Measurement Of Fractal Dimension Research Articles

Retinal Oxygen Delivery and Extraction in Ophthalmologically Healthy Subjects With Different Blood Pressure Status.

PurposeTo compare retinal oxygen delivery (DO2) and oxygen extraction (VO2) in ophthalmologically healthy subjects with different blood pressure (BP) status.MethodsIn this case-control study, we prospectively included 93 eyes of 93 subjects (aged 50–65 years) from a Dutch cohort (n = 167,000) and allocated them to four groups (low BP, normal BP [controls], treated arterial hypertension [AHT], untreated AHT). We estimated vascular calibers from fundus images and fractal dimension from optical coherence tomography angiography scans. We combined calibers, fractal dimension, BP, and intraocular pressure measurements in a proxy of retinal blood flow (RBF), using a Poiseuille-based model. We measured arterial and venous oxygen saturations (SaO2, SvO2) with a scanning laser ophthalmoscope. We calculated the DO2 and VO2 from the RBF, SaO2, and SvO2. We compared the DO2 and VO2 between groups and investigated the DO2–VO2 association.ResultsDO2 and VO2 were different between groups (P = 0.009, P = 0.036, respectively). In a post hoc analysis, the low BP group had lower DO2 than the untreated AHT group (P = 4.9 × 10−4). The low BP group and the treated AHT group had a lower VO2 than the untreated AHT group (P = 0.021 and P = 0.034, respectively). There was a significant DO2–VO2 correlation (Robs = 0.65, bobs = 0.51, P = 2.4 × 10−12). After correcting for shared measurement error, the slope was not significant.ConclusionsThe DO2 and VO2 were altered in ophthalmologically healthy subjects with different BP status. Future studies could elucidate whether these changes can explain the increased risk of ophthalmic pathologies in those subjects.Translational RelevanceUnderstanding the baseline interplay between BP, retinal perfusion, and oxygenation allows for improved evaluation of retinal disease manifestation.

Investigation of anodised surface complexity and its correlation with surface hydrophilicity using fractal analysis

Anodising is a process of developing oxide coating on surface of metal electrolytically to improve its corrosion resistance. However, there has been inadequate research on the impact of the anodised surface characteristics on hydrophobicity or hydrophilicity. Surface roughness and porosity are often used to quantify surface characteristics, while each alone could not be enough to reflect all complexity of the surface. Hence, the fractal theory utilised to quantify the complexity of the anodised surface and decode its relation with the hydrophobicity or hydrophilicity of the surface. In this study, experiments of anodising for aluminium 6061 were carried out with three concentrations of electrolyte (3.5, 2.5 and 1.5 mol) and three current densities (1.0, 1.5 and 2.0 A/dm2). In addition, the surface characteristics after anodising was studied by using Scanning Electron Microscopy (SEM) analysis. Furthermore, surface roughness measurement was performed to obtain the surface roughness profile for fractal analysis. Moreover, a hydrophobicity test was implemented on anodised samples to obtain the contact angle between the water droplet and the surface. The outcomes showed that higher fractal dimension of anodised surface resulted in a smaller contact angle presenting a more hydrophilic surface. Furthermore, anodised samples with higher current density and concentration of electrolyte will result in higher fractal dimension and hence lower contact angle indicating the anodised surface will become more hydrophilic. Therefore, it is shown that measurement of fractal dimension is a reliable indicator for predication of surface wettability after anodising in order to improve the paint adhesion.

Fractal Dimension Analysis to Detect the Progress of Cancer Using Transmission Optical Microscopy

Fractal dimension, a measure of self-similarity in a structure, is a powerful physical parameter for the characterization of structural property of many partially filled disordered materials. Biological tissues are fractal in nature and reports show a change in self-similarity associated with the progress of cancer, resulting in changes in their fractal dimensions. Here, we report that fractal dimension measurement is a potential technique for the detection of different stages of cancer using transmission optical microscopy. Transmission optical microscopy of a thin tissue sample produces intensity distribution patterns proportional to its refractive index pattern, representing its mass density distribution. We measure fractal dimension detection of different cancer stages and find its universal feature. Many deadly cancers are difficult to detect in their early to different stages due to the hard-to-reach location of the organ and/or lack of symptoms until very late stages. To study these deadly cancers, tissue microarray (TMA) samples containing different stages of cancers are analyzed for pancreatic, breast, colon, and prostate cancers. The fractal dimension method correctly differentiates cancer stages in progressive cancer, raising possibilities for a physics-based accurate diagnosis method for cancer detection.

Evaluation of architectural changes in mandibular trabecular and cortical bone pattern after functional treatment

Abstract Purpose: To assess the changes in mandibular trabecular and cortical bone following functional appliance treatment through fractal dimension (FD) and cortical thickness (CorT) measurements. Material and methods The study was performed on 45 mandibular retrognathia cases. While the treatment group (T) comprised 30 patients treated using a functional appliance for one year during puberty, the control group (C) consisted of 15 patients who did not receive any orthodontic treatment due to insufficient oral hygiene. FD and CorT analyses were bilaterally evaluated for each mandible. FD measurements were performed on the condylar process, the antegonial notch, and ramus regions on panoramic radiographs. A paired t-test was applied for group analysis, before (T1) and after treatment (T2) and, correspondingly, before (C1) and after (C2) controls. In addition, an independent t-test was used to determine differences between the treatment (∆T = T2−T1) and the control group (∆C = C2−C1). Results Statistically significant differences were found in the treatment group between the initial and post-treatment FD values of the right (p < 0.05) and left condyles (p < 0.05), and the CorT measurements on the right (p < 0.01) and the left sides (p < 0.05). There was no statistically significant difference in FD parameters in the control group and a significant difference was only found in the left CorT (p < 0.05). A comparison of the treatment and control groups revealed that the changes in FD and CorT measurements were not statistically significantly different between the groups (p > 0.05). Conclusion: Mandibular protraction appliances do not produce trabecular bone alteration in the mandibular condyles, the antegonial notch and ramus over a 12-month time period.

A comparison between “rod counting” and “box counting” methods in linear fractal dimensions measurements

In this work, the “rod counting” method is reviewed in comparison with the “box counting” method applied to linear measurements on irregular figures. Both methods are applied in measurements of fractal dimension of some knowing fractals. Results shows that the “rod counting” method is more accurate in linear measurements. Later the method is applied in a Mandelbrot fractal figure to measure its perimeter fractal dimension.

The analysis of F-actin structure of mesenchymal stem cells by quantification of fractal dimension.

The actin cytoskeleton is indispensable for the motility and migration of all types of cells; therefore, it plays a crucial role in the ability of the tissues to repair. Mesenchymal stem cells are intensively used in regenerative medicine, but usually relatively low percent of transplanted cells reaches the injury. To overcome this evident limitation, researchers try to enhance the motility and migration rate of the cells. As one of the approaches, co-cultivation and preconditioning of stem cells with biologically active compounds, which can cause actin cytoskeleton rearrangements followed by an increase of migratory properties of the cells, could be applied. The observed changes in F-actin structure induced by the compounds require quantitative estimation, and measurement of fluorescence intensity of the F-actin image captured by various microscopic techniques is commonly used nowadays. However, this approach could not always accurately detect the observed changes in the shape and structure of actin cytoskeleton. At this time, the image of F-actin has an irregular geometric pattern, and thus could be considered and characterized as a fractal object. To quantify the re-organization of cellular F-actin in terms of fractal geometry Minkovsky’s box-counting method is suitable, but it is not widely used nowadays. We modified and improved the previously described method for fractal dimension measurement, and successfully applied it for the quantification of the F-actin structures of human mesenchymal stem cells.

Fractal and Multifractal Analysis of PET-CT Images for Therapy Assessment of Metastatic Melanoma Patients under PD-1 Inhibitors: A Feasibility Study.

Simple SummaryThe fractal dimension (FD) and the multifractal spectrum (MFS) are nonlinear quantitative measures which express the heterogeneity in the distribution of the tracer, F-18-fluorodeoxyglucose, (18F-FDG), in the body of patients suffering from metastatic melanoma. Given the well-documented, high accumulation of the tracer in tumor/metastatic sites, the measures expressing the tracer distribution also express the extent of metastases in the body. As such, FD and MFS can be employed to detect the presence of melanoma and to monitor the therapeutic outcome using the PET-CT follow-up digitized scans of the patients. In the present study, the FD and MFS measures of patients are evaluated before and during treatment with PD-1 inhibitors and are compared with the corresponding values of healthy controls. The MFS predictions agree with the PET Response Evaluation Criteria for Immunotherapy (PERCIMT) in 81% of the cases, while the FD agrees in 77% of all cases. Therefore, the quantitative MFS is proposed as an additional, alternative biomarker for monitoring the immunotherapy outcome in melanoma patients, after treatment with PD-1 inhibitors.Longitudinal whole-body PET-CT scans with F-18-fluorodeoxyglucose (18F-FDG) in patients suffering from metastatic melanoma were analyzed and the tracer distribution in patients was compared with that of healthy controls. Nineteen patients with metastatic melanoma were scanned before, after two and after four cycles of treatment with PD-1 inhibitors (pembrolizumab, nivolumab) applied as monotherapy or as combination treatment with ipilimumab. For comparison eight healthy controls were analyzed. As quantitative measures for the comparison between controls and patients, the nonlinear fractal dimension (FD) and multifractal spectrum (MFS) were calculated from the digitized PET-CT scans. The FD and MFS measures, which capture the dispersion of the tracer in the body, decreased with disease progression, since the tracer particles tended to accumulate around metastatic sites in patients, while the measures increased when the patients’ clinical condition ameliorate. The MFS measure gave better predictions and were consistent with the PET Response Evaluation Criteria for Immunotherapy (PERCIMT) in 81% of the cases, while FD agreed in 77% of all cases. These results agree, qualitatively, with a previous study of our group when treatment with ipilimumab monotherapy was considered.

Therapeutic Hypothermia Reduces Peritoneal Dialysis Induced Myocardial Blood Flow Heterogeneity and Arrhythmia.

Background: Moderate therapeutic hypothermia (TH) is a well-recognized cardio-protective strategy. The instillation of fluid into the peritoneum provides an opportunity to deliver moderate hypothermia as primary prevention against cardiovascular events. We aimed to to investigate both cardiac perfusion consequences (overall blood flow and detailed assessment of perfusion heterogeneity) and subsequently simulate the associated arrhythmic risk for patients undergoing peritoneal dialysis (PD) induced TH.Methods: Patients underwent high resolution myocardial perfusion scanning using high resolution 256 slice CT scanning, at rest and with adenosine stress. The first visit using the patient's usual PD regimen, on the second visit the same regime was utilized but with cooled peritoneal dialysate at 32°C. Myocardial blood flow (MBF) was quantified from generated perfusion maps, reconstructed in 3D. MBF heterogeneity was assessed by fractal dimension (FD) measurement on the 3D left ventricular reconstruction. Arrhythmogenicity was quantified from a sophisticated computational simulation using a multi-scale human 3D ventricle wedge electrophysiological computational model.Results: We studied 7 PD patients, mean age of 60 ± 7 and mean vintage dialysis of 23.6 ± 17.6 months. There were no significant different in overall segmental MBF between normothermic condition (NT) and TH. MBF heterogeneity was significantly decreased (−14%, p = 0.03) at rest and after stress (−14%, p = 0.03) when cooling was applied. Computational simulation showed that TH allowed a normalization of action potential, QT duration and T wave.Conclusion: TH-PD results in moderate hypothermia leading to a reduction in perfusion heterogeneity and simulated risk of non-terminating malignant ventricular arrhythmias.

Effects of hyperlipidemia on trabecular and cortical structures of the mandible.

To evaluate the mandibular bone structure of patients with hyperlipidemia by fractal dimension (FD) analysis and panoramic radiomorphometric indices including mandibular cortical thickness measurement, panoramic mandibular index (PMI), mandibular cortical index (MCI) and to compare with the healthy group. In total, 60 panoramic radiographs were included, including panoramic radiographs of 30 individuals with hyperlipidemia and 30 individuals with systemically healthy. FD analysis in the mandibular condyle, angle of the mandible, the distal side of the second premolar and anterior to mental foramen, PMI, MCI, and mandibular cortical thickness measurements were evaluated on radiographs. Independent samples t-test was used for differences between healthy and hyperlipidemia groups with regard to age and PMI. Repeated measurement of variance with one within and one between factors in the comparison of four regions and two groups in terms of FD and cortical thickness measurements. Following this analysis, significant differences were detected by post-hoc Sidak test. Fisher-Freeman-Halton analysis was applied to determine the relationship between categorical variables. FD values of the hyperlipidemic patients were found to be lower than the healthy group. Between the hyperlipidemic and healthy groups, there was a difference in the angle of the mandible FD values (p = 0.020). There were no differences in the cortical thickness measurements and PMI between the groups (p > 0.05). There was a difference in MCI values between the groups (p < 0.05). The trabecular structure of the angle of the mandible and the cortical bone structure of the mandible were found to be negatively affected by hyperlipidemia.

The ecological importance of habitat complexity to the Caribbean coral reef herbivore Diadema antillarum: three lines of evidence

When Caribbean long-spined sea urchins, Diadema antillarum, are stable at high population densities, their grazing facilitates scleractinian coral dominance. Today, populations remain suppressed after a mass mortality in 1983–1984 caused a loss of their ecosystem functions, and led to widespread declines in ecosystem health. This study provides three lines of evidence to support the assertion that a lack of habitat complexity on Caribbean coral reefs contributes to their recovery failure. Firstly, we extracted fractal dimension (D) measurements, used as a proxy for habitat complexity, from 3D models to demonstrate that urchins preferentially inhabit areas of above average complexity at ecologically relevant spatial scales. Secondly, controlled behaviour experiments showed that an energetically expensive predator avoidance behaviour is reduced by 52% in complex habitats, potentially enabling increased resource allocation to reproduction. Thirdly, we deployed a network of simple and cost-effective artificial structures on a heavily degraded reef system in Honduras. Over a 24-month period the adult D. antillarum population around the artificial reefs increased by 320% from 0.05 ± 0.01 to 0.21 ± 0.04 m−2 and the juvenile D. antillarum population increased by 750% from 0.08 ± 0.02 to 0.68 ± 0.07 m−2. This study emphasises the important role of habitat structure in the ecology of D. antillarum and as a barrier to its widespread recovery.

Improved box-counting methods to directly estimate the fractal dimension of a rough surface

Rough surfaces exist widely in nature, and the measurement of these surfaces’ fractal dimension is beneficial for understanding their formation mechanism and effect. The basic principles of previous cubic covering methods are described, and then the stable cubic covering method (SCCM) and stable differential cubic covering method (SDCCM) are proposed based on the box-counting method. Afterward, a real sandstone fracture surface and Takagi surfaces are adopted to compare these methods’ differences. The results show that different measurement methods are needed to measure surfaces with different theoretical fractal dimensions. Meanwhile, the SCCM and SDCCM can obtain more stable measurement results than previous methods. Then, the recommended methods and their corresponding scale factors are summarized. Finally, the potential of these cubic covering methods to measure a thick film is described. The research is of great significance to the fractal dimension measurement of a rough surface or a thick film.

Market efficiency in the art markets using a combination of long memory, fractal dimension, and approximate entropy measures

In this paper, we investigate the efficiency in the art markets, using a generalized spectral test (GST) in a rolling window approach to detect departure from the martingale difference hypothesis (MDH) and trace the periods of market efficiency over time. Then we complement our results using the approximate entropy, the rescaled range analysis, and fractal dimension. We combine the three measures in an Efficiency Index for each market. Applying these methods, we find that the Modern Art, Paintings, Post-war, Prints, the USA market, and the global market in Euro show the largest values for the Approximate Entropy. Using the rescaled range estimates, we find that all markets are characterized by persistent behavior and, then using the Efficiency Index, our results indicate overwhelming evidence of market inefficiency in almost all sectors. Finally, we support our findings with some explanation of the reasons behind market inefficiency, related to asymmetrical information, influential galleries power, and differentiated pieces and talents in the art markets.

Real Time Cognitive State Prediction Analysis using Brain Wave Signal

The teaching-learning process is seeing a big transformation in this digital age. It involves digital classrooms with various accessories of online tools such as video conferencing, digital materials, and other platforms for learning and assessment with options for both real-time and self-paced work in addition to the availability of teachers over video conferencing, text, phone, email, etc. To improve the online learning efficiency, assessing the cognitive state during the learning phase is highly required for the success of these developments. This work focused on cognitive state analysis during different learning tasks is determined by EEG brain signals that are captured using 128 channels Emotive Epoch headset device. Artifacts prominent in raw signals are filtered by linear filtering. Feature extraction for determination of concentration levels is done by applying fuzzy fractal dimension measures and Discrete Wavelet Transform (DWT) on the processed signals. The classification of extracted parameters into concentration levels is done by using deep learning algorithms like Enhanced Convolutional Neural Network (ECNN). This ECNN deep learning classification is highly accurate amongst all other remaining classifiers and is used as a feedback model to regulate this cognitive state.

Forensic and reliability analyses of fixed dental prostheses.

This article describes the protocol for determining the cause of failure for retrieved failed implant supported fixed dental prostheses (FDPs) in a clinical study of three-unit bridges. The results of loading of flexure bars of different veneer compositions at different stress rates were presented for two veneer materials (leucite reinforced and fluorapatite glass-ceramic veneers) and a Y-TZP core zirconia ceramic used in the clinical study. From these results, the strengths of the fast loading conditions were used to determine the fracture toughness of these materials. Fractal dimension measurements of the flexure bars and selected FDPs of the same materials demonstrated that the values were the same for both the bars and the FDPs. This allowed the use of fracture toughness values from the flexure bars to determine the strengths of the FDPs. The failure analysis of clinically obtained FDP replicates to determine the size of the fracture initiating cracks was then performed. Using the information from the flexure bars and the size of the fracture initiating cracks for the failed FDPs, the strengths of the FDPs were determined. The clinical failures were determined to be most likely the result of repeated crack growth due to initial overload and continuous use after initial cracking.

Macular vessel density, branching complexity and foveal avascular zone size in normal tension glaucoma

The aim of this study was to investigate the relationship between glaucoma severity and perifoveal vessel density (pfVD), branching complexity, and foveal avascular zone (FAZ) size in normal tension glaucoma (NTG). 31 patients with NTG washed out of glaucoma medications were subjected to tests including; intraocular pressure measurement; standard automated perimetry; optical coherence tomography (OCT) measurement of macular ganglion cell complex (mGCC), inner macular thickness (IMT) and circumpapillary retinal nerve fibre layer (cpRNFL); and OCT angiography measurement of pfVD, FAZ perimeter and multispectral fractal dimensions (MSFD). Eyes with more severe glaucoma had significantly thinner mGCC and cpRNFL and lower pfVD. MD decreased by 0.4 dB (95% CI 0.1 to 0.6 dB, P = 0.007) for every 1% decrease in pfVD. Lower MSFD was observed in eyes with lower pfVD and in patients with systemic hypertension. Multivariable analysis, accounting for age and OCTA quality, found lower pfVD remained significantly associated with thinner IMT, thinner mGCC and worse MD but not with MSFD. pfVD was reduced in NTG and was diminished in eyes with worse MD. Macular vessel branching complexity was not related to severity of visual field loss but was lower in patients with systemic hypertension.

Pupillary Complexity for the Screening of Glaucoma

Glaucoma is a leading cause of irreversible visual field loss. The early detection and diagnosis of the disease are therefore necessary to prevent blindness. Pupillary light responses are an interesting new technique for the detection of glaucoma. However, the analysis of pupillary signals has been associated with manual supervision or involved high computational costs. The present paper is to propose an analysis framework to automatically investigate changes in the complexity of pupillary signals under ambient light conditions for the screening of glaucoma. In this work, pupillary data of 13 glaucoma patients, 13 age-matched controls, and 11 young controls were recorded at the light intensity of 100 cd/m2 using a commercial eye tracker. The pupillary complexity of the participants was analysed using Higuchi’s fractal dimension, permutation entropy, and conditional entropy. We found that there was a statistically significant difference in the pupillary complexity between glaucoma patients and control groups (P < 0.0001). Specifically, the difference was more pronounced when using the fractal dimension measure. These results confirm the potential of using pupillary complexity for the screening of glaucoma using commercial devices.

Assessment the Effect of Exposure Conditions and Geometry Parameters on Calculated Fractal Dimension of Mandibular Bone

Introduction: One of the fractal analysis methods to examine the structure of a texture is fractal dimension (F.D.) measurement. F.D is a quantitative method to show the complexity of a structure using a number. The aim of this study was to determine the effect of different exposure conditions, voltages and angle of x-ray tube on F.D. values of mandibular bone. Methods: This lab-trial analytical research was conducted on ten healthy, non-fracturing human mandibles. Periapical digital images were obtained by the Peri-Apical Focus (Planmeca, Finland) with a constant time of 0.2 seconds and changes in exposure conditions and angle of the tube. Periapical radiographs were obtained with 2 kV voltages of 60, 70, with2 mA of 400, 500, and 3 tube angles of -5, 0, +5 degrees. Data was analyzed by SPSS version 16 software and Kolmogorov–Smirnov test, mann whitney test‌and ANOVA test. Results: No significant difference was observed in fractal mean values between 60 and 70 kVp and among 5-, 0, 5+ degrees in all 10 mandibles.There was a significant difference between the 400 and 500 mA just in one case (p≤0.05). Conclusion: Considering the incompatibility of the amount of calculated fractal dimension from kVp, mA and tube angle, this method can be used as a useful tool in dentistry to examine the structure of spongy bone and its changes in various pathological conditions. Then, standardize the periapical imaging technique to compare it is not necessary.

Test-retest reliability of multiscale fractal dimension measurements of plantar pressure maps during dynamic tasks

The tools used to evaluate foot types are divergent since they adopt classic linear analyzes, based on anthropometric or image measurements, which do not dynamically contemplate the variability of foot shape. The use of newer techniques such as multiscale fractal dimension (MFD) may be a key to this type of problem. However, for these measures to be used safely and consistently, it is essential to evaluate their reliability. The aim of this study was to evaluate the test-retest reliability of MFD measurements of adult plantar pressure maps during gait, as well as the standard error of measurement (SEM), and minimal detectable change (MDC90). Seventy-two subjects were included in the test-retest, with a one week interval. The plantar pressure maps were constructed using a pressure platform. The data were processed in a routine for extracting the MFD curve measurements (maximum and integral values). The Intraclass Correlation Coefficient results (ICC3,k) were excellent for both measurements (maximum value 0.96, 95% confidence interval [0.93–0.97], and integral 0.95 [0.92–0.97]) with low SEM and MDC90 values below 10% of the mean. The application of MFD to the plantar pressure data generated by the pressure platform is reliable and could allow exploration of the complexity of foot shapes, enabling their classification.

A quantitative comparison of four optical coherence tomography angiography devices in healthy eyes.

Optical coherence tomography angiography (OCT-A) is a novel imaging modality for the diagnosis of chorioretinal diseases. A number of FDA-approved OCT-A devices are currently commercially available, each with unique algorithms and scanning protocols. Although several published studies have compared different combinations of OCT-A machines, there is a lack of agreement on the consistency of measurements across OCT-A devices. Therefore, we conducted a prospective quantitative comparison of four available OCT-A platforms. Subjects were scanned on four devices: Optovue RTVue-XR, Heidelberg Spectralis OCT2 module, Zeiss Plex Elite 9000 Swept-Source OCT, and Topcon DRI-OCT Triton Swept-Source OCT. 3 mm × 3 mm images were utilized for analysis. Foveal avascular zone (FAZ) area was separately and independently measured by two investigators. Fractal dimension (FD), superficial capillary plexus (SCP), and deep capillary plexus (DCP) vessel densities (VD) were calculated from binarized images using the Fiji image processing software. SCP and DCP VD were further calculated after images were skeletonized. Repeated measures ANOVA, post hoc tests, and interclass correlation coefficient (ICC) were performed for statistical analysis. Sixteen healthy eyes from sixteen patients were scanned on the four devices. Images of five eyes from the Triton device were excluded due to poor image quality; thus, the authors performed two sets comparisons, one with and one without the Triton machine. FAZ area showed no significant difference across devices with an ICC of > 95%. However, there were statistically significant differences for SCP and DCP VD both before and after skeletonization (p < 0.05). Fractal analysis revealed no significant difference of FD at the SCP; however, a statistically significant difference was found for FD at the DCP layer (p < 0.05). The results showed that FAZ measurements were consistent across all four devices, while significant differences in VD and FD measurements existed. Therefore, we suggest that for both clinical follow-up and research studies, FAZ area is a useful parameter for OCT-A image analysis when measurements are made on different machines, while VD and FD show significant variability when measured across devices.

FRACTAL ANALYSIS OF DIGIT ROCK CORES

The rock cores of low permeability reservoirs have special pore structures, which are the essential factors to determine the seepage capacity and oil displacement efficiency and directly affect oil and gas reserves and oil well productivity. This paper studies 16 digital rock core samples. Based on the fractal theory for porous media, we carried out the fractal characterization of the pore structure of the samples by an approach combined with binarized CT images and fractal theory. The computing software based on the Box-counting method was used to measure and calculate the fractal dimension and porosity of the samples, and the calculated results were compared with the binarized CT data from the laboratory. It was found that among the tested samples, the results of 12 rock core samples were in good agreement with the experimental data, indicating that the fractal theory is effective in the measurement of fractal dimension and in the calculation of porosity of digital rock core samples. For the results with larger errors compared to laboratory data, we also analyzed and elaborated the reasons from the relevant binarized images and pore distribution images of samples. It is also found that the minimum pore size has a significant impact on the results when the fractal theory was applied to analyze the digital rock core samples. Finally, a standard or criterion is established whether the pore/particle size distribution in a digit rock core/porous medium is fractal or non-fractal.