Fractal dimension and lacunarity analysis of retinal microvascular morphology in hypertension and diabetes

ABSTRACTObjectives: The aim was to assess whether Fractal Dimension and Lacunarity analysis can discriminate patients having different mandibular cortical shape.Methods: Panoramic radiographs of 52 patients were evaluated for mandibular cortical index. Weighted Kappa between the observations were varying between 0.718-0.805. These radiographs were scanned and converted to binary images. Fractal Dimension and Lacunarity were calculated from the regions where best represents the cortical morphology.Results: It was found that there were statistically significant difference between the Fractal Dimension and Lacunarity of radiographs which were classified as having Cl 1 and Cl 2 (Fractal Dimension P:0.000; Lacunarity P:0.003); and Cl 1 and Cl 3 cortical morphology (Fractal Dimension P:0.008; Lacunarity P:0.001); but there was no statistically significant difference between Fractal Dimension and Lacunarity of radiographs which were classified as having Cl 2 and Cl 3 cortical morphology (Fractal Dimension P:1.000; Lacunarity P:0.758).Conclusions: FD and L can differentiate Cl 1 mandibular cortical shape from both Cl 2 and Cl 3 mandibular cortical shape but cannot differentiate Cl 2 from Cl 3 mandibular cortical shape on panoramic radiographs. (Eur J Dent 2008;2:283-290)

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Fractal dimension and lacunarity analysis of mandibular bone on digital panoramic radiographs of tobacco users

Journal of Dental Research Dental Clinics Dental Prospects ◽

10.34172/joddd.2021.024 ◽

2021 ◽

Vol 15 (2) ◽

pp. 140-146

Author(s):

Suman Basavarajappa ◽

Vijayalakshmi Konddajji Ramachandra ◽

Shrawan Kumar

Keyword(s):

Fractal Dimension ◽

Trabecular Bone ◽

Control Group ◽

Healthy Controls ◽

Control Groups ◽

Panoramic Radiographs ◽

Significant Difference ◽

The Mean ◽

And Control ◽

Lacunarity Analysis

Background. This study aimed to evaluate and compare changes in the mandibular trabecular bone pattern using the fractal dimension (FD) and lacunarity analysis in tobacco users with healthy controls. Methods. This study was carried out on digital panoramic radiographs of 225 subjects divided into three groups: smokeless tobacco users (SLTs), smokers, and control (n=75). ImageJ program with FracLac plugin was used to assess the FD and lacunarity of mandibular trabecular bone on the digital panoramic radiographs. Results. The differences in the mean FD values of the study and control groups were statistically significant (P<0.001). Mean FD was lower in the case groups than the control group, with SLTs having the least FD value. A significant difference in lacunarity was noted between SLTs and controls (P<0.001). On the contrary, there was no significant difference in lacunarity between smokers and controls. Conclusions. FD values were lower in tobacco users, suggesting that tobacco users have a less complex trabecular bone pattern than healthy controls. Higher lacunarity values in SLTs indicated a more heterogeneous bone pattern. These findings signify that FD and lacunarity analysis on digital panoramic radiographs can serve as promising predictive tools to assess bone quality for osteoporotic changes in tobacco users, thereby facilitating prompt referral for further management.

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Surface texture characterization of selective laser melted Ti-6Al-4V components using fractal dimension and lacunarity analysis

Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture ◽

10.1177/0954405420971081 ◽

2020 ◽

pp. 095440542097108

Author(s):

Akhil V ◽

Arunachalam N ◽

Raghav G ◽

Sivasrinivasu Devadula

Keyword(s):

Surface Roughness ◽

Fractal Dimension ◽

Additive Manufacturing ◽

Surface Texture ◽

Surface Characterization ◽

Transform Method ◽

Study Results ◽

Lacunarity Analysis ◽

Surface Images

The Selective Laser Melting (SLM) process based additive manufacturing has wide applications in medical, aerospace, defense, and automotive industries. To qualify the components for certain tribological applications, the characterization of surface texture is very important. But the applicability of traditional methods and parameters to characterize the surface texture were under evaluation. As the nature manufacturing the components were very different and complex, the unconventional surface characterization methods also under evaluation to reveal much more meaningful information. This study demonstrates the surface characterization of Ti-6Al-4V SLM components using fractal analysis of the surface images. The computed fractal dimension using the Fourier transform method showed a strong correlation of more than 0.8 with the measured 3D surface roughness parameters. The change in anisotropic nature of the surface images with the process parameter variation is studied and found that the surface textures showed a weaker anisotropic nature at lower laser power ranges, high scanning speed, and high hatch distance values. The lacunarity analysis is carried out using the gliding box algorithm to study the homogeneity nature of the surface texture and found that the surface texture is more homogeneous at higher surface roughness conditions. The study results can be utilized for the development of a quick, low-cost surface monitoring system in real-time for additive manufacturing industries.

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Use of fractals to describe microstructures of porous thick-film platinum electrodes

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100121971 ◽

1992 ◽

Vol 50 (1) ◽

pp. 314-315

Author(s):

Steven D. Toteda

Keyword(s):

Fractal Dimension ◽

Power Plants ◽

Electrical Response ◽

Cubic Phase ◽

Platinum Electrodes ◽

Fine Grained ◽

Impedance Response ◽

Platinum Particles ◽

Energy Surfaces ◽

Highly Porous

Zirconia oxygen sensors, in such applications as power plants and automobiles, generally utilize platinum electrodes for the catalytic reaction of dissociating O2 at the surface. The microstructure of the platinum electrode defines the resulting electrical response. The electrode must be porous enough to allow the oxygen to reach the zirconia surface while still remaining electrically continuous. At low sintering temperatures, the platinum is highly porous and fine grained. The platinum particles sinter together as the firing temperatures are increased. As the sintering temperatures are raised even further, the surface of the platinum begins to facet with lower energy surfaces. These microstructural changes can be seen in Figures 1 and 2, but the goal of the work is to characterize the microstructure by its fractal dimension and then relate the fractal dimension to the electrical response. The sensors were fabricated from zirconia powder stabilized in the cubic phase with 8 mol% percent yttria. Each substrate was sintered for 14 hours at 1200°C. The resulting zirconia pellets, 13mm in diameter and 2mm in thickness, were roughly 97 to 98 percent of theoretical density. The Engelhard #6082 platinum paste was applied to the zirconia disks after they were mechanically polished ( diamond). The electrodes were then sintered at temperatures ranging from 600°C to 1000°C. Each sensor was tested to determine the impedance response from 1Hz to 5,000Hz. These frequencies correspond to the electrode at the test temperature of 600°C.

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