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.

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.

Fractal dimension applied to plant identification

This article discusses methods to identify plants by analysing leaf complexity based on estimating their fractal dimension. Leaves were analyzed according to the complexity of their internal and external shapes. A computational program was developed to process, analyze and extract the features of leaf images, thereby allowing for automatic plant identification. Results are presented from two experiments, the first to identify plant species from the Brazilian Atlantic forest and Brazilian Cerrado scrublands, using fifty leaf samples from ten different species, and the second to identify four different species from genus Passiflora, using twenty leaf samples for each class. A comparison is made of two methods to estimate fractal dimension (box-counting and multiscale Minkowski). The results are discussed to determine the best approach to analyze shape complexity based on the performance of the technique, when estimating fractal dimension and identifying plants. (C) 2008 Elsevier Inc. All rights reserved.

Fractal dimension and Shannon's entropy analyses of the architectural complexity caused by the inflammatory reactions induced by highly crystalline polyvinyl alcohol) microspheres implanted in subcutaneous tissues of the Wistar rats

The results of the histopathological analyses after the implantation of highly crystalline PVA microspheres in subcutaneous tissues of Wistar rats are here in reported. Three different groups of PVA microparticles were systematically studied: highly crystalline, amorphous, and commercial ones. In addition to these experiments, complementary analyses of architectural complexity were performed using fractal dimension (FD), and Shannon's entropy (SE) concepts. The highly crystalline microspheres induced inflammatory reactions similar to the ones observed for the commercial ones, while the inflammatory reactions caused by the amorphous ones were less intense. Statistical analyses of the subcutaneous tissues of Wistar rats implanted with the highly crystalline microspheres resulted in FD and SE values significantly higher than the statistical parameters observed for the amorphous ones. The FD and SE parameters obtained for the subcutaneous tissues of Wistar rats implanted with crystalline and commercial microparticles were statistically similar. Briefly, the results indicated that the new highly crystalline microspheres had biocompatible behavior comparable to the commercial ones. In addition, statistical tools such as FD and SE analyses when combined with histopathological analyses can be useful tools to investigate the architectural complexity tissues caused by complex inflammatory reactions. © 2012 WILEY PERIODICALS, INC.

A comparative study on multiscale fractal dimension descriptors

Fractal theory presents a large number of applications to image and signal analysis. Although the fractal dimension can be used as an image object descriptor, a multiscale approach, such as multiscale fractal dimension (MFD), increases the amount of information extracted from an object. MFD provides a curve which describes object complexity along the scale. However, this curve presents much redundant information, which could be discarded without loss in performance. Thus, it is necessary the use of a descriptor technique to analyze this curve and also to reduce the dimensionality of these data by selecting its meaningful descriptors. This paper shows a comparative study among different techniques for MFD descriptors generation. It compares the use of well-known and state-of-the-art descriptors, such as Fourier, Wavelet, Polynomial Approximation (PA), Functional Data Analysis (FDA), Principal Component Analysis (PCA), Symbolic Aggregate Approximation (SAX), kernel PCA, Independent Component Analysis (ICA), geometrical and statistical features. The descriptors are evaluated in a classification experiment using Linear Discriminant Analysis over the descriptors computed from MFD curves from two data sets: generic shapes and rotated fish contours. Results indicate that PCA, FDA, PA and Wavelet Approximation provide the best MFD descriptors for recognition and classification tasks. (C) 2012 Elsevier B.V. All rights reserved.

Fractal Dimension in Quantifying Experimental-Pulmonary-Hypertension-Induced Cardiac Dysfunction in Rats

Abstract Background: Right-sided heart failure has high morbidity and mortality, and may be caused by pulmonary arterial hypertension. Fractal dimension is a differentiated and innovative method used in histological evaluations that allows the characterization of irregular and complex structures and the quantification of structural tissue changes. Objective: To assess the use of fractal dimension in cardiomyocytes of rats with monocrotaline-induced pulmonary arterial hypertension, in addition to providing histological and functional analysis. Methods: Male Wistar rats were divided into 2 groups: control (C; n = 8) and monocrotaline-induced pulmonary arterial hypertension (M; n = 8). Five weeks after pulmonary arterial hypertension induction with monocrotaline, echocardiography was performed and the animals were euthanized. The heart was dissected, the ventricles weighed to assess anatomical parameters, and histological slides were prepared and stained with hematoxylin/eosin for fractal dimension analysis, performed using box-counting method. Data normality was tested (Shapiro-Wilk test), and the groups were compared with non-paired Student t test or Mann Whitney test (p < 0.05). Results: Higher fractal dimension values were observed in group M as compared to group C (1.39 ± 0.05 vs. 1.37 ± 0.04; p < 0.05). Echocardiography showed lower pulmonary artery flow velocity, pulmonary acceleration time and ejection time values in group M, suggesting function worsening in those animals. Conclusion: The changes observed confirm pulmonary-arterial-hypertension-induced cardiac dysfunction, and point to fractal dimension as an effective method to evaluate cardiac morphological changes induced by ventricular dysfunction.

Fractal dimension for Gaussian colored processes

The exact analytical expression for the Hausdorff dimension of free processes driven by Gaussian noise in n-dimensional space is obtained. The fractal dimension solely depends on the time behavior of the arbitrary correlation function of the noise, ranging from DX=1 for Orstein-Uhlenbeck input noise to any real number greater than 1 for fractional Brownian motions.

Comments on "On the relationship between fractal dimension and the performance of multi-resonant dipole antennas using Koch curves"

Comentaris referits a l'article següent: K. J. Vinoy, J. K. Abraham, and V. K. Varadan, “On the relationshipbetween fractal dimension and the performance of multi-resonant dipoleantennas using Koch curves,” IEEE Transactions on Antennas and Propagation, 2003, vol. 51, p. 2296–2303.

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.

Fractal dimension and anisotropy of soil CO2 emission in a mechanically harvested sugarcane production area

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Maximum entropy, fractal dimension and lacunarity in quantification of cellular rejection in myocardial biopsy of patients submitted to heart transplantation

This paper presents a method for the quantification of cellular rejection in endomyocardial biopsies of patients submitted to heart transplant. The model is based on automatic multilevel thresholding, which employs histogram quantification techniques, histogram slope percentage analysis and the calculation of maximum entropy. The structures were quantified with the aid of the multi-scale fractal dimension and lacunarity for the identification of behavior patterns in myocardial cellular rejection in order to determine the most adequate treatment for each case.

Temperature dependence of fractal dimension of grain boundary region in SnO2 based ceramics

Fractal dimensions of grain boundary region in doped SnO2 ceramics were determined based on previously derived fractal model. This model considers fractal dimension as a measure of homogeneity of distribution of charge carriers. Application of the derived fractal model enables calculation of fractal dimension using results of impedance spectroscopy. The model was verified by experimentally determined temperature dependence of the fractal dimension of SnO2 ceramics. Obtained results confirm that the non-Debye response of the grain boundary region is connected with distribution of defects and consequently with a homogeneity of a distribution of the charge carriers. Also, it was found that C-T-1 function has maximum at temperature at which the change in dominant type of defects takes place. This effect could be considered as a third-order transition.

Fractal dimension and anisotropy of soil CO2 emission in an agricultural field during fallow

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

Estimating crowd density with Minkowski fractal dimension

The estimation of the number of people in an area under surveillance is very important for the problem of crowd monitoring. When an area reaches an occupation level greater than the projected one, people's safety can be in danger. This paper describes a new technique for crowd density estimation based on Minkowski fractal dimension. Fractal dimension has been widely used to characterize data texture in a large number of physical and biological sciences. The results of our experiments show that fractal dimension can also be used to characterize levels of people congestion in images of crowds. The proposed technique is compared with a statistical and a spectral technique, in a test study of nearly 300 images of a specific area of the Liverpool Street Railway Station, London, UK. Results obtained in this test study are presented.

Plant species identification using multi-scale fractal dimension applied to images of adaxial surface epidermis

This paper presents the study of computational methods applied to histological texture analysis in order to identify plant species, a very difficult task due to the great similarity among some species and presence of irregularities in a given species. Experiments were performed considering 300 ×300 texture windows extracted from adaxial surface epidermis from eight species. Different texture methods were evaluated using Linear Discriminant Analysis (LDA). Results showed that methods based on complexity analysis perform a better texture discrimination, so conducting to a more accurate identification of plant species. © 2009 Springer Berlin Heidelberg.