Skin Lesion Classification Based on Surface Fractal Dimensions and Statistical Color Cluster Features Using an Ensemble of Machine Learning Techniques

(1) Background: An approach for skin cancer recognition and classification by implementation of a novel combination of features and two classifiers, as an auxiliary diagnostic method, is proposed. (2) Methods: The predictions are made by k-nearest neighbor with a 5-fold cross validation algorithm and a neural network model to assist dermatologists in the diagnosis of cancerous skin lesions. As a main contribution, this work proposes a descriptor that combines skin surface fractal dimension and relevant color area features for skin lesion classification purposes. The surface fractal dimension is computed using a 2D generalization of Higuchi’s method. A clustering method allows for the selection of the relevant color distribution in skin lesion images by determining the average percentage of color areas within the nevi and melanoma lesion areas. In a classification stage, the Higuchi fractal dimensions (HFDs) and the color features are classified, separately, using a kNN-CV algorithm. In addition, these features are prototypes for a Radial basis function neural network (RBFNN) classifier. The efficiency of our algorithms was verified by utilizing images belonging to the 7-Point, Med-Node, and PH2 databases; (3) Results: Experimental results show that the accuracy of the proposed RBFNN model in skin cancer classification is 95.42% for 7-Point, 94.71% for Med-Node, and 94.88% for PH2, which are all significantly better than that of the kNN algorithm. (4) Conclusions: 2D Higuchi’s surface fractal features have not been previously used for skin lesion classification purpose. We used fractal features further correlated to color features to create a RBFNN classifier that provides high accuracies of classification.

Study on the Influence of Three Factors on Mass Loss and Surface Fractal Dimension of Concrete in Sulfuric Acid Environments

When exposed to sulfuric acid environments, the service life of concrete structures would be reduced due to the high alkalinity of concrete. The influence of three factors including water/cement ratio, the pH value of the solution, and the chemical composition of the aggregate on the resistance of concrete subjected to sulfuric acid has been widely investigated by previous researchers. This paper aims to investigate the influence of these three factors on the durability evaluation indicators including mass loss and surface fractal dimension through orthogonal experiments, which has been reported rarely in previous research. Four combinations of coarse and fine aggregate including gravel and river sand, gravel and crushed marble sand, crushed marble stone and river sand, and crushed marble stone and marble sand were adopted, and three water/cement ratios including 0.35, 0.45, and 0.55 were selected, and the sulfuric acid solution pH values 0.95, 2, and 4 were chosen in this paper. The results showed that the larger the water/cement ratio, the smaller the mass loss and the surface fractal dimension of the specimens, and with the decrease of the pH value of the sulfuric acid solution, the mass loss and the surface fractal dimension of the specimens would be increased. The concrete specimen containing gravel and river sand had the greatest surface fractal dimension and greatest mass loss, while the concrete specimen containing crushed marble sand had a smaller surface fractal dimension and a smaller mass loss. The dominant and secondary order of three factors on mass loss and surface fractal dimension of concrete subjected to sulfuric acid was the pH value of the solution > the chemical composition of the aggregate > the water/cement ratio.

Contrast Variation Small Angle Neutron Scattering Investigation of Micro- and Nano-Sized TATB

Small angle neutron scattering (SANS) with contrast variation was used to characterize the fractal behavior and embedded porosity of micro/nano-sized 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) crystallites, gauging the effects of particle sizes on the microstructural features. Scattering results reveal that the external surface of micro-sized TATB crystallites are continuous and smooth interfaces and their internal pores display a surface fractal structure (surface fractal dimension 2.15 < DS < 2.25), while the external surface of nano-sized TATB particles exhibit a surface fractal structure (surface fractal dimension 2.36 < DS < 2.55) and their internal pores show a two-level volume fractal structure (large voids consist of small voids). The voids volume fraction of nano-sized TATB particles are found increased distinctively when compared with micro-sized TATB particles on length scale between 1 nm and 100 nm. Specific surface areas are also estimated based on Porod law method, which are coincident with Brunauer-Emmett-Teller (BET) measurements. The contrast variation technique distinguishes the information of internal voids from external surface, suggesting SANS is a powerful tool for determining the microstructural features, which can be used to establish the relationship between microstructures and properties of micro/nano-energetic materials.

FRACTAL MODEL FOR THE CORRELATION RELATING TOTAL SUCTION TO WATER CONTENT OF BENTONITES

Great efforts have been made to determine total suction using elaborate laboratory tests, because there is no a specific correlation relating the total suction to the water content of bentonites. However, elaborate laboratory tests are difficult and time consuming to perform on bentonites. Thus, a theoretical equation is a necessary choice to correlate the total suction to the water content. A simple method is proposed to calculate the total suction from the water content based on the surface fractal model for bentonites. The correlation relating the total suction to the water content is expressed by a power-law function with the exponent of [Formula: see text] is the surface fractal dimension of bentonites. The surface fractal dimension can be determined using the nitrogen adsorption isotherm tests. The total suction of bentonites calculated from the proposed method is in satisfactory agreement with the experimental data found in the literature. In addition, the correlation of the total suction to the water content also offers another method to determine the surface fractal dimension of bentonites.

Relevance of coral geometry in the outcomes of the coral-algal benthic war

Corals have built reefs on the benthos for millennia, becoming an essential element in marine ecosystems. Climate change and human impact, however, are favoring the invasion of non-calcifying benthic algae and reducing coral coverage. Corals rely on energy derived from photosynthesis and heterotrophic feeding, which depends on their surface area, to defend their outer perimeter. But the relation between geometric properties of corals and the outcome of competitive coral-algal interactions is not well known. To address this, 50 coral colonies interacting with algae were sampled in the Caribbean island of Curaçao. 3D and 2D digital models of corals were reconstructed to measure their surface area, perimeter, and polyp sizes. A box counting algorithm was applied to calculate their fractal dimension. The perimeter and surface dimensions were statistically non-fractal, but differences in the mean surface fractal dimension captured relevant features in the structure of corals. The mean fractal dimension and surface area were negatively correlated with the percentage of losing perimeter and positively correlated with the percentage of winning perimeter. The combination of coral perimeter, mean surface fractal dimension, and coral species explained 19% of the variability of losing regions, while the surface area, perimeter, and perimeter-to-surface area ratio explained 27% of the variability of winning regions. Corals with surface fractal dimensions smaller than two and small perimeters displayed the highest percentage of losing perimeter, while corals with large surface areas and low perimeter-to-surface ratios displayed the largest percentage of winning perimeter. This study confirms the importance of fractal surface dimension, surface area, and perimeter of corals in coral-algal interactions. In combination with non-geometrical measurements such as microbial composition, this approach could facilitate environmental conservation and restoration efforts on coral reefs.