Multifractal-based lacunarity analysis of trabecular bone in radiography

A highly generalized classifier for osteoporosis radiography based on multiscale fractal, lacunarity, and entropy distributions

Background: Osteoporosis is a common degenerative disease with high incidence among aging populations. However, in regular radiographic diagnostics, asymptomatic osteoporosis is often overlooked and does not include tests for bone mineral density or bone trabecular condition. Therefore, we proposed a highly generalized classifier for osteoporosis radiography based on the multiscale fractal, lacunarity, and entropy distributions. Methods: We collected a total of 104 radiographs (92 for training and 12 for testing) of lumbar spine L4 and divided them into three groups (normal, osteopenia, and osteoporosis). In parallel, 174 radiographs (116 for training and 58 for testing) of calcaneus from health and osteoporotic fracture groups were collected. The texture feature data of all the radiographs were pulled out and analyzed. The Davies-Bouldin index was applied to optimize hyperparameters of feature counting. Neighborhood component analysis was performed to reduce feature dimension and increase generalization. A support vector machine classifier was trained with only the most effective six features for each binary classification scenario. The accuracy and sensitivity performance were estimated by calculating the area under the curve. Results: Interpretable feature trends of osteoporotic pathological changes were depicted. On the spine test dataset, the accuracy and sensitivity of binary classifiers were 0.851 (95% CI: 0.730-0.922), 0.813 (95% CI: 0.718-0.878), and 0.936 (95% CI: 0.826-1) for osteoporosis diagnosis; 0.721 (95% CI: 0.578-0.824), 0.675 (95% CI: 0.563-0.772), and 0.774 (95% CI: 0.635-0.878) for osteopenia diagnosis; and 0.935 (95% CI: 0.830-0.968), 0.928 (95% CI: 0.863-0.963), and 0.910 (95% CI: 0.746-1) for osteoporosis diagnosis from osteopenia. On the calcaneus test dataset, they were 0.767 (95% CI: 0.629-0.879), 0.672 (95% CI: 0.545-0.793), and 0.790 (95% CI: 0.621-0.923) for osteoporosis diagnosis. Conclusion: This method showed the capacity of resisting disturbance on lateral spine radiographs and high generalization on the calcaneus dataset. Pixel-wise texture features not only helped to understand osteoporosis on radiographs better but also shed new light on computer-aided osteopenia and osteoporosis diagnosis.

Lacunarity as a quantitative measure of mixing—a micro-CT analysis-based case study on granular materials

In practically every industry, mixing is a fundamental process, yet its 3D analysis is scarce in the literature. High-resolution computed tomography (micro-CT) is the perfect X-ray imaging tool to investigate the mixing of granular materials. Other than qualitative analysis, 3D micro-CT images provide an opportunity for quantitative analysis, which is of utmost importance, in terms of efficiency (time and budget) and environmental impact of the mixing process. In this work, lacunarity is proposed as a measure of mixing. By the lacunarity calculation on the repeated micro-CT measurements, a temporal description of the mixing can be given in three dimensions. As opposed to traditional mixing indices, the lacunarity curve provides additional information regarding the spatial distribution of the grains. Discrete element method simulations were also performed and showed similar results to the experiments.

Fractal methods applied to the seminiferous lumen images can quantify testicular changes induced by heat stress

Male infertility affects many couples around the world and can be related to environmental factors such as exposure to high temperatures. Even so, automated methods evaluating the seminiferous tubules to detect testicular damage are still scarce. In search of new approaches to automation in the microscopic analysis of the testis; the present study used the fractal dimension, lacunarity, multifractality and quantitative morphometry to quantify changes in microphotographs of the seminiferous lumen in testicles reversibly damaged by heat stress (43 °C, 12 min). The parameters fractal dimension, lacunarity, multifractality (Dq and α), perimeter, feret and circularity were able to detect changes in the seminiferous lumen at 7, 15 and 30 days after the testicular damage. These methods also detected the recovery of spermatogenesis at 60 days after heat stress. Area, f(α), centroid X and Y, roundness, rectangle height and width were unable to detect changes caused by heat stress. In conclusion, computer assisted methods applied to the seminiferous lumen images can be a useful new viewpoint to analyze microscopic changes in the testicles, a fast low-cost tool to assist in the automated quantification of testicular damage.