Box-counting Fractal Dimension Research Articles

Fractal-Based Pattern Quantification of Mineral Grains: A Case Study of Yichun Rare-Metal Granite

The quantification of the irregular morphology and distribution pattern of mineral grains is an essential but challenging task in ore-related mineralogical research, allowing for tracing the footprints of pattern-forming geological processes that are crucial to understanding mineralization and/or diagenetic systems. In this study, a large model, namely, the Segmenting Anything Model (SAM), was employed to automatically segment and annotate quartz, lepidolite and albite grains derived from Yichun rare-metal granite (YCRMG), based on which a series of fractal and multifractal methods, including box-counting calculation, perimeter–area analysis and multifractal spectra, were implemented. The results indicate that the mineral grains from YCRMG show great scaling invariance within the range of 1.04~52,300 μm. The automatic annotation of mineral grains from photomicrographs yields accurate fractal dimensions with an error of only 0.6% and thus can be utilized for efficient fractal-based grain quantification. The resultant fractal dimensions display a distinct distribution pattern in the diagram of box-counting fractal dimension (Db) versus perimeter–area fractal dimension (DPA), in which lepidolites are sandwiched between greater-valued quartz and lower-valued albites. Snowball-textured albites, i.e., concentrically arranged albite laths in quartz and K-feldspar, exhibit characteristic Db values ranging from 1.6 to 1.7, which coincide with the fractal indices derived from the fractal growth model. The zonal albites exhibit a strictly increasing trend regarding the values of fractal and multifractal exponents from core to rim, forming a featured “fractal-index banding” in the radar diagram. This pattern suggests that the snowball texture gradually evolved from rim to core, thus leading to greater fractal indices of outer zones, which represent higher complexity and maturity of the evolving system, which supports a metasomatic origin of the snowball texture. Our study demonstrates that fractal analyses with the aid of a large model are effective and efficient in characterizing and understanding complex patterns of mineral grains.

Relationship between box-counting fractal dimension and properties of fracture networks

Due to the capacity to quantify the complexity of a fracture network, fractal dimension (D) is widely applied in analyzing fracture network-related issues, such as connectivity and permeability. While the relationship between D and individual properties of a fracture network has been extensively studied, D is influenced by a combination of multiple attributes of the fracture network. Therefore, this work utilizes multivariate analysis to establish an equation for predicting D, taking into account various properties of the fracture network, namely fracture length, number, and orientation. Monte Carlo simulation is employed to generate a substantial number of fracture network models. Subsequently, relationships between the fractal dimension (D) and various properties are derived for three types of fracture networks with (1) invariant fracture length and random orientation, (2) exponential fracture length and random orientation, and (3) exponential fracture length and von-Mises orientation. The initial analysis focuses on the simplest relationship, wherein the fundamental formula of fractional expression is determined. Then the second and third relationships are obtained through replacing the fixed parameter in the first relationship with the distribution parameters of fracture properties. Correlation analyses between the predicted D and the actual values reveal a remarkably high correlation (>0.99). To validate the established relationships, a fracture network obtained from geological outcrops is utilized. The results demonstrate the validity of the derived relationships. The utilization of these equations enhances the efficiency, practicality, and convenience of estimating fractal dimensions from fracture properties. As a result, the analysis of fracture network-related issues becomes more feasible and accessible.

An improved sand 3D printing method for better reproduction of high-strength and high-brittleness rock mechanical properties is proposed

3D printing is an emerging technology which can provide valuable insights into the laboratory characterization and testing of rock mechanics. The binder jetting technology (BJT) process in 3D printing is one of the most promising tools for laboratory testing of rocks but still cannot reproduce high-strength and high-brittleness rocks. In this study, quartz sand and furan resin are chosen as the printing materials, and sand 3D printed rock-like specimens are used as the study objects. Based on this, the specimens are post treated, including vacuum infiltration with phenolic resin and high-temperature baking, and then these specimens are further subjected to uniaxial compression tests and Brazilian splitting tests to study their mechanical properties. A micromechanical explanation is given for the mechanical property enhancement using scanning electron microscopy (SEM) analysis and box-counting fractal dimension. The results show that the improved sand 3D printed rock-like specimens proposed in this study can reproduce the mechanical properties of high-strength and high-brittleness rocks in terms of the stress‒strain relationship, uniaxial compressive strength, elastic modulus, tensile strength and brittleness index. From the microstructure perspective, the mechanical properties are enhanced because of the improved micro-pore structure and increased bond strength between the particles. The micro-pore structure morphology of sand 3D printed specimens shows fractal characteristics, and the micro-pore pore area and the fractal dimension are positively correlated. The findings can support, to a certain extent, the future systematic investigation of the mechanical behavior of high-strength and high-brittleness rocks in underground engineering.

Retinal microvascular complexity as a putative biomarker of biological age: a pilot study.

Physiological changes associated with aging increase the risk for the development of age-related diseases. This increase is non-specific to the type of age-related disease, although each disease develops through a unique pathophysiologic mechanism. People who age at a faster rate develop age-related diseases earlier in their life. They have an older "biological age" compared to their "chronological age". Early detection of individuals with accelerated aging would allow timely intervention to postpone the onset of age-related diseases. This would increase their life expectancy and their length of good quality life. The goal of this study was to investigate whether retinal microvascular complexity could be used as a biomarker of biological age. Retinal images of 68 participants ages ranging from 19 to 82years were collected in an observational cross-sectional study. Twenty of the old participants had age-related diseases such as hypertension, type 2 diabetes, and/or Alzheimer's dementia. The rest of the participants were healthy. Retinal images were captured by a hand-held, non-mydriatic fundus camera and quantification of the microvascular complexity was performed by using Sholl's, box-counting fractal, and lacunarity analysis. In the healthy subjects, increasing chronological age was associated with lower retinal microvascular complexity measured by Sholl's analysis. Decreased box-counting fractal dimension was present in old patients, and this decrease was 2.1 times faster in participants who had age-related diseases (p = 0.047). Retinal microvascular complexity could be a promising new biomarker of biological age. The data from this study is the first of this kind collected in Montenegro. It is freely available for use.

A novel approach for quantitative characterization of aqueous in-situ foam dynamic structure based on fractal theory

In this study, a quantitative characterization method of in-situ foam microstructure is proposed based on fractal theory and the captured two dimension(2D) microstructure image for the study of its fractal characteristic, evolution law, sensitivity of temperature and concentration, as well as the relationship between average particle size and fractal dimension of in-situ foam. The results demonstrate that in-situ aqueous foam in the bulk phase exhibits fractal characteristics with a box-counting fractal dimension ranging from 1.4 to 2.0. Distinct from the “exponential” evolution law of conventional foam, in-situ foam displays the “check mark” evolution law, which can be precisely described by two items with clear physical meaning in our proposed fitting model. Additionally, the in-situ foam's evolutionary characteristic exhibits high adaptability towards temperature and foaming agent concentration. Elevated temperatures accelerate coalescence, resulting in shorter effective times, while higher concentrations of foaming agents prolong the overall stability of in-situ foam. Besides, the variation of average particle size of in-situ foam correspond closely with the evolution of fractal dimension under different temperatures and foaming agent concentrations, providing the potential for predicting changes in microstructure of in-situ foam by fractal dimension.

Study on the Drying Process and the Influencing Factors of Desiccation Cracking of Cohesive Soda Saline-Alkali Soil in the Songnen Plain, China

The surface of cohesive soda saline-alkali soil in the Songnen Plain of China exhibits obvious desiccation cracking phenomenon during water evaporation. Quantitative research on the process and influencing factors of desiccation cracking are significant for determining the mechanical properties of salt-affected soil, improving the salinization status and the local ecological environment. This study aims to conduct laboratory-controlled cracking experiments on soda saline-alkali soils, and to regularly measure the soil moisture and the cracking status of 40 soil samples. After processing the crack images uniformly, crack characteristics including crack length, crack area, contrast texture feature, and box-counting fractal dimension are extracted. The results indicate that the decrease in soil moisture can be divided into three stages such as fast evaporation stage, slow evaporation stage and stable evaporation stage, and that the evaporation rate shows a linear negative correlation with soil salinity. The measurements also indicate that crack length rapidly increases and reaches stability with a decrease in water content compared with the crack area. The high correlation between different crack characteristics and the soil total salinity (correlation coefficient from 0.44 to 0.95) shows that salt content is the dominant factor affecting the desiccation cracking of soda saline-alkali soil. A multiple linear regression prediction model was finally established based on crack characteristics for different salinity parameters with high prediction accuracy for Na+, EC and total salinity (R2 > 0.91 and RPD > 2.5) and also certain prediction accuracy for Cl− and CO32− (R2 > 0.66 and RPD > 1.5).

Effect of Different Fine Aggregate Characteristics on Fracture Toughness and Microstructure of Sand Concrete.

The fracture toughness of sand concrete is affected by aggregate characteristics. In order to study the possibility of exploiting tailings sand, available in large quantities in sand concrete, and find an approach to improve the toughness of sand concrete by selecting appropriate fine aggregate. Three distinct fine aggregates have been used. After characterizing the fine aggregate used, the mechanical properties were tested to characterize the toughness of sand concrete, the box-counting fractal dimensions were calculated to analyze the roughness of fracture surfaces, and the microstructure was tested to observe the path and width of microcracks and hydration products in sand concrete. The results show that the mineral composition of fine aggregates is close, but their fineness modulus, fine aggregate angularity (FAA) and gradation vary considerably; FAA has a significant impact on the fracture toughness of sand concrete. The higher the FAA value, the more resistant it is to crack expansion; with the FAA values of from 32 s to 44 s, the microcrack width in sand concrete was reduced from 0.25 um to 0.14 um; The fracture toughness and microstructure of sand concrete are also related to the gradation of fine aggregates, the better gradation can improve the performance of the interfacial transition zone (ITZ). The hydration products in the ITZ are also different because more reasonable gradation of aggregates reduces the voids between the fine aggregates and the cement paste and restrains the full growth of crystals. These results demonstrate that sand concrete has promising applications in the field of construction engineering.

EXPERIMENTAL INVESTIGATION ON FRACTAL CHARACTERIZATION OF IN-SITU FOAM IN POROUS MEDIA

The in-situ foam technology has been extensively applied in the complex reservoir reconstruction since it improves the sweep efficiency by diverting the flow of injected fluids into areas with lower permeability and as a result enhances the oil recovery. The in-situ foam structure inside the pores can significantly affect the sweep efficiency, however, quantitative characterizations on foam structure are inadequate. Here, we propose a quantitative method based on fractal theory and the two-dimensional (2D) micro physical simulation experiment for the study of fractal characteristic, evolution law and sensitivity analysis. The findings demonstrate that foam confined within porous media exhibits fractal characteristics, as evidenced by the measured box-counting fractal dimensions ranging between 1.05 and 1.752 based on acquired structural images. Notably, a higher fractal dimension corresponds to a more irregular in-situ foam structure. Besides, in-situ foam in the porous media presents the “quasi check sign” evolution law, which can be divided into three time-dependent stages. Moreover, the evolution laws of in-situ foam within porous media remains consistent across varying temperatures and concentrations of foaming agents, and increasing temperature and decreasing concentration can shorten the time to reach the inflection point.

Novel method to delineate palatal rugae and assess their complexity using fractal analysis

Palatal rugae constitute significant morphological landmarks, with wide clinical applications in forensics, insertion of mini-screws, and superimposition. Their morphology has been studied mainly with indices relevant to their qualitative characteristics. The present paper aims at presenting a new quantitative method to evaluate their complexity, by means of box-counting fractal dimension analysis, and to investigate its inter- and intra-rater reliability. Twenty maxillary plaster models were scanned for the needs of this study. A sequence of steps, including cropping of the mesh, ball pivoting, distance mapping and fractal dimension analysis, performed with Viewbox 4 software, was followed. Box-counting fractal dimensions were calculated as a measure of rugae’s complexity. Inter- and intra-rater reliability were investigated, using Bland–Altman analysis. Fractal dimensions ranged from 1.274 to 1.491 (average: 1.412). Bland–Altman analysis of inter- and intra-examiner reliability demonstrated that the 95% limits of agreement ranged from − 0.012 to 0.011 and from − 0.004 to 0.004, respectively. The method is reliable and can be applied in research and forensics. It offers comprehensive evaluation of the rugae’s complexity and a complete set of information about their outlines and height profiles, with minimum user intervention.

Fractal Dimension of Digital 3D Rock Models with Different Pore Structures

The macroscopic physical properties of rocks are profoundly determined by their microstructure, and the research of accurately characterizing rock pore structure has been extensively carried out in the fields of petroleum engineering and geoscience. Fractal geometry is an effective means of quantitatively estimating the pore structure properties of porous media. In this study, the evolution law of the fractal dimension and the quantitative relationship between the fractal dimension and porosity were investigated based on the digital 3D rock models. First, three kinds of models with gradually changing pore structures, namely sedimentation, compaction, and cementation, were systematically reconstructed by the process-based approach. Then, the fractal dimensions of the skeleton, pore, and surface of the models were computed and analyzed. Finally, the relationships among the fractal dimension, porosity, and complexity were explored qualitatively. These works reveal the changing laws of three types of fractal dimensions for different pore structure models. The pore structure differences in sedimentation model can only be distinguished by the surface fractal dimension, while both pore and surface fractal dimensions are available parameters for characterizing different pore structures in compaction and cementation models. The quantitative relations between box-counting fractal dimension and porosity were established, which can be expressed by combining linear and logarithmic formulas. The comparison of fractal dimensions of compaction and cementation models proves that fractal dimensions can distinguish the subtle pore structure differences in digital 3D rock models. Understanding the evolution law between the fractal dimension and pore structure parameters provides more references for classifying and evaluating rock pore structure features using fractal dimensions.

Study of Fault Identification of Clearance in Cam Mechanism

The clearance between the main roller and the cylinder cam has an important impact on the operational status of the bolt. In order to achieve the clearance and recoil of the cylinder cam mechanism, a bolt model was built and studied. The leading dynamic roller group and the dynamic bolt were analyzed. Positive stress and friction force change quickly on the high-speed leading roller group, influencing multiple aspects. When the main roller suddenly rotates or reverses in several short intervals, the assembling clearance and the massive friction force between the main roller and the cam curve slot are the main wear factors in theoretical analysis and test experiments. The leading roller group, the pure rolling criterion of the cylindrical cam mechanism of the automaton, is derived in this paper. Moreover, a new fault diagnosis method is developed, based on the Variational Box Dimension Kernel Fuzzy Mean Clustering Algorithm (VK) algorithm, which combines the variational mode decomposition and fractal box-counting dimension (VMD-FBCD) and the fuzzy clustering algorithms with a kernelized Mahalanobis distance (KMD-FC). With the simulation validation from 2810 samples, diagnosis using the VK algorithm is found to have a higher accuracy rate and slightly lower fallacy rate and to be faster than other diagnostic methods of similar studies. The results in terms of the recoil cylinder cam mechanism’s multi-body dynamic analysis and high-speed fault identification also have significance as a reference for solving similar problems.

Differentiation of osteosarcoma from osteomyelitis using microarchitectural analysis on panoramic radiographs

Diagnosing osteosarcoma (OS) is very challenging and OS is often misdiagnosed as osteomyelitis (OM) due to the nonspecificity of its symptoms upon initial presentation. This study investigated the possibility of detecting OS-induced trabecular bone changes on panoramic radiographs and differentiating OS from OM by analyzing fractal dimensions (FDs) and degrees of anisotropy (DAs). Panoramic radiographs of patients with histopathologically proven OS and OM of the jaw were obtained. A total of 23 patients with OS and 40 patients with OM were enrolled. To investigate whether there was a microarchitectural difference between OS lesions and normal trabecular areas in each patient, two regions of interest (ROIs) were located on the CT images. Three microarchitectural parameters (box-counting FD, fast Fourier transform-based FD, and DA) were calculated. For both OS and OM, significant differences were found for all three microarchitectural parameters. Compared to normal trabecular bone, trabecular bone affected by OS and OM became isotropic and more complex. When comparing OS and OM, a statistically significant difference was found only in DA. Trabecular bones affected by OS became more isotropic than those affected by OM. Microarchitectural analysis, especially DA, could be useful for detecting OS-induced trabecular alterations and differentiating OS from OM.

Fractal analysis of aggregates: Correlation between the 2D and 3D box-counting fractal dimension and power law fractal dimension

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.

A new method for evaluating the pore structure complexity of digital rocks based on the relative value of fractal dimension

Natural porous media have extremely complex pore structures, which greatly affect the material properties. However, it remains a challenge to characterize the pore structure complexity accurately. Fractal geometry is one of the effective tools for this task, which allows for quantitative analysis. In this paper, a new method is proposed for evaluating the pore structure complexity of digital rock models by using the relative value of box-counting fractal dimension. The proposed method transforms the judgment criterion from the comparison of the absolute value to the comparison of the relative value in the fractal dimension by establishing an intermediate fractal reference model. Firstly, the digital core model with progressively changing porosity and pore structure is reconstructed using a numerical modeling means, and three kinds of fractal dimensions of the model are estimated by the box-counting algorithm. Meanwhile, the relationship curve between fractal dimension and porosity is employed as the fractal reference model. Then, the fractal dimensions of the study samples and the reference model are mapped to the same coordinate system. By comparing their relative positional relationship, the pore structure complexity of samples is effectively evaluated and classified. Finally, CT samples are taken as a concrete example to illustrate the application of the proposed method. The correctness and availability of this method are verified through the comprehensive analysis of digital images, pore structure, porosity, and permeability. The constructed method provides a reference for a more accurate evaluation and classification of the complexity of pore space in digital rock physics.

Comparative study on the abilities of different crack parameters to estimate the salinity of soda saline-alkali soil in Songnen Plain, China

Salinity is commonly considered to be the main factor determining the crack extent of clayey soda saline-alkali soil in the Songnen Plain in China. However, there are great variations among different parameters in quantifying the extent of desiccation cracks in salt-affected soil, leading to substantial uncertainty in their abilities to characterize soil salinity. This study aimed to analyze the relationships between different types of crack parameters and the salinity of soil samples to establish optimal prediction models for the electrical conductivity (EC) values. To achieve these objectives, 104 soil samples with different salinity levels were obtained and pre-processed based on a unified standard for binary crack patterns. Thereafter, three common types of crack parameters including the crack intensity factor (CIF); box-counting dimensions under equal-partitions of 2, 3, 5, and 7; and four gray-level co-occurrence matrix (GLCM) texture features were extracted for correlation coefficients with the EC values of the soil samples based on a series of regression analyses. The results indicate that although different types of crack parameters all have a clear correlation with EC, CIF shows a poor relationship with EC values compared to those of the fractal dimensions and the GLCM texture features. The CIF, box-counting fractal dimensions based on 2 equal-partition, and contrast (CON) texture feature were then selected as the most ideal indices to develop exponential regression models for EC estimation. In addition, fitting results from verification work showed that CON was the best predictor of EC (R2 of 0.85), with an accuracy much higher than box-counting dimension based on 2 equal-partition (R2 of 0.68) and CIF (R2 of only 0.56).

Hardness, plasticity, and oil binding capacity of binary mixtures of natural waxes in olive oil

In this study, olive oil oleogels structured with less than 4% binary blends of sunflower wax (SFW), rice bran wax (RBW), candelilla wax (CDW), and beeswax (BW) were characterized. Among the different binary wax oleogels, samples structured with 3% (w/w) of binary mixtures of SFW and RBW, as well as binary mixtures of CDW and BW, displayed a high oil binding capacity relative to any other mixtures. Moreover, in some binary wax oleogels, back extrusion hardness and elastic constant were significantly higher than that of oleogels prepared using the individual waxes. This was interpreted as a synergism between these waxes. Image analysis of oleogel brightfield micrographs indicated that the samples with a higher elastic constant had a lower box-counting fractal dimension and larger crystals, suggesting that this increase in the elastic constant was a consequence of the lower fractal dimension of the wax crystal network, in agreement with established fractal structural-mechanical models for van der Waals colloidal networks. The crystal structure of the individual waxes and their blends showed orthorhombic perpendicular subcell packing arrangements, which did not change upon mixing, suggesting this length scale did not play a role in the observed synergism. The melting point of binary mixtures of waxes in olive oil was in the range of 43.2 °C to 67.4 °C and pseudo-ideal mixing behavior was observed. The hardness and plasticity (brittleness) of the 2% and 3% binary wax mixtures in olive oil characterized using back extrusion, were similar to those of a commercial soft margarine, suggesting a potential use of the wax oleogels as margarine or spread replacers.

Fractal Analysis of Aggregates: Correlation between the 2d and 3d Box-Counting Fractal Dimension and Power Law Fractal Dimension

Fractal Analysis of Aggregates: Correlation between the 2d and 3d Box-Counting Fractal Dimension and Power Law Fractal Dimension

Age-related changes in the fractal dimension of the retinal microvasculature, effects of cardiovascular risk factors and smoking behaviour.

PurposeThis cross‐sectional study investigates the association between retinal vessel complexity and age and studies the effects of cardiovascular health determinants.MethodsRetinal vessel complexity was assessed by calculating the box‐counting fractal dimension (Df) from digital fundus photographs of 850 subjects (3–97 years). All photographs were labelled as ‘non‐pathological’ by the treating ophthalmologist.ResultsStatistical models showed a significantly decreasing relationship between age and Df (linear: R‐squared = 0.1897, p < 0.0001; quadratic: R‐squared = 0.2343, p < 0.0001; cubic: R‐squared = 0.2721, p < 0.0001), with the cubic regression model offering the best compromise between accuracy and model simplicity. Multivariate cubic regression showed that age, spherical equivalent and smoking behaviour have an effect (p < 0.0001) on Df. A significantly increasing effect of the number of pack‐years on Df was observed (effect: 0.0004, p = 0.0017), as well as a significantly decreasing effect of years since tobacco abstinence (effect: −0.0149, p < 0.0001).ConclusionWe propose using a cubic trend with age, refractive error and smoking behaviour when interpreting retinal vessel complexity.

Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks.

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.

Non-invasive sensing techniques to phenotype multiple apple tree architectures

Tree fruit architecture results from combination of the training system and pruning and thinning processes across multiple growth and development years. Further, the tree fruit architecture contributes to the light interception and improves tree growth, fruit quality, and fruit yield, in addition to easing the process of orchard management and harvest. Currently tree architectural traits are measured manually by researchers or growers, which is labor-intensive and time-consuming. In this study, the remote sensing techniques were evaluated to phenotype critical architectural traits with the final goal to assist tree fruit breeders, physiologists and growers in collecting architectural traits efficiently and in a standardized manner. For this, a consumer-grade red–green–blue (RGB) camera was used to collect apple tree side-images, while an unmanned aerial vehicle (UAV) integrated RGB camera was programmed to image tree canopy at 15 m above ground level to evaluate multiple tree fruit architectures. The sensing data were compared to ground reference data associated with tree orchard blocks within three training systems (Spindle, V-trellis, Bi-axis), two rootstocks (‘WA 38 trees grafted on G41 and M9-Nic29) and two pruning methods (referred as bending and click pruning). The data were processed to extract architectural features from ground-based 2D images and UAV-based 3D digital surface model. The traits extracted from sensing data included box-counting fractal dimension (DBs), middle branch angle, number of branches, trunk basal diameter, and tree row volume (TRV). The results from ground-based sensing data indicated that there was a significant (P < 0.0001) difference in DBs between Spindle and V-trellis training systems, and correlations between DBs with tree height (r = 0.79) and total fruit yield per unit area (r = 0.74) were significant (P < 0.05). Moreover, correlations between average or total TRV and ground reference data, such as tree height and total fruit yield per unit area, were significant (P < 0.05). With the reported findings, this study demonstrated the potential of sensing techniques for phenotyping tree fruit architectural traits.