0.1), whereas depressed patients showed an alteration of that pattern (α:1.2±0.15, p<0.01), towards a smoother organisation. CONCLUSION: The alteration of fractal pattern of hand activity by depression further supports the role of a central internal clock in the temporal organisation of movements. This novel way of studying motor changes in depression might have an important role in the detection of endophenotypes and potential predictors of treatment response.

GPS analysis of human locomotion: further evidence for long-range correlations in stride-to-stride fluctuations of gait parameters.

During free walking, gait is automatically adjusted to provide optimal mechanical output and minimal energy expenditure; gait parameters, such as cadence, fluctuate from one stride to the next around average values. It was described that this fluctuation exhibited long-range correlations and fractal-like patterns. In addition, it was suggested that these long-range correlations disappeared if the participant followed the beep of metronome to regulate his or her pace. Until now, these fractal fluctuations were only observed for stride interval, because no technique existed to adequately analyze an extended time of free walking. The aim of the present study was to measure walking speed (WS), step frequency (SF) and step length (SL) with high accuracy (<1 cm) satellite positioning method (global positioning system or GPS) in order to detect long-range correlations in the stride-to-stride fluctuations. Eight participants walked 30 min under free and constrained (metronome) conditions. Under free walking conditions, DFA (detrended fluctuation analysis) and surrogate data tests showed that the fluctuation of WS, SL and SF exhibited a fractal pattern (i.e., scaling exponent alpha: 0.5 < alpha < 1) in a large majority of participants (7/8). Under constrained conditions (metronome), SF fluctuations became significantly anti-correlated (alpha < 0.5) in all participants. However, the scaling exponent of SL and WS was not modified. We conclude that, when the walking pace is controlled by an auditory signal, the feedback loop between the planned movement (at supraspinal level) and the sensory inputs induces a continual shifting of SF around the mean (persistent anti-correlation), but with no effect on the fluctuation dynamics of the other parameters (SL, WS).

Dendritic branching of pyramidal cells in the visual cortex of the nocturnal owl monkey: A fractal analysis

The branching structure of neurones is thought to influence patterns of connectivity and how inputs are integrated within the arbor. Recent studies have revealed a remarkable degree of variation in the branching structure of pyramidal cells in the cerebral cortex of diurnal primates, suggesting regional specialization in neuronal function. Such specialization in pyramidal cell structure may be important for various aspects of visual function, such as object recognition and color processing. To better understand the functional role of regional variation in the pyramidal cell phenotype in visual processing, we determined the complexity of the dendritic branching pattern of pyramidal cells in visual cortex of the nocturnal New World owl monkey. We used the fractal dilation method to quantify the branching structure of pyramidal cells in the primary visual area (V1), the second visual area (V2) and the caudal and rostral subdivisions of inferotemporal cortex (ITc and ITr, respectively), which are often associated with color processing. We found that, as in diurnal monkeys, there was a trend for cells of increasing fractal dimension with progression through these cortical areas. The increasing complexity paralleled a trend for increasing symmetry. That we found a similar trend in both diurnal and nocturnal monkeys suggests that it was a feature of a common anthropoid ancestor.

Intrinsic fractal dynamics in the respiratory system by means of pressure-volume loops

This contribution presents novel concepts for analysis of pressure–volume curves, which offer information about the time domain dynamics of the respiratory system. The aim is to verify whether a mapping of the respiratory diseases can be obtained, allowing analysis of (dis)similarities between the dynamical pattern in the breathing in children. The groups investigated here are children, diagnosed as healthy, asthmatic, and cystic fibrosis. The pressure–volume curves have been measured by means of the noninvasive forced oscillation technique during breathing at rest. The geometrical fractal dimension is extracted from the pressure–volume curves and a power-law behavior is observed in the data. The power-law model coefficients are identified from the three sets and the results show that significant differences are present between the groups. This conclusion supports the idea that the respiratory system changes with disease in terms of airway geometry, tissue parameters, leading in turn to variations in the fractal dimension of the respiratory tree and its dynamics.

Modeling of fractal antennas

In this Master Thesis the characteristics of the chosen fractal microstrip antennas are investigated. For modeling has been used the structure of the square Serpinsky fractal curves. During the elaboration of this Master thesis the following steps were undertaken: 1) calculation and simulation of square microstrip antennа, 2) optimizing for obtaining the required characteristics on the frequency 2.5 GHz, 3) simulation and calculation of the second and third iteration of the Serpinsky fractal curves, 4) radiation patterns and intensity distribution of these antennas. In this Master’s Thesis the search for the optimal position of the port and fractal elements was conducted. These structures can be used in perspective for creation of antennas working at the same time in different frequency range.

Can the fractal dimension be applied for the early diagnosis of non-proliferative diabetic retinopathy?

The fractal dimension has been employed as a useful parameter in the diagnosis of retinal disease. Avakian et al. (Curr Eye Res 2002; 24: 274-280), comparing the vascular pattern of normal patients with mild to moderate non-proliferative diabetic retinopathy (NPDR), found a significant difference between them only in the macular region. This significant difference in the box-counting fractal dimension of the macular region between normal and mild NPDR patients has been proposed as a method of precocious diagnosis of NPDR. The aim of the present study was to determine if fractal dimensions can really be used as a parameter for the early diagnosis of NPDR. Box-counting and information fractal dimensions were used to parameterize the vascular pattern of the human retina. The two methods were applied to the whole retina and to nine anatomical regions of the retina in 5 individuals with mild NPDR and in 28 diabetic but opthalmically normal individuals (controls), with age between 31 and 86 years. All images of retina were obtained from the Digital Retinal Images for Vessel Extraction (DRIVE) database. The results showed that the fractal dimension parameter was not sensitive enough to be of use for an early diagnosis of NPDR.

Characterization and classification of tumor lesions using computerized fractal-based texture analysis and support vector machines in digital mammograms

Objective: This paper presents a detailed study of fractal-based methods for texture characterization of mammographic mass lesions and architectural distortion. The purpose of this study is to explore the use of fractal and lacunarity analysis for the characterization and classification of both tumor lesions and normal breast parenchyma in mammography. Materials and methods: We conducted comparative evaluations of five popular fractal dimension estimation methods for the characterization of the texture of mass lesions and architectural distortion. We applied the concept of lacunarity to the description of the spatial distribution of the pixel intensities in mammographic images. These methods were tested with a set of 57 breast masses and 60 normal breast parenchyma (dataset1), and with another set of 19 architectural distortions and 41 normal breast parenchyma (dataset2). Support vector machines (SVM) were used as a pattern classification method for tumor classification. Results: Experimental results showed that the fractal dimension of region of interest (ROIs) depicting mass lesions and architectural distortion was statistically significantly lower than that of normal breast parenchyma for all five methods. Receiver operating characteristic (ROC) analysis showed that fractional Brownian motion (FBM) method generated the highest area under ROC curve (A z = 0.839 for dataset1, 0.828 for dataset2, respectively) among five methods for both datasets. Lacunarity analysis showed that the ROIs depicting mass lesions and architectural distortion had higher lacunarities than those of ROIs depicting normal breast parenchyma. The combination of FBM fractal dimension and lacunarity yielded the highest A z value (0.903 and 0.875, respectively) than those based on single feature alone for both given datasets. The application of the SVM improved the performance of the fractal-based features in differentiating tumor lesions from normal breast parenchyma by generating higher A z value. Conclusion: FBM texture model is the most appropriate model for characterizing mammographic images due to self-affinity assumption of the method being a better approximation. Lacunarity is an effective counterpart measure of the fractal dimension in texture feature extraction in mammographic images. The classification results obtained in this work suggest that the SVM is an effective method with great potential for classification in mammographic image analysis.

Shape classification using complex network and Multi-scale Fractal Dimension

Shape provides one of the most relevant information about an object. This makes shape one of the most important visual attributes used to characterize objects. This paper introduces a novel approach for shape characterization, which combines modeling shape into a complex network and the analysis of its complexity in a dynamic evolution context. Descriptors computed through this approach show to be efficient in shape characterization, incorporating many characteristics, such as scale and rotation invariant. Experiments using two different shape databases (an artificial shapes database and a leaf shape database) are presented in order to evaluate the method. and its results are compared to traditional shape analysis methods found in literature. (C) 2009 Published by Elsevier B.V.

PLANT LEAF IDENTIFICATION BASED ON VOLUMETRIC FRACTAL DIMENSION

Texture is an important visual attribute used to describe the pixel organization in an image. As well as it being easily identified by humans, its analysis process demands a high level of sophistication and computer complexity. This paper presents a novel approach for texture analysis, based on analyzing the complexity of the surface generated from a texture, in order to describe and characterize it. The proposed method produces a texture signature which is able to efficiently characterize different texture classes. The paper also illustrates a novel method performance on an experiment using texture images of leaves. Leaf identification is a difficult and complex task due to the nature of plants, which presents a huge pattern variation. The high classification rate yielded shows the potential of the method, improving on traditional texture techniques, such as Gabor filters and Fourier analysis.

ENHANCING MULTISCALE FRACTAL DESCRIPTORS USING FUNCTIONAL DATA ANALYSIS

This work presents a novel approach in order to increase the recognition power of Multiscale Fractal Dimension (MFD) techniques, when applied to image classification. The proposal uses Functional Data Analysis (FDA) with the aim of enhancing the MFD technique precision achieving a more representative descriptors vector, capable of recognizing and characterizing more precisely objects in an image. FDA is applied to signatures extracted by using the Bouligand-Minkowsky MFD technique in the generation of a descriptors vector from them. For the evaluation of the obtained improvement, an experiment using two datasets of objects was carried out. A dataset was used of characters shapes (26 characters of the Latin alphabet) carrying different levels of controlled noise and a dataset of fish images contours. A comparison with the use of the well-known methods of Fourier and wavelets descriptors was performed with the aim of verifying the performance of FDA method. The descriptor vectors were submitted to Linear Discriminant Analysis (LDA) classification method and we compared the correctness rate in the classification process among the descriptors methods. The results demonstrate that FDA overcomes the literature methods (Fourier and wavelets) in the processing of information extracted from the MFD signature. In this way, the proposed method can be considered as an interesting choice for pattern recognition and image classification using fractal analysis.

Fractal character of the SAXS correlation volume in poly(ethylene glycol)/silica hybrid wet gels

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Análise histológica, histométrica e fractal de enxerto ósseo autógeno, em elevação de seio maxilar: estudo clínico

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Previsão espacial da densidade de carga nos sistemas de distribuição de energia elétrica considerando a geometria fractal da zona urbana

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Correlation of Fractal Dimension with Histomorphometry in Maxillary SinuLifting Using Autogenous Bone Graft

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Color texture analysis based on fractal descriptors

Color texture classification is an important step in image segmentation and recognition. The color information is especially important in textures of natural scenes, such as leaves surfaces, terrains models, etc. In this paper, we propose a novel approach based on the fractal dimension for color texture analysis. The proposed approach investigates the complexity in R, G and B color channels to characterize a texture sample. We also propose to study all channels in combination, taking into consideration the correlations between them. Both these approaches use the volumetric version of the Bouligand-Minkowski Fractal Dimension method. The results show a advantage of the proposed method over other color texture analysis methods. (C) 2011 Elsevier Ltd. All rights reserved.