Optimal Voxel Size Research Articles

Influence of Leaf Area Index Inversion and the Light Transmittance Mechanism in the Apple Tree Canopy

Light plays a crucial role in the growth of fruit trees, influencing not only nutrient absorption but also fruit appearance. Therefore, understanding fruit tree canopy light transmittance is essential for agricultural and forestry practices. However, traditional measurement methods, such as using a canopy analyzer, are time-consuming, labor-intensive, and susceptible to external influences, lacking convenience and automation. To address this issue, we propose a novel method based on point clouds to estimate light transmittance, with the Leaf Area Index (LAI) serving as the central link. Focusing on apple trees, we utilized handheld LiDAR for three-dimensional scanning of the canopy, acquiring point cloud data. Determining the optimal voxel size at 0.015 m via standardized point cloud mean spacing, we applied the Voxel-based Canopy Profile method (VCP) to estimate LAI. Subsequently, we established a function model between LAI and canopy light transmittance using a deep neural network (DNN), achieving an overall correlation coefficient R2 of 0.94. This model was then employed to estimate canopy light transmittance in dwarfed and densely planted apple trees. This approach not only provides an evaluation standard for pruning effects in apple trees but also represents a critical step towards visualizing and intelligentizing light transmittance.

Comparison of Three Approaches for Estimating Understory Biomass in Yanshan Mountains

Aboveground biomass (AGB) of shrubs and low-statured trees constitutes a substantial portion of the total carbon pool in temperate forest ecosystems, contributing much to local biodiversity, altering tree-regeneration growth rates, and determining above- and belowground food webs. Accurate quantification of AGB at the shrub layer is crucial for ecological modeling and still remains a challenge. Several methods for estimating understory biomass, including inventory and remote sensing-based methods, need to be evaluated against measured datasets. In this study, we acquired 158 individual terrestrial laser scans (TLS) across 45 sites in the Yanshan Mountains and generated metrics including leaf area and stem volume from TLS data using voxel- and non-voxel-based approaches in both leaf-on and leaf-off scenarios. Allometric equations were applied using field-measured parameters as an inventory approach. The results indicated that allometric equations using crown area and height yielded results with higher accuracy than other inventory approach parameters (R2 and RMSE ranging from 0.47 to 0.91 and 12.38 to 38.11 g, respectively). The voxel-based approach using TLS data provided results with R2 and RMSE ranging from 0.86 to 0.96 and 6.43 to 21.03 g. Additionally, the non-voxel-based approach provided similar or slightly better results compared to the voxel-based approach (R2 and RMSE ranging from 0.93 to 0.96 and 4.23 to 11.27 g, respectively) while avoiding the complexity of selecting the optimal voxel size that arises during voxelization.

Reconstruction of a large-scale realistic three-dimensional (3-D) mountain forest scene for radiative transfer simulations

ABSTRACT The realistic three-dimensional (3D) forest scene is an important input to 3D radiative transfer simulations, which are essential for analyzing the reflective properties of forest canopies. Previous studies utilized the voxel as an essential element to reconstruct the 3D forest scene, while they mainly focused on the small flattened areas and ignored the wood components. This study introduces a novel approach for reconstructing a realistic 3D mountain forest scene by incorporating branches into the voxel crown. To determine the optimal voxel size for simulating Bidirectional Reflectance Functions (BRFs) in a temperate deciduous mountain forest, this study reconstructed the forest scene using eight different voxel sizes, ranging from 30 to 100 cm with a step of 10 cm. Two forest scenes were examined to evaluate the impact of branches on radiative transfer simulations: one with branch voxel-based scenes and one without branches. The radiative transfer simulation is conducted using an efficient Monte Carlo path-tracing algorithm and has been implemented in the LargE-Scale remote sensing data and image Simulation framework (LESS) model, facilitating high-quality, large-scale simulations of forested environments. The finding revealed that the optimal voxel size for simulating BRFs in 30 m resolution is approximately 90 cm, smaller than the 100 cm used in flat areas. This study emphasized the significant impact of branches on the BRF simulations and underscored their critical role in scene reconstruction. The impact of branches is two-fold: branches themselves increase the simulated BRFs, whereas their shadows decrease them. Moreover, the effects of branches and their shadows decrease as the voxel size increases. The simulated spectral albedo exhibits maximum deviations of 0.71% and 1.04% in the red and NIR wavebands, respectively, while remaining below 0.2% in the blue waveband. Furthermore, the study suggests that if the precise branch architecture is unknown, constructing branches of the first generation is recommended to achieve better results. Additionally, the results demonstrate that the proposed scene achieves greater accuracy and robustness when compared to both the ellipsoid-based and the boundary-based scenes. The finding of this study can help researchers to better understand the underlying mechanisms driving the reflective properties of forest canopies, which can inform future studies and improve the accuracy of forest monitoring and ecological modeling.

LiDAR Voxel-Size Optimization for Canopy Gap Estimation

Terrestrial laser scanning of forest structure is used increasingly in place of traditional technologies; however, deriving physical parameters from point clouds remains challenging because LiDAR returns do not have defined areas or volumes. While voxelization methods overcome this challenge, estimation of canopy gaps and other structural attributes are often performed by reducing the point cloud to two-dimensions, thus decreasing the fidelity of the data. Furthermore, relatively few studies have evaluated voxel-size effects on estimation accuracy. Here, we show that voxelized laser-scanning data can be used for canopy-gap estimation without performing dimensionality reduction to the point cloud. Both airborne and terrestrial LiDAR were used to estimate canopy gaps along six vertical transects and four height intervals. Voxel-based estimates were evaluated against hemispherical photography and a sensitivity analysis was performed to identify an optimal voxel size. While the results indicate that our approach can be used with both airborne and terrestrial LiDAR, voxel size has a considerable influence on canopy-gap estimation. Results from our sensitivity analysis indicate that TLS estimation performs best when using 10 cm voxels, yielding canopy gaps ranging from 32–78%. The optimal voxel size for ALS estimation was obtained with 25 cm voxels, yielding estimates ranging from 25–68%.

Errors in the Estimation of Leaf Area Density From Aerial LiDAR Data: Influence of Statistical Sampling and Heterogeneity

In this study, several approaches were evaluated for estimation of the 3-D distribution of leaf area from aerial light detection and ranging (LiDAR) data. Two general leaf area density (LAD) inversion methods were evaluated against “synthetic” LiDAR data for a range of grid resolutions and canopy architectures: 1) inversion based on cumulative transmission of LiDAR pulses through the volume of interest (i.e., the cumulative distribution function (CDF) of transmission, or Beer’s law), and 2) inversion based on the probability density function (PDF) of beam propagation distance within the volume of interest (i.e., probability distribution fitting). Results indicated that the Beer’s law-based method consistently outperformed the PDF-based methods. In a homogeneous canopy, the average error in LAD estimation using the Beer’s law approach decreased exponentially as the number of voxel statistical samples <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N_{v}}$ </tex-math></inline-formula> (i.e., laser pulses reaching the voxel) was increased. The normalized error also decreased exponentially as leaf area index of the voxel LAI <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>v</i></sub> increased. Heterogeneity increased the magnitude of errors in LAD inversion, with errors tending to increase as vegetation density increased, but plant spacing had a negligible impact. For sufficiently dense heterogeneous canopies, there was an optimal voxel size that balanced errors due to poor statistical sampling (small voxels) and errors due to crown-scale heterogeneity that violated the turbid medium assumption (large voxels). This optimum, if present, occurred at around <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N_{v}=40}$ </tex-math></inline-formula> or a voxel width of 2 m regardless of canopy geometry. Sub-crown-scale clumping had a minimal effect on average errors in estimated LAD for the tree geometries explored in this work.

Influence of voxel size on forest canopy height estimates using full-waveform airborne LiDAR data

BackgroundForest canopy height is a key forest structure parameter. Precisely estimating forest canopy height is vital to improve forest management and ecological modelling. Compared with discrete-return LiDAR (Light Detection and Ranging), small-footprint full-waveform airborne LiDAR (FWL) techniques have the capability to acquire precise forest structural information. This research mainly focused on the influence of voxel size on forest canopy height estimates.MethodsA range of voxel sizes (from 10.0 m to 40.0 m interval of 2 m) were tested to obtain estimation accuracies of forest canopy height with different voxel sizes. In this study, all the waveforms within a voxel size were aggregated into a voxel-based LiDAR waveform, and a range of waveform metrics were calculated using the voxel-based LiDAR waveforms. Then, we established estimation model of forest canopy height using the voxel-based waveform metrics through Random Forest (RF) regression method.Results and conclusionsThe results showed the voxel-based method could reliably estimate forest canopy height using FWL data. In addition, the voxel sizes had an important influence on the estimation accuracies (R2 ranged from 0.625 to 0.832) of forest canopy height. However, the R2 values did not monotonically increase or decrease with the increase of voxel size in this study. The best estimation accuracy produced when the voxel size was 18 m (R2 = 0.832, RMSE = 2.57 m, RMSE% = 20.6%). Compared with the lowest estimation accuracy, the R2 value had a significant improvement (33.1%) when using the optimal voxel size. Finally, through the optimal voxel size, we produced the forest canopy height distribution map for this study area using RF regression model. Our findings demonstrate that the optimal voxel size need to be determined for improving estimation accuracy of forest parameter using small-footprint FWL data.

A voxel matching method for effective leaf area index estimation in temperate deciduous forests from leaf-on and leaf-off airborne LiDAR data

The quantification of leaf area index (LAI) is essential for modeling the interaction between atmosphere and biosphere. The airborne LiDAR has emerged as an effective tool for mapping plant area index (PAI) in a landscape consisting of both woody and leaf materials. However, the discrimination between woody and leaf materials and the estimation of effective LAI (eLAI) have, to date, rarely been studied at landscape scale. We applied a voxel matching algorithm to estimate eLAI of deciduous forests using simulated and field LiDAR data under leaf-on and leaf-off conditions. We classified LiDAR points as either a leaf or a woody hit on leaf-on LiDAR data by matching the point with leaf-off data. We compared the eLAI result of our voxel matching algorithm against the subtraction method, where the leaf-off effective woody area index (eWAI) is subtracted from the effective leaf-on PAI (ePAI). Our results, which were validated against terrestrial LiDAR derived eLAI, showed that the voxel matching method, with an optimal voxel size of 0.1 m, produced an unbiased estimation of terrestrial LiDAR derived eLAI with an R2 of 0.70 and an RMSE of 0.41 (RRMSE: 20.1%). The subtraction method, however, yielded an R2 of 0.62 and an RMSE of 1.02 (RRMSE: 50.1%) with a significant underestimation of 0.94. Reassuringly, the same outcome was observed using a simulated dataset. In addition, we evaluated the performance of 96 LiDAR metrics under leaf-on conditions for eLAI prediction using a statistical model. Based on the importance scores derived from the random forest regression, nine of the 96 leaf-on LiDAR metrics were selected. Cross-validation showed that eLAI could be predicted using these metrics under leaf-on conditions with an R2 of 0.73 and an RMSE of 0.27 (RRMSE: 17.4%). The voxel matching method yielded a slightly lower accuracy (R2: 0.70, RMSE:0.41, RRMSE: 20.1%) than the statistical model. We, therefore, suggest that the voxel matching method offers a new opportunity for the estimating eLAI and other ecological applications that require the classification between leaf and woody materials using airborne LiDAR data. It potentially allows transferability to different sites and flight campaigns.

Optimizing acquisition and fitting conditions for 1 H MR spectroscopy investigations in global brain pathology.

To optimize acquisition and fitting conditions for nonfocal disease in terms of voxel size and use of individual coil element data. Increasing the voxel size yields a higher signal-to-noise ratio, but leads to larger linewidths and more artifacts. Several ways to improve the spectral quality for large voxels are exploited and the optimal use of individual coil signals investigated. Ten human subjects were measured at 3T using a 64-channel receive head coil with a semi-LASER localization sequence under optimized and deliberately mis-set field homogeneity. Eight different voxel sizes (8 to 99cm3 ) were probed. Spectra were fitted either as weighted sums of the individual coil elements or simultaneously without summation. Eighteen metabolites were included in the fit model that also included the lineshapes from all coil elements as reflected in water reference data. Fitting errors for creatine, myo-Inositol and glutamate are reported as representative parameters to judge optimal acquisition and evaluation conditions. Minimal Cramér-Rao lower bounds and thus optimal acquisition conditions were found for a voxel size of ~ 70cm3 for the representative upfield metabolites. Spectral quality in terms of lineshape and artifact appearance was determined to differ substantially between coil elements. Simultaneous fitting of spectra from individual coil elements instead of traditional fitting of a weighted sum spectrum reduced Cramer-Rao lower bounds by up to 17% for large voxel sizes. The optimal voxel size for best precision in determined metabolite content is surprisingly large. Such an acquisition condition is most relevant for detection of low-concentration metabolites, like NAD+ or phenylalanine, but also for longitudinal studies where very small alterations in metabolite content are targeted. In addition, simultaneous fitting of single channel spectra enforcing lineshape and coil sensitivity information proved to be superior to traditional signal combination with subsequent fitting.

Detection of alveolar bone defects with three different voxel sizes of cone-beam computed tomography: an in vitro study

This study was conducted to assess the accuracy of cone-beam computed tomography (CBCT) of different voxel sizes in the detection of alveolar bone defects, and to select the optimal voxel size for clinical use. 46 in-vitro teeth were placed in bovine ribs in which alveolar bone defects were randomly simulated. In total, 32 alveolar bone defects and 14 teeth without periodontal defects were used. CBCT images were acquired with the use of three different voxel sizes: 0.125-mm, 0.2-mm and 0.4-mm. The scan data were 3D-reconstructed in Mimics software and evaluated by two observers with more than 5 years of experience in CBCT. Receiver operating characteristic (ROC) curves and diagnostic values were obtained. Pairwise comparison of ROC curves was made for evaluation of the diagnostic values of different voxel sizes. Kappa statistics assessed the observer reliability. Results were considered significant at P < 0.05. It showed no statistically significant difference between 0.125-mm group and 0.2-mm group, but 0.4-mm group had lower Az values that differed significantly from 0.125-mm and 0.2-mm groups (P < 0.05). Based on diagnostic value and radiation protection, 0.2-mm voxel size may be a good choice for the detection of bone defects with CBCT.

Effect of Leaf Occlusion on Leaf Area Index Inversion of Maize Using UAV–LiDAR Data

The leaf area index (LAI) is a key parameter for describing crop canopy structure, and is of great importance for early nutrition diagnosis and breeding research. Light detection and ranging (LiDAR) is an active remote sensing technology that can detect the vertical distribution of a crop canopy. To quantitatively analyze the influence of the occlusion effect, three flights of multi-route high-density LiDAR dataset were acquired at two time points, using an Unmanned Aerial Vehicle (UAV)-mounted RIEGL VUX-1 laser scanner at an altitude of 15 m, to evaluate the validity of LAI estimation, in different layers, under different planting densities. The result revealed that normalized root-mean-square error (NRMSE) for the upper, middle, and lower layers were 10.8%, 12.4%, 42.8%, for 27,495 plants/ha, respectively. The relationship between the route direction and ridge direction was compared, and found that the direction of flight perpendicular to the maize planting ridge was better than that parallel to the maize planting ridge. The voxel-based method was used to invert the LAI, and we concluded that the optimal voxel size were concentrated on 0.040 m to 0.055 m, which was approximately 1.7 to 2.3 times of the average ground point distance. The detection of the occlusion effect in different layers under different planting densities, the relationship between the route and ridge directions, and the optimal voxel size could provide a guideline for UAV–LiDAR application in the crop canopy structure analysis.

OA158] Noise equivalent number of quanta (NEQ): A tool for choosing the optimal reconstruction algorithm in computed tomography (CT)

Purpose Evaluate optimal reconstruction algorithm and voxel size for a breast CT system using NEQ. Methods CT scans of a wire phantom and a homogeneous cylindrical sample have been performed using a tomographic acquisition system for breast-CT with synchrotron radiation. By setting a monochromatic beam of 38 KeV , the images have been acquired using a CdTe photon-counting detector with a pixel size of 60 μ m. The optimal CT reconstruction algorithm has been investigated comparing the Filtered Back Projection (FBP), the Simultaneous Algebraic Reconstruction Technique (SART) and the Simultaneous Iterative Reconstruction Technique (SIRT). CT images have been reconstructed using two voxel sizes ( V 60 = 60 3 μ m3 and V 120 = 120 3 μ m3). The spatial resolution and the noise have been evaluated on CT reconstructions respectively trough the modulation transfer function (MTF) and the normalized noise power spectrum (NNPS). MTF has been evaluated with the thin wire method and the NNPS has been measured on the CT reconstructions of the homogeneous sample. The NEQ is defined as the ratio between the squared MTF and the NNPS. It is a measure of the signal to noise ratio in frequency domain and has been used to compare the performances of the considered reconstruction algorithms. Results For both used voxel sizes, compared to SART and FBP algorithms, SIRT algorithm shows highest values of NEQ for all accessible frequencies. Apart from the reconstruction algorithm, compared to V 60 , V 120 lead to better NEQ values for frequencies below 3.3 mm - 1 thus, for this system, details with diameter lower than 300 μ m are better resolved by the smallest voxel size available. Conclusions Summarizing information about spatial resolution and noise, NEQ is an extremely comprehensive metric which contains all the key issues for the global image quality assessment. For a given CT system, the comparison between NEQ curves measured on CT reconstructions provides a general method for choosing the best reconstruction algorithm and the voxel size to be used for achieving optimal performances in terms of spatial resolution and noise.

Estimation of the vertical leaf area profile of corn (Zea mays) plants using terrestrial laser scanning (TLS)

It remains challenging to estimate a crop’s leaf area profile accurately and automatically. Terrestrial laser scanning (TLS) offers a potential solution, since it has a small footprint and can be used to rapidly and accurately resolve the canopy’s 3D structure. To improve the accuracy of vertical leaf area profile estimation, we selected point clouds from three corn plants scanned in two TLS experiments and used an improved voxel-based leaf area profile estimation method based on Wilson’s contact-frequency theory. The improvement has three aspects: First, it separates corn leaf points from stalk points using the difference-of-normals (DoN) method, which is commonly used to separate different surfaces of manmade objects such as tables or walls. The DoN method captures the geometrical difference between corn leaves and stalks. Second, it determines the optimal voxel size based on the calculated contact frequency. Third, it applies Wilson’s voxel-based contact-frequency method to the LiDAR point clouds. Comparing the estimated and measured leaf area profiles showed that separating leaf and stalk points improved the leaf area accuracy, which depended on the voxel size. The optimal voxel sizes were 10 cm × 10 cm × 10 cm and 5 cm × 5 cm × 5 cm, respectively, in the two study years based on irradiation of the corn plant with a single laser beam. The estimated vertical and cumulative leaf area profiles agreed well with the measured profiles; mean absolute errors for the samples ranged from 15.7 to 18.9%.

Bayesian Optimization for Neuroimaging Pre-processing in Brain Age Classification and Prediction.

Neuroimaging-based age prediction using machine learning is proposed as a biomarker of brain aging, relating to cognitive performance, health outcomes and progression of neurodegenerative disease. However, even leading age-prediction algorithms contain measurement error, motivating efforts to improve experimental pipelines. T1-weighted MRI is commonly used for age prediction, and the pre-processing of these scans involves normalization to a common template and resampling to a common voxel size, followed by spatial smoothing. Resampling parameters are often selected arbitrarily. Here, we sought to improve brain-age prediction accuracy by optimizing resampling parameters using Bayesian optimization. Using data on N = 2003 healthy individuals (aged 16–90 years) we trained support vector machines to (i) distinguish between young (<22 years) and old (>50 years) brains (classification) and (ii) predict chronological age (regression). We also evaluated generalisability of the age-regression model to an independent dataset (CamCAN, N = 648, aged 18–88 years). Bayesian optimization was used to identify optimal voxel size and smoothing kernel size for each task. This procedure adaptively samples the parameter space to evaluate accuracy across a range of possible parameters, using independent sub-samples to iteratively assess different parameter combinations to arrive at optimal values. When distinguishing between young and old brains a classification accuracy of 88.1% was achieved, (optimal voxel size = 11.5 mm3, smoothing kernel = 2.3 mm). For predicting chronological age, a mean absolute error (MAE) of 5.08 years was achieved, (optimal voxel size = 3.73 mm3, smoothing kernel = 3.68 mm). This was compared to performance using default values of 1.5 mm3 and 4mm respectively, resulting in MAE = 5.48 years, though this 7.3% improvement was not statistically significant. When assessing generalisability, best performance was achieved when applying the entire Bayesian optimization framework to the new dataset, out-performing the parameters optimized for the initial training dataset. Our study outlines the proof-of-principle that neuroimaging models for brain-age prediction can use Bayesian optimization to derive case-specific pre-processing parameters. Our results suggest that different pre-processing parameters are selected when optimization is conducted in specific contexts. This potentially motivates use of optimization techniques at many different points during the experimental process, which may improve statistical sensitivity and reduce opportunities for experimenter-led bias.

Estimating Forest Structural Parameters Using Canopy Metrics Derived from Airborne LiDAR Data in Subtropical Forests

Accurate and timely estimation of forest structural parameters plays a key role in the management of forest resources, as well as studies on the carbon cycle and biodiversity. Light Detection and Ranging (LiDAR) is a promising active remote sensing technology capable of providing highly accurate three dimensional and wall-to-wall forest structural characteristics. In this study, we evaluated the utility of standard metrics and canopy metrics derived from airborne LiDAR data for estimating plot-level forest structural parameters individually and in combination, over a subtropical forest in Yushan forest farm, southeastern China. Standard metrics, i.e., height-based and density-based metrics, and canopy metrics extracted from canopy vertical profiles, i.e., canopy volume profile (CVP), canopy height distribution (CHD), and foliage profile (FP), were extracted from LiDAR point clouds. Then the standard metrics and canopy metrics were used for estimating forest structural parameters individually and in combination by multiple regression models, including forest type-specific (coniferous forest, broad-leaved forest, mixed forest) models and general models. Additionally, the synergy of standard metrics and canopy metrics for estimating structural parameters was evaluated using field measured data. Finally, the sensitivity of vertical and horizontal resolution of voxel size for estimating forest structural parameters was assessed. The results showed that, in general, the accuracies of forest type-specific models (Adj-R2 = 0.44–0.88) were relatively higher than general models (Adj-R2 = 0.39–0.77). For forest structural parameters, the estimation accuracies of Lorey’s mean height (Adj-R2 = 0.61–0.88) and aboveground biomass (Adj-R2 = 0.54–0.81) models were the highest, followed by volume (Adj-R2 = 0.42–0.78), DBH (Adj-R2 = 0.48–0.74), basal area (Adj-R2 = 0.41–0.69), whereas stem density (Adj-R2 = 0.39–0.64) models were relatively lower. The combination models (Adj-R2 = 0.45–0.88) had higher performance compared with models developed using standard metrics (only) (Adj-R2 = 0.42–0.84) and canopy metrics (only) (Adj-R2 = 0.39–0.83). The results also demonstrated that the optimal voxel size was 5 × 5 × 0.5 m3 for estimating most of the parameters. This study demonstrated that canopy metrics based on canopy vertical profiles can be effectively used to enhance the estimation accuracies of forest structural parameters in subtropical forests.

Tree species classification in subtropical forests using small-footprint full-waveform LiDAR data

The accurate classification of tree species is critical for the management of forest ecosystems, particularly subtropical forests, which are highly diverse and complex ecosystems. While airborne Light Detection and Ranging (LiDAR) technology offers significant potential to estimate forest structural attributes, the capacity of this new tool to classify species is less well known. In this research, full-waveform metrics were extracted by a voxel-based composite waveform approach and examined with a Random Forests classifier to discriminate six subtropical tree species (i.e., Masson pine (Pinus massoniana Lamb.)), Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.), Slash pines (Pinus elliottii Engelm.), Sawtooth oak (Quercus acutissima Carruth.) and Chinese holly (Ilex chinensis Sims.) at three levels of discrimination. As part of the analysis, the optimal voxel size for modelling the composite waveforms was investigated, the most important predictor metrics for species classification assessed and the effect of scan angle on species discrimination examined. Results demonstrate that all tree species were classified with relatively high accuracy (68.6% for six classes, 75.8% for four main species and 86.2% for conifers and broadleaved trees). Full-waveform metrics (based on height of median energy, waveform distance and number of waveform peaks) demonstrated high classification importance and were stable among various voxel sizes. The results also suggest that the voxel based approach can alleviate some of the issues associated with large scan angles. In summary, the results indicate that full-waveform LIDAR data have significant potential for tree species classification in the subtropical forests.

Quantitative model selection for enhanced magnetic nanoparticle imaging in magnetorelaxometry.

The performance of an increasing number of biomedical applications is dependent on the accurate knowledge of the spatial magnetic nanoparticle (MNP) distribution in the body. Magnetorelaxometry (MRX) imaging is a promising and noninvasive technique for the reconstruction of this distribution. To date, no accurate and quantitative measure is available to compare and optimize different MRX imaging models and setups independent of the MNP distribution. In this paper, the authors employ statistical parameters to develop quantitative MRX imaging models. Using these models, a straightforward optimization of setups and models is possible resulting in improved MNP reconstructions. A MRX imaging setup is considered with different coil configurations, each corresponding to a MRX imaging model. The models can be represented by a sensitivity matrix. These are compared by employing the matrices as inputs to statistical parameters such as conditional entropy and mutual information (MI). These parameters determine the best model to reconstruct the MNP amount for each volume-element (voxel) in the sample. The matrix is transformed by multiplying the columns with different weightings depending on the performance of the MRX imaging model with respect to the other models. This transformed matrix is compared to the original sensitivity matrix without weightings. Compared to the original sensitivity matrix, an increased numerical stability and improved noise robustness for the transformed sensitivity matrix are observed. The reconstruction of the MNP shows improvements: a correlation to the actual MNP distribution of 99.2%, whereas the original matrix only had 82.5%. By selecting the MRX models with the smallest MI, the authors are able to reduce the measurement time by 65% and still obtain an improved imaging accuracy and noise robustness. The statistical parameters allow a direct measure of the relative information content within the setup such that the optimal voxel size for the MRX setup is determined to be between 5 and 15 mm, while other sizes show a significant change in the statistical parameters. The use of statistical parameters in MRX imaging models results in quantitative models which can optimize MRX setups in a very fast and elegant way such that improved MNP imaging can be realized. Finally, the presented measure allows to quantitatively and accurately compare different MRX models and setups independent of the MNP distribution.

Automated voxelization of 3D atom probe data through kernel density estimation

Identifying nanoscale chemical features from atom probe tomography (APT) data routinely involves adjustment of voxel size as an input parameter, through visual supervision, making the final outcome user dependent, reliant on heuristic knowledge and potentially prone to error. This work utilizes Kernel density estimators to select an optimal voxel size in an unsupervised manner to perform feature selection, in particular targeting resolution of interfacial features and chemistries. The capability of this approach is demonstrated through analysis of the γ / γ’ interface in a Ni–Al–Cr superalloy.

A methodology for optimal voxel size computation in collision detection algorithms for virtual reality

Real-time Virtual Reality applications require accuracy but are also time dependent; therefore, in these environments, the time consumption is particularly important. For that reason, when facing the problem of Collision Detection for a Virtual Reality application, we firstly focus our attention on optimizing time performance for collisions among objects. Spatial Partitioning algorithms have been broadly used in Collision Detection. In particular, voxel-based methods are simple and quick, but finding the optimum voxel size is not trivial. We propose a methodology to easily determine the optimal voxel size for Collision Detection algorithms. Using an algorithm which represents volumetric objects with tetrahedra as an example, a performance cost function is defined in order to analytically bound the voxel size that gives the best computation times. This is made by inferring and estimating all the parameters involved. Thus, the cost function is delimited to depend only on geometric data. By doing so, it is possible to determine the optimal voxelization for any algorithm and scenario. Several solutions have been researched and compared. Experimental results with theoretical and real 3D models have validated the methodology. The reliability of our research has also been compared with traditional experimental solutions given by previous works.

The influence of voxel size on atom probe tomography data

A methodology for determining the optimal voxel size for phase thresholding in nanostructured materials was developed using an atom simulator and a model system of a fixed two-phase composition and volume fraction. The voxel size range was banded by the atom count within each voxel. Some voxel edge lengths were found to be too large, resulting in an averaging of compositional fluctuations; others were too small with concomitant decreases in the signal-to-noise ratio for phase identification. The simulated methodology was then applied to the more complex experimentally determined data set collected from a (Co(0.95)Fe(0.05))(88)Zr(6)Hf(1)B(4)Cu(1) two-phase nanocomposite alloy to validate the approach. In this alloy, Zr and Hf segregated to an intergranular amorphous phase while Fe preferentially segregated to a crystalline phase during the isothermal annealing step that promoted primary crystallization. The atom probe data analysis of the volume fraction was compared to transmission electron microscopy (TEM) dark-field imaging analysis and a lever rule analysis of the volume fraction within the amorphous and crystalline phases of the ribbon.

Approximation of Optimal Voxel Size for Collision Detection in Maintainability Simulations within Massive Virtual Environments

AbstractThis paper describes a Collision Method for massive virtual environments composed of millions of triangles. It has been applied in the aeronautics industry for maintainability simulations using virtual aircraft engine mock‐ups. The method performs well and has a good interactive frame rate even when it is used for computing force feedback with haptic devices. Space sorting problems chiefly related to voxel techniques, such as memory requirements and optimal voxel size, have been solved. We use advanced memory structures and hashing techniques. To find the optimal voxel size, several analytical solutions have been proposed and compared. These solutions are based on the performance cost function of the algorithm used. Experiments have been undertaken to verify these analytical solutions.