Color texture classification is an important step in image segmentation and recognition. The color information is especially important in textures of natural scenes, such as leaves surfaces, terrains ...models, etc. In this paper, we propose a novel approach based on the fractal dimension for color texture analysis. The proposed approach investigates the complexity in R, G and B color channels to characterize a texture sample. We also propose to study all channels in combination, taking into consideration the correlations between them. Both these approaches use the volumetric version of the Bouligand–Minkowski Fractal Dimension method. The results show a advantage of the proposed method over other color texture analysis methods.
► We propose two fractal dimension-based approaches to characterize a color texture. ► The first approach investigates the complexity in R, G and B color channels. ► The second one investigates the complexity in the interaction among these three color channels. ► To achieve this, a new fractal descriptor is also proposed.
Objectives
Aim of the present analysis is to investigate the biodistribution and pharmacokinetics of the recently clinically introduced radioligand
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F-PSMA-1007 in patients with biochemical ...recurrence or progression of prostate cancer (PC) by means of multiparametric (dynamic and whole-body) PET/CT.
Methods
Twenty-five (25) patients with PC biochemical relapse or progression (median age = 66.0 years) were enrolled in the analysis. The median PSA value was 1.2 ng/mL (range = 0.1–237.3 ng/mL) and the median Gleason score was 7 (range = 6–10). All patients underwent dynamic PET/CT (dPET/CT) scanning (60 min) of the pelvis and lower abdomen as well as whole-body PET/CT with
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F-PSMA-1007. PET/CT assessment was based on qualitative evaluation, SUV calculation, and quantitative analysis based on a two-tissue compartment model and fractal analysis.
Results
15/25 patients were PET-positive. Plasma PSA values in the
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F-PSMA-1007 positive group were higher (median = 3.6 ng/mL; range = 0.2–237.3 ng/mL) than in the
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F-PSMA-1007 negative group (median value = 0.7 ng/mL; range = 0.1–3.0 ng/mL). Semi-quantitative analysis in the PC lesions demonstrated a mean SUV
average
= 25.1 (median = 15.4; range = 3.5–119.2) and a mean SUV
max
= 41.5 (median = 25.7; range = 3.8–213.2). Time–activity curves derived from dPET/CT revealed an increasing tracer accumulation during the 60 min of dynamic PET acquisition into the PC lesions, higher than in the urinary bladder and the colon. Significant correlations were observed between
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F-PSMA-1007 uptake (SUV), influx, and fractal dimension (FD).
Conclusions
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F-PSMA-1007 PET/CT could detect PC lesions in 60% of the patients of a mixed population, including also patients with very low PSA values. Higher PSA values were associated with a higher detection rate. Dynamic PET analysis revealed an increasing tracer uptake during the dynamic PET acquisition as well as high binding and internalization of the radiofluorinated PSMA ligand in the PC lesions.
Nanofluids are used to achieve maximum thermal performance with the smallest concentration of nanoparticles and stable suspension in conventional fluids. The effectiveness of nanofluids in convection ...processes is significantly influenced by their increased thermophysical characteristics. However, this technology is not ended here; binary and ternary nanofluids are now used to improve the efficiency of regular fluids. Therefore, this paper aims to analyze the natural convection Newtonian ternary nanofluid flow in a vertical channel. The tri‐hybridized nanoparticles of zinc oxide ZnO, Aluminum oxide Al2O3, and titanium oxide TiO2 is dissolved in base fluid distilled water (DW) to form a homogenous suspension. The impact of thermal radiation, joule heating, and viscous dissipation are also assumed. The classical Newtonian ternary nanofluid model has been generalized by using fractal‐fractional derivative (FFD) operator. The generalized model has been discretized by using the Crank–Nicolson scheme and then solved by using computational software. To analyze the behavior of fluid flow and heat distribution in fluid, the obtained solution was computed numerically and then plotted in response to different physical parameters. It is noted from the figure that when the volume fraction ϕ reaches to 0.04 (4% of the base fluid), the ternary nanofluid flow shows a significant amount of enhancement in heat transfer rate as compared to binary and unary nanofluid flows. This enhancement in the rate of heat transfer leads to improve the thermophysical characteristics such as viscosity, thermal expansion, and heat capacity etc. of the base fluid. It is also worth mentioning here that the thermal field is also enhance with the higher values of Eckert number Ec$Ec$, radiation parameter Rd$Rd$, and joule heating parameter Jh${J_h}$.
Nanofluids are used to achieve maximum thermal performance with the smallest concentration of nanoparticles and stable suspension in conventional fluids. The effectiveness of nanofluids in convection processes is significantly influenced by their increased thermophysical characteristics. However, this technology is not ended here; binary and ternary nanofluids are now used to improve the efficiency of regular fluids. Therefore, this paper aims to analyze the natural convection Newtonian ternary nanofluid flow in a vertical channel.…
Multimodal image fusion is the process of combing relevant biological information that can be used for automated industrial application. In this article, we present a novel framework combining ...fractal constraint with group sparsity to achieve the optimal fusion quality. First, we adopt the idea of patch division and componentwise separation to perceive the fractal characteristics across multimodality sources. Then, to preserve the spatial information against the redundancy of component-entanglement, the group sparsity is proposed. A dual variable weighting rule is inherently embedded to mitigate the overfitting across the component penalty. Furthermore, the alternating direction method of multipliers is conducted to the proposed model optimization. The experiments show that our model has a better performance in quantitative visual quality and qualitative evaluation analysis. Finally, a real segmentation application of positron emission tomography/computed tomography image fusion proves the effectiveness of our algorithm.
Identification of geochemical anomalies is of particular importance for tracing the footprints of anomalies. This can be implemented by advanced techniques of exploratory data analysis, such as ...fractal/multi-fractal approaches based on priori or posteriori distribution of geochemical elements. The latter workflow involves analysis of 2D/3D produced maps, which can be mostly obtained by geostatistical algorithms. There are two challenging issues for such an analysis. The first one corresponds to handling the cross-correlation structures among the data, and the second one relates to the compositional nature of data. To tackle these problems, this paper investigates the application of Gaussian co-simulation for modeling the cross-correlated compositional data in order to recognize the multivariate geochemical anomalies in integration with fractal analysis. In this context, an innovative algorithm, namely co-simulated size number (CoSS-N), is introduced for this purpose. The compositional nature of data is addressed by additive log-ratio transformation of original data while the Gaussian co-simulation handles the reproduction of cross-correlation among the components. The co-simulated outputs are then taken into account for capturing different geochemical populations, showing different levels of backgrounds and anomalies. The algorithm is illustrated via a real case study located in Philippine wherever seven geochemical components are required to be considered. The accuracy of results is examined by statistical validation techniques, indicating the capability of the CoSS-N algorithm for multivariate identification of geochemical anomalies.
Investigate the growth adaptation law of the Tamarix chinensis root system in response to the groundwater level in a muddy coastal zone.
The high groundwater level (0.7–0.9 m), medium groundwater ...level (1.1–1.3 m) and low groundwater level (1.5–1.7 m) T. chinensis forests on the beaches of the Yellow River Delta were used as the research objects. Full excavation methods were used to excavate root systems with different groundwater levels; then, the aboveground biomass, root biomass, root spatial distribution, root topological structure and fractal characteristics of T. chinensis response characteristics to groundwater level were measured and analysed.
The results showed that with the decrease in the groundwater level, the soil water content and soil salt content showed upward trends. At high groundwater levels, T. chinensis reduced root biomass allocation to reduce the damage to roots caused by salinity. At low groundwater levels, T. chinensis strengthened the development of root systems, which greatly enhanced the ability of T. chinensis to balance its water intake. The root biomass at the high groundwater level was 43.06% lower than that at the low groundwater level. The relationship between root and shoot growth of T. chinensis at high groundwater levels and medium groundwater levels indicated allometric growth, and at low groundwater levels, roots and shoots grew uniformly. The root distribution of T. chinensis tended to be shallow at the different groundwater levels, showing the characteristics of a horizontal root type. At high groundwater levels, the root topological structure tended to be dichotomous, and the fractal dimension and fractal abundance values were both large, at 1.31 and 2.77, respectively. The branch complexity increased to achieve spatial expansion and increase plant stability. However, the topological structure of the medium and low groundwater level T. chinensis tended to be herringbone-like, the fractal dimension and fractal abundance values were small, the second branch was limited, and the structure was simple. The topological structure and fractal characteristics of the T. chinensis root system responded to different groundwater levels in a coordinated manner.
Based on the differences in the growth and architecture of the T. chinensis root system, the T. chinensis root system has strong phenotypic plasticity to the heterogeneous water-salt habitat of the groundwater-soil system, and the T. chinensis root system shows strong root adaptability to water and salt stress.
•Groundwater level and salinity significantly affect soil water and salt, thereby affecting the root growth of T. chinensis.•At the low groundwater level, T. chinensis strengthened root development and enhanced the ability to balance water intake.•The root cap showed different allometric growth to adapt to different groundwater level conditions.•T. chinensis can adapt high soil water content by increasing the branch complexity.•Synergistic response of topological structure and fractal characteristics of T. chinensis roots to different water levels.
This paper investigates the dynamical characteristics for meminductor and memcapacitor via fractal–fractional-order domain of Caputo–Fabrizio. A chaos circuit is modeled for the highly nonlinear and ...non-fractional governing differential equations of meminductor and meminductor for knowing the hyperchaos, abrupt chaos and coexisting attractors. The time-scale transformation on dynamical equations is invoked within non-classical approach through newly presented fractal–fractional differential operator of Caputo–Fabrizio. The nonlinear fractionalized governing differential equations of meminductor and meminductor have been simulated by means of Adams–Bashforth–Moulton method. In order to disclose the functionalities of capacitive and inductive elements so-called meminductor and memcapacitor, we specified the fractal–fractional differential operator of Caputo–Fabrizio in three categories as (i) variation in both fractional and fractal parameters, (ii) variation in fractional parameter keeping fractal parameters equal to one, and (iii) variation in fractal parameter keeping fractional parameters equal to one. At the end, our numerically simulated results elaborate that chaotic behavior and unpinched hysteresis loops obtained via fractal–fractional approach are more efficient than ordinary approach.
•Microscopic pore structures of coals were measured by N2 and CO2 adsorption method.•Microscopic pore structure was changed with the increasing gas pressures.•Two conceptual models are introduced to ...explain the reasons for the decreased mesopore volume and increased micropore volume.•Fractal characteristics are used to analyze pore complexity and the roughness.
The characteristics of micropore (0.32–2 nm), mesopores (2–50 nm) and fractal dimensions of bituminous coal during the process of cyclic gas adsorption/desorption were revealed by combining N2 (77 K) and CO2 (273 K) adsorption experiments from microscopic aspect. The results indicate that the pore structure characterization in the coal matrix are changed, resulting in decreased mesopore volumes and increased micropore volumes. The mesopore volumes are mainly constituted by the pores of 10–20, and 20–30 nm, and it will increase at first and then decrease with the increasing pressures. The maximum change of micropore volume reaches 65.6%, indicating a great effect on the micropores influenced by pressures. In addition, the main micropore size range, major peak and the model diameter of coals all increase with the increasing pressures, the higher the adsorb pressure is, the higher swelling is. With the help of the conceptual models, we then analyzed the variation reasons, which may be result from transformation of mesopores and the connection of the inaccessible pores. D1 and D2 in #1 and D2 in #2 all increase with the increasing adsorption pressures, enhancing the roughness of surface and complexity of structure, while D1 in #2 shows an opposite property. The study of variations of microscopic pore structure by cyclic adsorption/desorption was aimed at providing new understanding for the exploration of the changes of diffusion and permeability.
Theory is developed for the local electrochemical impedance spectroscopy (LEIS) at rough electrode under reversible charge transfer. Theory is used for analyzing the onset of non-uniform local growth ...or deposition on rough electrode which may cause unstable growth, viz. whiskers and dendrites, on lithium electrode. Model is also used to simulate temporal frequency dependent local admittance density and local growth velocity over a sinusoidal and a random fractal surfaces. For sinusoidal checkers surface, peak positions of electrode show preferential “whisker” growth for low roughness while for moderate and high roughness, anomalous “dendritic” growth may occur besides peaks. At low temporal frequency, LEIS indicates higher growth rate at cliff positions and depletion at the peak positions. The multiscale (fractal) roughness is modeled using Weierstrass function and shows a complex distribution of growth velocity over the surface. These surfaces show the curvature dependent localization of growth sites. The complex random growth pattern over fractal surface is described in terms of probability distribution function of growth velocities. Distribution function of growth velocity is analyzed for different roughness parameters, viz. width of roughness, finest scale of roughness and fractal dimensions. Results show that high growth rate sites increases with increase in these roughness features. Finally, LEIS theory for rough electrode provides an alternative approach to understand the problem of unstable growth in various electrochemical systems.
•LEIS theory is developed for diffusion limited reversible charge transfer process on rough electrode.•Theory simulates temporal frequency dependent local admittance density and growth velocity.•Roughness is modeled as sinusoidal checkers and Weierstrass fractal functions.•Theory provides insights into the onset of non-uniform local growth or deposition on rough electrode.•Width of distribution function of growth velocity for random surface is measure of non-uniform growth.
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