In this work we present a new version of the Hyper-Fractal Analysis C# .Net application for estimating the fuzzy fractal dimension of hyperspectral images. As an example, we also present some initial ...results on 116D algal images obtained from the HYPSO-1 satellite.
Program Title: Hyper-Fractal Analysis v08.
CPC Library link to program files:https://doi.org/10.17632/z9knmny56p.4.
Licensing provisions: GPLv2.
Programming language: C# 7.3 /.Net Framework 4.8.
Journal reference of previous version: Computer Physics Communications 276 (2022) 108335.
Does the new version supersede the previous version?: Yes.
Nature of problem: Estimating the fuzzy fractal dimension of Hyperspectral images.
Solution method: Optimized algorithm for Hyperspectral images stored in a specific csv file format.
Reasons for the new version: Develop a set of tools for facilitating fuzzy fractal analysis of Hyperspectral images (more than 100 dimensions).
Fractal dimension is extensively in use as features in computer vision applications to characterize roughness and self-similarity of objects in an image for many years. These features have been ...adopted successfully mainly in texture segmentation and classification. Differential box counting method is one of the widely accepted approaches, those exist in literature to estimate fractal dimension of an image. In this work, we comprehensively reviewed the available differential box counting methods. First, the differential box counting method is discussed in detail along with its computer vision applications and drawbacks. Second, various variants of differential box counting method are thoroughly studied and grouped using different parameters of differential box counting method. Third, the synthetic and real-world databases, considered for demonstrating experimental results by the state-of-the-art methods have been presented. Fourth, some of the state-of-the-art methods have been implemented and corresponding results obtained in this study are reported. Fifth, three evaluation metrics have also been reviewed. However, these metrics work only for synthetic fractal Brownian motion images because the theoretical fractal dimension values for these images are known and have been used as a set of ground truths. Finally, we concluded the status of differential box counting methods and explored the possible future directions.
Fractal dimension (Df) has been extensively used for many years to characterize the morphological properties of aggregate systems. There are two main methods to estimate the fractal dimension of ...aggregates, namely the box-counting (BC) and power law (PL) methods. However, the relationship between the BC fractal dimension (Df, BC) and PL fractal dimension (Df, PL) has not been discussed yet. In this work, a series of three-dimensional aggregates with different input parameters (Df, PL and the number of primary particles) is generated by a tunable aggregation model. Then, the fractal dimensions (Df, BC, 3D) of all the aggregates are estimated by the 3D BC method. The relationship between Df, BC, 3D and Df, PL is investigated. We found that Df, BC, 3D is greater than Df, PL when Df, PL≤ 2.5. However, the situation is reversed when Df, PL> 2.5. Further, a novel projection method is proposed and applied to all the 3D aggregates to obtain their 2D projection images. In this projection method, the minimum projection overlapping area of all the primary particles in the aggregate is considered. Then, the fractal dimensions (Df, BC, 2D) of 2D projection images are estimated using the 2D BC method. Finally, correlations between Df, BC, 3D and Df, PL with Df, BC, 2D are established.
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•Relationship established between BC and PL fractal dimension in 3D.•Novel projection method proposed to minimize the projection overlapping area.•Correlation between 2D BC and 3D PL fractal dimension established.
In last three decades, fractal geometry (FG) has been the focus of attention by several researchers owing to it exhibiting excellent properties and robust application with respect to current research ...scenario. Fractal Dimension (FD) plays a vital role in order to analyse complex objects that are found in nature which was failed to be analysed by Euclidian geometry. FD is an imperative aspect of FG to provide indicative application in different areas of research including image processing, pattern recognition, computer graphics and many more. Analysis of an image is an important technique of image processing to describe image features like texture, roughness, smoothness etc., and is only possible through FG. Due to this reason many more technique were evolved to estimate the fractal dimension. The main aim of this article is to give a comprehensive review, which summarizes recent research progress on analysis of surface roughness and an overview of different concepts, and the way they work and their benefits and their limitations, and also we deliver how the different concepts taken into consideration to estimate FD depend upon different algorithms. This article also discusses several factors affecting FD estimation; types of similarity property, spatial resolution, sampling process, region of interest, spectral band and box-height criteria are discussed. Furthermore, we have tried to present the application area oriented versus core area of FG. There are several contradictory results found in many kinds of literature on the influence of different parameters while conducting FD analysis. Mainly it has been observed that the FD estimation will be affected by texture property, gray scale range, color property, color distance and the other parameters which are already mentioned. Hence this article will be beneficial for researchers in order to select precise FD estimation. However different algorithms lead to different results even with the use of the same kind of database images, so selection of appropriate technique is a major challenge for accurate estimation. Therefore an in-depth and proper understanding is required in order to choose the appropriate algorithm and also a robust algorithm for analysing roughness in better and precise way needs to be developed.
•Fractal dimension plays vital role for analysing complex objects found in nature but failed to analyse by Euclidian geometry.•This article gives a comprehensive review, which summarizes recent research progress on analysis of surface roughness.•The detailed overview of different concept, and the way they work and their benefits and their limitations are presented.•We also deliver how the different influence factors affects in FD estimation in different algorithms.•We have also presented the application area verses core area of different fractal dimensions algorithm.
Combustion is essential to the manufacture of carbon black, fumed oxides, optical fibers and, recently, new high-value products like carbon nanotubes, nanosilver and biomagnetic nanofluids that are ...driven to market predominantly by start-ups. This technology is attractive for material synthesis for its proven scalability as it does not involve the tedious steps of wet chemistry and can readily form stably metastable compositions and high purity products.
Recent advances in aerosol and combustion sciences reveal that coagulation and sintering and/or surface growth control product particle size and morphology through the high temperature particle residence time, self-preserving size distribution and power laws for fractal-like particles. This motivates synthesis of an array of unique particle compositions and morphologies primarily by spray combustion leading to new catalysts, gas sensors, bio-materials and, most recently, to hand-held devices such as breath analysis sensors for monitoring chronic illnesses. In particular, multi-scale process design integrating mesoscale and molecular dynamics facilitates understanding of combustion product development.
The latter also contributes to understanding of aggregation and surface growth of nascent soot, a bona fide nanostructured material! So here nascent soot dynamics, after nucleation or inception, are investigated through accounting of soot agglomeration and surface growth by acetylene pyrolysis. Neglecting the fractal-like nature of soot underestimates its mobility diameter and polydispersity up to 40%. The evolution of nascent soot structure from spheres to aggregates is quantified by the mass fractal dimension and mass–mobility exponent, in excellent agreement with microscopic and mass–mobility measurements in a standard burner-stabilized stagnation ethylene flame. Surface growth chemically bonds the constituent primary particles of these aggregates, while the effect of soot volume fraction on soot morphology is elucidated. Based on aggregate projected area, a scaling law is derived for determining the primary particle size of nascent soot aggregates from mass–mobility measurements rather than tedious image counting.
The study used the fractal dimension (FD), browning incidence, and grayscale values using machine vision to describe the bruise magnitude and quality of mechanically damaged ‘Fard’ bananas bruised ...from 20, 40, 60 cm drop heights by 66, 98, and 110 g ball weights conditioned at different storage temperatures (5, 13, 22 °C) after 48 h. Conventional analyses like bruise area (BA), bruise volume (BV), and bruise susceptibility (BS) were also conducted. A correlation was performed to determine the relationship between image processing and conventional assessment of bruise damage in bananas. Weight, firmness, color, sugar content, and acidity were investigated. The results demonstrated that bananas bruised from the highest force and stored at 5 and 22 °C reported the lowest FD with values of 1.7162 and 1.7403, respectively. Increasing the level of damage reduced the fractal dimension and grayscale values and increased browning incidence and bruise susceptibility values after 48 h of storage. The total color change values showed a strong Pearson's correlation coefficient (r≥-0.81) with image analysis fractal dimension and grayscale values. The findings also indicated that higher bruising and temperature can induce weight loss, firmness reduction, lightness, and yellowness increment, and sugar and acidity changes. Overall, the fractal image analysis conducted in this study was highly effective in describing the bruising magnitude of bananas under different conditions.
•Fractal dimension (FD) by imaging was used to evaluate banana bruising.•After 48 h of storage, grayscale and FD reduced, and browning incidence increased.•Temperature controlled the magnitude of bruising after storage.•The performance of storage at 13 °C was promising.•Higher damage levels and storage conditions accelerate weight and firmness reduction.
The entropies of Shannon, Rényi and Kolmogorov are analyzed and compared together with their main properties. The entropy of some particular antennas with a pre-fractal shape, also called fractal ...antennas, is studied. In particular, their entropy is linked with the fractal geometrical shape and the physical performance.
The laminar combustion characteristics of CH4-H2-CO-Air are studied in a constant volume combustion chamber with different hydrogen content ratios and the initial conditions of 300 K and 0.2 MPa by ...schlieren technology. The influence laws of flame instability are analyzed through the influence laws of hydrogen content ratio and equivalence ratio (Φ) on the fractal dimensions of the flame contour and the ratio of the total flame face cracks' lengths to the flame radius (L/R), as well as the influence laws of hydrodynamic instability and thermal-diffusive instabilities on the flames. The results show that L/R is more sensitive to flame instabilities than flame front fractal dimensions due to a wider sampling range. After R exceeds a certain value, for lean and rich combustion conditions with the same distance from the stoichiometric ratio, the L/R is greater during lean combustion, and as the equivalence ratio gradually increases from 0.6 to 1.4, the effect of increasing hydrogen content (Hydrogen mole fraction ranges from 60% to 66.67%) on flame instability gradually shifts from promotion to suppression. This study has certain reference value for the combustion application of biomass synthesis gas.
•Research on flame characteristics based on flame cracks and fractal dimensions.•Recording of combustion flow fields using schlieren photography technique.•Flame cracks are more sensitive to changes in hydrogen content (in 6.67%).•Use of computer programs to accomplish flame information extraction.
•The fractal growth of chromium dendrites in electrodeposition was studied.•The DLA simulation results are consistent with the actual experimental results.•Dendrite morphology is closely related to ...particle motion.•The dendritic clusters are primarily composed of three-dimensional grains.
This investigated the fractal growth behavior of dendrites during the electrodeposition of chromium metal within two-dimensional confined interface. The effect of influencing factors (voltage, electrolyte concentration, catalyst concentration, and deposition time) on the morphology and fractal dimension of the deposited dendrites was investigated using zero-dimensional point electrodes and one-dimensional wire electrodes. The results indicate that as the voltage and electrolyte concentration increase, the fractal dimension of the point electrode decreases, while that of the wire electrode increases. Additionally, increasing the concentration of the catalyst and the deposition time led to an increase in the fractal dimension for both the point electrode and the wire electrode. This is due to the morphology of the dendritic clusters growing more open or denser depending on the aggregation mode of particles under different experimental conditions. This further leads to changes in fractal dimension. A diffusion-limited aggregation (DLA) model was developed to simulate the motion of particles during deposition. The model demonstrates that the changes in fractal dimension and the morphology of the aggregates formed by particles moving randomly are consistent with the experimental results. Finally, the distribution of grains on the sediment surface revealing that fractal dendrite clusters in a two-dimensional sediment interface consist of three-dimensional grains.
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