Local Fractal Dimension Research Articles

Experimental analysis of liquid–gas interface at low Weber number: interface length and fractal dimension

The present paper reports an experimental investigation on atomizing liquid flows produced by simplified cavity nozzles. The Weber number being kept low, the sprays produced by these injectors depend on the liquid flow characteristics only, and more precisely, on the non-axial kinetic energy and of the turbulent kinetic energy at the nozzle exit. The investigation reported here concentrates on the characterization of liquid flows during atomization by measuring the spatial variation of the local interface length and of the local interface fractal dimension. Both parameters were found representative of the physics of atomization process: they depend on the characteristics of the flow issuing from the nozzle and they are related to the subsequent drop size distribution. The local interface length is representative of the amount of liquid–gas interface surface area, and is a function of both the non-axial and the turbulent kinetic energies at the nozzle exit. The fractal dimension is representative of the tortuosity of the liquid–gas interface and, as expected, is mainly related to the turbulent kinetic energy at the nozzle exit. As far as the drop size distribution is concerned, it is found that the local interface length at the instant of break-up determines a representative drop diameter of some kind, whereas the fractal dimension at the same instant controls the dispersion of the distribution.

Fractal-Based Fuzzy Technique For Detection Of Active Regions From Solar Images

Fractal concepts are used to describe the irregular structures and regions of interest of solar images. The most common and easiest way to extract regions of interest from an image is through segmentation. Segmentation techniques vary from conventional edge-detection mechanism to fuzzy c-means clustering. In this study, the pixelwise local fractal dimension of solar images is computed by different techniques. This is followed by different segmentation procedures including the fuzzy-based approach, for extracting the active regions from chromospheric images and assessing their performance. These techniques have also been applied on solar images to extract active regions from Solar Heliospheric Observatory (SOHO) Extreme Ultraviolet Telescope (EIT) images.

Fractal coding based on image local fractal dimension

Fractal codification of images is based on self-similar and self-affine sets. The codification process consists of construction of an operator which will represent the image to be encoded. If a complicated picture can be represented by an operator then it will be transmitted or stored very efficiently. Clearly, this has many applications on data compression. The great disadvantage of the automatic form of fractal compression is its encoding time. Most of the time spent in construction of such operator is due on finding the best match between parts of the image to be encoded. However, since the conception of automatic fractal image compression, researches on improvement of the compression time are widespread. This work aims to provide a new idea for decrease the encoding time: a classification of image parts based on their local fractal dimension. The idea is implemented on two steps. First, a preprocessing analysis of the image identify the complexity of each image block computing its dimension. Then, only parts within the same range of complexity are used for testing the better self-affine pairs, reducing the compression time. The performance of this proposition, is compared with others fractal image compression methods. The points considered are image fidelity, encoding time and amount of compression on the image file.

Fractal coding based on image local fractal dimension

Fractal coding based on image local fractal dimension

鼻部皮膚温度画像の局所フラクタル次元解析による主観的理解度の推定

The purpose of this study is to estimate the information understanding level through the nasal skin thermal image which reflects the human emotion. The information understanding in communication is supposed to be concerned with the emotion. The local fractal dimension analysis was applied to the nasal skin thermal image. Based on the relationship among the local fractal dimension and the subjective understanding measured in English listening tests, the information understanding level has been estimated by the neural network. As a result, the estimated understanding level has been obviously classified in two groups according to the difficulty of the test.

Local fuzzy fractal dimension and its application in medical image processing

The local fuzzy fractal dimension (LFFD) is proposed to extract local fractal feature of medical images. The definition of LFFD is an extension of the pixel-covering method by incorporating the fuzzy set. Multi-feature edge detection is implemented with the LFFD and the Sobel operator. The LFFD can also serve as a characteristic of motion in medical image sequences. The experimental results show that the LFFD is an important feature of edge areas in medical images and can provide information for segmentation of echocardiogram image sequences.

空撮画像を用いた局所フラクタル次元による樹冠解析

空撮画像を用いた局所フラクタル次元による樹冠解析

Quantification of the global and local complexity of the epithelial-connective tissue interface of normal, dysplastic, and neoplastic oral mucosae using digital imaging.

This study aimed at quantifying the complexity of the epithelial-connective tissue interface (ECTI) in human normal mucosa, premalignant, and malignant lesions using fractal geometry. Two approaches were used to describe the complexity of 377 oral mucosa ECTI profiles. The box counting method was used to estimate their global fractal dimension, while local fractal dimensions were estimated using the mass radius relation at various local scales. The ECTI complexity significantly increased from normal through premalignant to malignant profiles in both global and local (over 283 microm) scales. Normal mucosa samples from different sites of the oral cavity also had different degrees of global complexity. Fractal geometry is a useful morphological marker of tissue complexity changes taking place during epithelial malignancy and premalignancy, and we propose it as a quantitative marker of epithelial complexity.

The Application of Identification Method of Ground Surfaces using Fractal Dimension to Millimeter Wave Radar Altimeter

Data of scattering coefficient on vertical incidence against ground surface at U-band are obtained by Millimeter Wave Radar Altimeter using FM-CW ranging. Noise suppression by wavelet shrinkage can be utilized to extract feature parameter in high spatial frequency band, in which level of fractal noise is dominated by that of white noise. We propose approximate algorithm for estimation of local fractal dimension in high spatial frequency band which is the most effective parameter for identification for classification of ground surfaces such as vegetation, town area and rice field.

Near optimum estimation of local fractal dimension for image segmentation

This paper presents an algorithm for estimating the local fractal dimension (LFD) of textured images. The algorithm is established by an experimental approach based on the blanket method. The proposed method uses the near optimum number of blankets to obtain the LFD for a small local window. The robustness of the proposed method to consistently estimate the LFD using up to a 3×3 local window is confirmed by experimental evaluations. The LFD maps, created from natural scenes, are utilized in an image segmentation algorithm that demonstrates the capability of rough segmentation of fine-texture regions in natural images.

The Detection of Fracture Transition Point by the Local Self-Affine Fractal.

In the field of the fractography, fractal has been applied to investigate fracture mechanism. In this study, a new method detecting the transition point of fracture surface by calculating the local fractal dimension using Wavelet transformation is proposed. The high accurate evaluation is realized by using not the conventional self-similar fractal but anisotropic self-affine fractal "Hurst exponent" that is more suitable for fracture surface as an evaluation parameter. First, validity of our proposed method was verified by using the synthesized profile. Next, by applying our method to the brittle-ductile transition region of Charpy test specimen, the transition point was shown quantitatively. The homogeneity of fracture surface was checked in the case of TiAl creep and creep fatigue test specimen. Moreover, as compared with the conventional Box-Counting method for the self-similar fractal, it was found that our method with using self-affine fractal gave more exact Hurst exponent, and was suitable also for detection of the variation in local fractal dimension.

Fractal and Multifractal Analysis of Cassava Root System Grown by the Root-Box Method

The root system development and its localized distribution were examined using cassava plants grown in narrow root boxes of appropriate sizes which were adjusted to the root growth. Analyses based on fractal geometry were applied in addition to measurements of the weight and length of the root systems to evaluate the root distribution quantitatively. The root system distribution was converted to a digitized image, and the fractal dimension was calculated by the box-counting method (Dbox) for the whole root system and different positions in the soil. Furthermore, 1000 random measurements for local fractal dimension by the mass-radius method (Dlocal) were conducted per root system, and the multifractal spectrum was analyzed. The total root weight increased until 90 days after planting (DAP), whereas the total length ceased to increase at 60 DAP. Neither apparent bulking of storage root nor decrease in root length was observed during the experimental period. The potential rooting habit of cassava was two-dimensionally exhibited under a uniform soil environment in the boxes. The complexity in root distribution as a whole root system shown by the global D (Dbox) was almost constant. However, both the trends in positional Dbox difference and multifractal analysis showed that the root distribution was localized and heterogeneity in the localization changed with root system development. The root system of cassava grown in the boxes can be characterized as an abundant but uneven root distribution with a highly advanced branching pattern by large global D and kurtosis of the multifractal spectra.

電気トリーパターン解析のための局所フラクタル次元応用

電気トリーパターン解析のための局所フラクタル次元応用

Quantitative evaluation of magnetic resonance imaging of deep white matter hyperintensity in geriatric patients by multifractal analysis

Fractal analysis has played an important role in various fields such as physics, biology and medicine. Recently, multifractal analysis based on generalized concepts of fractals has been applied to biological tissues composed of complex structures. Deep white matter hyperintensity (DWMH) on brain magnetic resonance imaging (MRI) is more often observed in patients with geriatric depression than in healthy elderly subjects, and its clinical significance is receiving attention. We applied multifractal analysis to white matter images on brain T2-weighted MRI in 62 patients with geriatric depression (50–75 years). The local fractal dimensions, α max and α min, which serve as indices of complexity, and their difference, α max − α min, were closely correlated with the macroscopic grading according to Fazekas classification, suggesting that multifractal analysis is useful for quantitative evaluation of DWMH on MRI.

Theory of unstable laser modes: edge waves and fractality

For large Fresnel numbers N, unstable laser modes are highly irregular and resemble fractals. To explore this, we derive an explicit formula for the lowest-loss mode of a one-dimensional laser (i.e. where the cavity is two dimensional) in terms of edge-diffracted waves, and demonstrate its accuracy for large N. Between the size a of the mirror (outer scale), and the inner scale a/ N, there is no distinguished scale, and the graph of mode intensity has a fractal dimension close to 2. Near the inner scale, the scaling is scale dependent, and the crossover is described by an explicit formula for a `local fractal dimension' D( K), describing the mode on scales near Δx= a/(2 πNK). As K increases through the inner scale K=1, D( K) decreases from 2 when K≪1 to 1 when K≫1 (reflecting the smoothness of the mode on fine scales).

Fractal characterization of the distribution of reactive sites over a rough catalyst surface

The amount of reactive sites, usually dispersed noble metal atoms, on the top of a catalyst rough surface is characterized within the framework of fractal geometry. The problem is reduced to evaluating properties of a fractal set built on a self-affine profile. Numerical simulations are used to generate both support and different amounts of dispersed atoms. Three different parameters (local and global fractal dimension and roughness exponent) are used to analyze profiles obtained by three different processes. Results indicate that the quantitative characterization of dispersed atoms follows from the direct evaluation of the local fractal dimension. This, in turn, is achieved after a simple adaptation of an optimized box-counting algorithm.

Rapid inversion of 2-D geoelectrical data by multichannel deconvolution

Modern geoelectrical data acquisition systems can record more than 100 000 data values per field day. Despite the growth in computer power and the development of more efficient numerical algorithms, interpreting such data volumes remains a nontrivial computational task. We present a 2-D one‐pass inversion procedure formulated as a multichannel deconvolution. It is based on the equation for the electrical potential linearized under the Born approximation, and it makes use of the 2-D form of the Fréchet derivatives evaluated for the homogeneous half‐space. The inversion is formulated in the wavenumber domain so that the 2-D spatial problem decouples into many small 1-D problems. The resulting multichannel deconvolution algorithm is very fast and memory efficient. The inversion scheme is stabilized through covariance matrices representing the stochastic properties of the earth resistivity and data errors. The earth resistivity distribution is assumed to have the statistical characteristics of a two‐parameter, self‐affine fractal. The local apparent amplitude and fractal dimension of the earth resistivity are estimated directly from geoelectrical observations. A nonlinearity error covariance matrix is added to the conventional measurement error covariance matrix. The stochastic model for the dependence of nonlinearity error on electrode configuration as well as resistivity amplitude and fractal dimension is determined pragmatically through nonlinear simulation experiments. Tests on synthetic examples and field cases including well control support the conclusion that for long data profiles this method automatically produces linearized resistivity estimates which faithfully resolve the main model features.

Local Non-Stationary Nature of Brain Waves from Demented Persons

In the present paper, we show the local non-stationary nature of brain waves from demented persons by reconstructing various stochastic processes of averaged local quantities, e.g., fractal dimension, mean, variance, skewness and kurtosis. The characteristic random dynamic features of their local quantities are discussed in the two-dimensional (2D) phase space. The availability of their local non-stationary nature for diagnosing senile dementia is also discussed.

The Evaluation Method of Arousal Level by Local Fractal Analysis of Facial Skin Temperature

This paper proposes the method of objectively evaluating arousal level through facial skin temperature. There are two types in arousal level: one is based on circadian rhythm and the other is temporary depending on quantities of sensations. We tried to evaluate the latter. We applied local fractal dimension analysis to the thermogram. We examined the relationship between the thermogram and α rhythm amplitude of EEG, reflects arousal level. As a result, the local fractal dimension analysis of distribution of nasal temperature was valid for the system evaluation arousal level.

Topological effects in ring polymers. II. Influence Of persistence length

The interplay of topological constraints and the persistence length of ring polymers in their own melt is investigated by means of dynamical Monte Carlo simulations of a three-dimensional lattice model. We ask if the results are consistent with an asymptotically regime where the rings behave like (compact) lattice animals in a self-consistent network of topological constraints imposed by neighboring rings. Tuning the persistence length provides an efficient route to increase the ring overlap required for this mean-field picture to hold: The effective Flory exponent for the ring size decreases down to nu less, similar1/3 with increasing persistence length. Evidence is provided for the emergence of one additional characteristic length scale d(t) approximately N0, only weakly dependent on the persistence length and much larger than the excluded volume screening length xi. At distances larger than d(t) the conformational properties of the rings are governed by the topological interactions; at smaller distances rings and their linear chain counterparts become similar. (At distances smaller than xi both architectures are identical.) However, the crossover between both limits is intricate and broad, as a detailed discussion of the local fractal dimension (e.g., obtained from the static structure factor) reveals. This is due to various crossover effects which we are unable to separate even for the largest ring size (N=1024) presented here. The increased topological interactions also influence the dynamical properties. Mean-square displacements and their distributions depend crucially on the ring overlap, and show evidence of the existence of additional size and time scales. The diffusion constant of the rings goes down from effectively D(N) approximately N-1.22 for flexible rings with low overlap to D(N) approximately N-1.68 for strongly overlapping semiflexible rings.