A novel box-counting method for quantitative fractal analysis of threedimensional pore characteristics in sandstone

Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.

Identification of Geochemical Anomaly by Multifractal Analysis

The separation of anomalies from geochemical background is an important part of data analysis because lack of such identifications might have profound influence on or even distort the final analysis results. In this article, 1 672 geochemical analytical data of 11 elements, including Cu, Mo, Ag, Sn, and others, from a region within Tibet, South China, are used as one example. Together with the traditional anomaly recognition method of using the iterative mean ±2σ local multifractality theory has been utilized to delineate the ranges of geochemical anomalies of the elements. To different degrees, on the basis of original data mapping, C-A fractal analysis and singularity exponents, Sn differs from the other 10 elements. Moreover, geochemical mapping results based on values of the multifractal asymmetry index for all elements delineate the highly anomalous area. Similar to other 10 elements, the anomalous areas of Sn delineated by the asymmetry index distribute along the main structure orientations. According to the asymmetry indexes, the 11 elements could be classified into 3 groups： （1） Ag and Au, （2） As-Sb-Cu-Pb-Zn-Mo, and （3） Sn-Bi-W. This parageneflc association of elements can be used to interpret possible origins of mineralization, which is in agreement with petrological analysis and field survey results.

Fractal analysis of retinal vasculature in normal subjects on ultra-wide field fluorescein angiography

AIM: To evaluate the fractal feature of the retinal vasculature of normal eyes on a stereographic projected and montaged ultra-wide field(UWF) fluorescein angiography(FA).METHODS: Prospective, observational, cross-sectional study. Totally 59 eyes of 31 normal subjects were imaged using the Optos 200 Tx. Images obtained at different gaze angles stereographically projected and montaged. The early-phase UWF FA frames were processed to segment the retinal vasculature and the results were exported as binary masks. The fractal dimension(FD) was calculated using the box-counting method.RESULTS: The global FD for the entire retina was 1.6±0.04, with no difference between males and females(1.59±0.04 vs 1.61±0.04, P=0.084) or between right and left eyes(1.6±0.04 vs 1.6±0.05, P=0.61). FD was nonuniformly distributed among four quadrants(P<0.001) and decreased as the distance from the fovea increased(P<0.001). A negative association was observed between FD and age(R=-0.37, P=0.006), and this relationship was observed in the posterior and mid-peripheral retina(P<0.05) but absent in far-periphery(P>0.05).CONCLUSION: Fractal geometry is non-uniformly distributed across the retina in normal eyes and decreases from the fovea to the far-periphery. Subjects with an older age tend to have a smaller FD, however, the FD in the farperiphery does not appear to be influenced by age.

Fractal Analysis of Mobile Social Networks

Fractal and self similarity of complex networks have attracted much attention in recent years. The fractal dimension is a useful method to describe the fractal property of networks. However, the fractal features of mobile social networks （MSNs） are inadequately investigated. In this work, a box-covering method based on the ratio of excluded mass to closeness centrality is presented to investigate the fractal feature of MSNs. Using this method, we find that some MSNs are fractal at different time intervals. Our simulation results indicate that the proposed method is available for analyzing the fractal property of MSNs.

Hidden periodicity in Stripe 82 with Saraswati supercluster—a fractal analysis

The manuscript attempts to explore the periodicity in the distribution of galaxies in the recently reported Saraswati supercluster and the Stripe 82 region containing it as an example.The report of 120 Mpc periodicity in the Abell galaxy clusters by power spectrum analysis is the motivation behind the study.The power spectral analysis across the central part of the Stripe 82 region shows a periodic variation of 3.09°or 71 Mpc in fractal dimension whereas an average angular periodicity of 3.45°or 94 Mpc is observed across the Stripe 82 region.This refers to the periodicity of complexity or cluster density of galaxy distribution.The texture of the distribution pattern understood through lacunarity analysis indicates a near symmetric distribution.Fractal dimensions like box-counting dimension,information dimension and correlation dimension are also found through multifractal analysis.While the information dimension tells about the distribution density of galactic points,the correlation dimension details the distribution of galaxies in the neighbourhood.

Assessment of glaucoma using extreme learning machine and fractal feature analysis

Dear Sir,Iam Dr.Kavitha S,from the Department of Electronics and Communication Engineering,Nandha Engineering College,Erode,Tamil Nadu,India.I write to present the detection of glaucoma using extreme learning machine(ELM)and fractal feature analysis.Glaucoma is the second most frequent cause of permanent blindness in industrial

Microcrack analysis of Sanya grantite fragments from rockburst tests

Fractures running along a plane reflect the cracking progress.In this paper uniaxial and rockburst tests on a group of granite specimens from Sanya province are described.Scanning electron microscopic imaging was used to characterize the fragments.Fractal fracture mechanics were used to analyze the microcracks in terms of both the crack type and the mineral constituent.A statistical analysis showed that the area of inter-granular cracking exceeds that of intra-granular cracking.Several types of crack were observed in the cracked areas.The percentage of intra-granular cracks in fragments from rockburst tests exceeds that from uniaxial compression tests.The results also showed that feldspar deformation was the main cause of fracture and that the consolidation along quartz grain boundaries was another weak area in the granite.Cracking along quartz grains had enough energy to enter the quartz crystal in the rockburst samples.All these results contribute to further research on rockburst mechanics.

Multimodality Medical Image Fusion Based on Pixel Significance with Edge-Preserving Processing for Clinical Applications

Multimodal medical image fusion has attained immense popularity in recent years due to its robust technology for clinical diagnosis.It fuses multiple images into a single image to improve the quality of images by retaining significant information and aiding diagnostic practitioners in diagnosing and treating many diseases.However,recent image fusion techniques have encountered several challenges,including fusion artifacts,algorithm complexity,and high computing costs.To solve these problems,this study presents a novel medical image fusion strategy by combining the benefits of pixel significance with edge-preserving processing to achieve the best fusion performance.First,the method employs a cross-bilateral filter(CBF)that utilizes one image to determine the kernel and the other for filtering,and vice versa,by considering both geometric closeness and the gray-level similarities of neighboring pixels of the images without smoothing edges.The outputs of CBF are then subtracted from the original images to obtain detailed images.It further proposes to use edge-preserving processing that combines linear lowpass filtering with a non-linear technique that enables the selection of relevant regions in detailed images while maintaining structural properties.These regions are selected using morphologically processed linear filter residuals to identify the significant regions with high-amplitude edges and adequate size.The outputs of low-pass filtering are fused with meaningfully restored regions to reconstruct the original shape of the edges.In addition,weight computations are performed using these reconstructed images,and these weights are then fused with the original input images to produce a final fusion result by estimating the strength of horizontal and vertical details.Numerous standard quality evaluation metrics with complementary properties are used for comparison with existing,well-known algorithms objectively to validate the fusion results.Experimental results from the proposed research article exhibit superior performance compared to other competing techniques in the case of both qualitative and quantitative evaluation.In addition,the proposed method advocates less computational complexity and execution time while improving diagnostic computing accuracy.Nevertheless,due to the lower complexity of the fusion algorithm,the efficiency of fusion methods is high in practical applications.The results reveal that the proposed method exceeds the latest state-of-the-art methods in terms of providing detailed information,edge contour,and overall contrast.

Fractal Analyses Reveal the Origin of Aesthetics in Chinese Calligraphy

Chinese calligraphy is a thousand-year-old writing art. The question of how Chinese calligraphy artworks convey emotion has cast its spell over people for millennia. Calligraphers' joys and sorrows were expressed in the complexity of the character strokes, style variations and general layouts. Determining how Chinese calligraphy aesthetic patterns emerged from the general layout of artworks is a challenging objective for researchers. Here we investigate the statistical fluctuation structure of Chinese calligraphy characters sizes using characters obtained from the calligraphy artwork "Preface to the Poems Collected from the Orchid Pavilion" which was praised as the best running script under heaven. We found that the character size distribution is a stretched exponential distribution. Moreover, the variations in the local correlation features in character size fluctuations can accurately reflect expressions of the calligrapher's complex feelings. The fractal dimensions of character size fluctuations are close to the Fibonacci sequence. The Fibonacci number is first discovered in the Chinese calligraphy artworks, which inspires the aesthetics of Chinese calligraphy artworks and maybe also provides an approach to creating Chinese calligraphy artworks in multiple genres.

Enhanced endoscopic ultrasound imaging for pancreatic lesions: The road to artificial intelligence

Early detection of pancreatic cancer has long eluded clinicians because of its insidious nature and onset.Often metastatic or locally invasive when symptomatic,most patients are deemed inoperable.In those who are symptomatic,multi-modal imaging modalities evaluate and confirm pancreatic ductal adenocarcinoma.In asymptomatic patients,detected pancreatic lesions can be either solid or cystic.The clinical implications of identifying small asymptomatic solid pancreatic lesions(SPLs)of<2 cm are tantamount to a better outcome.The accurate detection of SPLs undoubtedly promotes higher life expectancy when resected early,driving the development of existing imaging tools while promoting more comprehensive screening programs.An imaging tool that has matured in its reiterations and received many image-enhancing adjuncts is endoscopic ultrasound(EUS).It carries significant importance when risk stratifying cystic lesions and has substantial diagnostic value when combined with fine needle aspiration/biopsy(FNA/FNB).Adjuncts to EUS imaging include contrast-enhanced harmonic EUS and EUS-elastography,both having improved the specificity of FNA and FNB.This review intends to compile all existing enhancement modalities and explore ongoing research around the most promising of all adjuncts in the field of EUS imaging,artificial intelligence.

Rheological properties and fractal-rheology analysis of peanut protein isolate suspension

This study focuses on the non-linear rheological property and microstructure of peanut protein isolate(PPI)aggregation suspension.The impact of higher harmonics(I3 and I5)on fundamental stress wave during large amplitude oscillatory shear test was studied.Rheological test show that storage modulus G′and loss modulus G″increased with increasing PPI concentration.The non-linear viscoelastic properties of PPI suspension with different concentration were investigated.Using confocal laser-scanning microscopy method,this research explored the microstructure of PPI suspension as well as the fractal dimensions.The new critical strain indirect method combined with Wu-Morbidelli model to calculate the fractal dimension(2.9225)is very close to the actual fractal dimension(2.9206).Fourier Transform Rheology was adopted to get the new critical strain for fractal dimension calculation,which was proved to be feasible.

Stereology in Materials Science

Quantitative analysis of populations having a geometric structure,which has developed into a special scientific subject called microstructology or stereology,is of great importance to the characterization and evaluation of microstructures and their evolution in various processes.This paper, besides a brief discussion on those topics such as the recent developments of computer assisted image analysis,mathematical morphology,and fractal analysis,will mainly focus on the scope,fundamen- tals,present status,and perspectives of classical stereology.Several case examples of its application to materials science will also be given.

The motion mechanism and characteristic of bubble in a pseudo-2D tapered fluidized bed

The different carbon nanotube(CNT)particles(^(@)A and^(@)V)were bed materials in the pseudo-2D tapered fluidized bed(TFB)with/without a distributor.A detailed investigation of the motion mechanism of bubbles was carried out.The high-speed photography and image analysis techniques were used to study bubble characteristic and mixing behavior in the tapered angle of TFB without a distributor.The fractal analysis method was used to analyze the degree of particles movement.Results showed that an S-shaped motion trajectory of bubbles was captured in the bed of^(@)V particles.The population of observational bubbles in the bed of^(@)V particles was more than that of^(@)A particles,and the bubble size was smaller in the bed of^(@)V particles than that of^(@)A particles.The motion mechanism of bubbles had been shown to be related to bed materials and initial bed height in terms of analysis and comparison of bubble diameter,bubble aspect ratio and bubble shape factor.Importantly,compared to the TFB with a distributor,the TFB without a distributor had been proved to be beneficial to the CNT fluidization according to the study of bubble characteristic and the degree of the particle movement.Additionally,it was found that the mixing behavior of^(@)V particles was better than^(@)A particles in the tapered angle of TFB without a distributor.

Medical images classification for skin cancer using quantitative image features with optical coherence tomography

Optical coherence tomography(OCT)is employed in the diagnosis of skin cancer.Particularly,quantitative image features extracted from OCT images might be used as indicators to classify the skin tumors.In the present paper,we investigated intensity-based,texture-based and fractalbased features for automatically classifying the melanomas,basal cell carcinomas and pigment nevi.Generalized estimating equations were used to test for differences between the skin tumors.A modified p value of<0.001 was considered statistically significant.Significant increase of mean and median of intensity and significant decrease of mean and median of absolute gradient were observed in basal cell carcinomas and pigment nevi as compared with melanomas.Significant decrease of contrast,entropy and fractal dimension was also observed in basal cell carcinomas and pigment nevi as compared with melanomas.Our results suggest that the selected quantitative image features of OCT images could provide useful information to differentiate basal cell carcinomas and pigment nevi from the melanomas.Further research is warranted to determine how this approach may be used to improve the classification of skin tumors.

Classified recognition for metal magnetic memory signals of welding defects in API 5L X65 pipeline steel

Feature extraction and selection from signals is a key issue for metal magnetic memory testing technique. In order to realize the classification of metal magnetic memory signals of welding defects, four fractal analysis methods, such as box- counting, detrended fluctuation, minimal cover and rescaled-range analysis, were used to extract the feature signal after the original metal magnet memory signal was de-noising and differential processing, then the Karhunen-Lo^e transformation was adopted as classification tool to identify the defect signals. The result shows that this study can provide an efficient classification method for metal magnetic memory signal of welding defects.

Advances in experimental methods for root system architecture and root development

Plant roots play important roles in acquisition of water and nutrients, storage, anchoring, transport, and symbiosis with soil microorganisms, thus quantitative researches on root developmental processes are essential to understand root functions and root turnover in ecosystems,and at the same time such researches are the most difficult because roots are hidden underground. Therefore, how to investigate efficiently root functions and root dynamics is the core aspect in underground ecology. In this article, we reviewed some experimental methods used in root researches on root development and root system architecture, and summarized the advantages and shortages of these methods. Based on the analyses, we proposed three new ways to more understand root processes：（1） new experimental materials for root development;（2） a new observatory system comprised of multiple components, including many observatory windows installed in field, analysis software,and automatic data transport devices;（3） new techniques used to analyze quantitatively functional roots.

The ”Hot Spots” Conjecture on Homogeneous Hierarchical Gaskets

In this paper, using spectral decimation, we prove that the "hot spots" conjecture holds on a class of homogeneous hierarchical gaskets introduced by Hambly,i.e., every eigenfunction of the second-smallest eigenvalue of the Neumann Laplacian(introduced by Kigami) attains its maximum and minimum on the boundary.

Fractal Characteristics of Dry Sliding Surfaces Based on 3-D Measurements

D surface morphology measurements of compact graphite irons were used to analyze the frac-tal characteristics of the surfaces to relate the dry sliding surface morphology to the fractal dimension. The measurements show that the fractal dimensions (Df ) of the sliding surfaces vary from1 to 2 and are closely related to the surface morphologies. Increasing depths of grooves or pits increases the Df values. At the same time, increasing densities of the grooves also causes the Df values to increase. The data can be used to discuss relationship between Df and the friction coefficient as well as the wear rate.

Tunnel geometry of the subterranean termite Reticulitermes grassei （Isoptera： Rhinotermitidae）in response to sand bulk density and the presence of food

The cryptic habits of subterranean termites restricts detailed analysis of their foraging patterns in situ, but the process is evidently dominated by tunnel constructions connecting the nest with woody resources discovered within the territory of each colony. In this study, tunnel formation and orientation were studied experimentally in the termite Reticulitermes grassei （Clement）, using 2-dimensional laboratory foraging arenas con- taining fine sand as the substratum. The building of exploratory tunnels over a 10-day period and the geometry of the resulting network are described. Fractal analysis showed that tunnel geometry had a fractal dimension, regardless of the total length tunnelled whether foragers encountered the food source or not. The bulk density of the sand in the arenas affected the distances tunnelled, with higher density reducing construction, but did not affect tunnel geometry. Tunnels were not discernibly orientated with respect to the positioning of the food source, even in a situation where termites had failed to find the food source at a distance of less than 50 mm, suggesting that volatiles from wood are not attractants.

EDT Method for Multiple Labelled Objects Subject to Tied Distances

The success of new scientific areas can be assessed by their potential for contributing to new theoretical approaches aligned with real-world applications.The Euclidean distance transform(EDT)has fared well in both cases,providing a sound theoretical basis for a number of applications,such as median axis transform,fractal analysis,skeletonization,and Voronoi diagrams.Despite its wide applicability,the discrete form of the EDT includes interesting properties that have not yet been fully exploited in the literature.In this paper,we are particularly interested in the properties of 1)working with multiple objects/labels;and 2)identifying and counting equidistant pixels/voxels from certain points of interest.In some domains(such as dataset classification,texture,and complexity analysis),the result of applying the EDT transform with different objects,and their respective tied distances,may compromise the performance.In this sense,we propose an efficient modification in the method presented in[1],which leads to a novel approach for computing the distance transform in a space with multiple objects,and for counting equidistant pixels/voxels.