Tree Geometry Research Articles

Reliability of a commercial platform for estimating flower cluster and fruit number, yield, tree geometry and light interception in apple trees under different rootstocks and row orientations

Modern horticulture is undergoing a rapid change with the introduction of new predictive technologies that help maximise the automation of orchard management practices. This study aimed to calibrate and validate a commercial sensorised mobile platform for the prediction of flower cluster number, fruit number and yield, tree geometry in ‘ANABP-01′ apples. In addition, this work (i) modelled the relationships between tree geometry and light interception, and (ii) determined the effects of light interception, rootstock and row orientation on flower cluster number, crop load, yield and tree geometry. Results showed that predictions were very accurate after initial calibration. Flower cluster detections had an error (RMSE) of ∼ 5 clusters / image. Fruit number and yield predictions needed independent calibration across rootstocks but errors after validation on a separate dataset were small (RMSE = 5 fruit / tree, and RMSE = 1 kg / fruit, for fruit number and yield, respectively). Orchard errors for fruit number and yield estimations were lower than 5 %. Canopy area, canopy density and canopy cross-sectional leaf area (CSLA) were all linearly related with effective area of shade (EAS, integrated daily canopy light interception) but CSLA had the most robust and stable relationship with intercepted light. Increasing CSLA led to higher flower cluster number, fruit number and yield. Row orientations and rootstocks significantly affected productive performance, tree size and geometry and light interception. The orchard heatmaps generated after data validation proved very useful to support orchard management decisions. Overall, the predictive technology demonstrated to be a valid tool to combine accurate estimates of several important fruit crop parameters (i.e. flower cluster number, fruit number, yield, tree size and geometry, and light interception) in a single platform.

Modeling transpiration in synthetic trees

Synthetic trees mimic the transpiration cycle of natural trees by connecting a reservoir and conduits to wetted nanopores that exhibit a negative Laplace pressure during evaporation. Here, we develop a comprehensive theoretical model of transpiration for synthetic trees comprised of a vertically-oriented tube array connected at the top to a nanoporous synthetic leaf. Our model illustrates that when the leaf is exposed to a convective gas flow, the diffusive boundary layer is negligible and the ambient humidity directly prescribes the negative Laplace pressure of water in the leaf. The resulting capillary-driven transpiration rate up the tree is then a function of both the Laplace pressure, which sets the hydraulic load, and the tree geometry, which sets the hydraulic resistance. Conversely, when the leaf is exposed to an atmospheric environment, it is the evaporation rate and tree geometry that prescribe the necessary Laplace pressure to conserve mass. Matching the Laplace and Kelvin pressures at the menisci results in a local humidity that differs from the ambient, such that a diffusive boundary layer necessarily forms. Our model also accounts for the dynamic evolution of the menisci, in particular their ability to tune their contact angle and, when necessary, partially retreat into the nanopores to self-stabilize. Over a wide variety of tree geometries and ambient conditions, we identify when the transpiration rate is evaporation-limited versus pressure-limited (bottlenecked by the leaf’s maximum Laplace pressure). These findings should inform the design and development of next-generation synthetic trees with applications in water extraction and solar steam generation.

Self-Organogenesis from 2D Micropatterns to 3D Biomimetic Biliary Trees.

Background and Aims: Globally, liver diseases account for 2 million deaths per year. For those with advanced liver disease the only curative approach is liver transplantation. However, less than 10% of those in need get a liver transplant due to limited organ availability. To circumvent this challenge, there has been a great focus in generating a bioengineered liver. Despite its essential role in liver functions, a functional biliary system has not yet been developed. In this framework, exploration of epithelial cell self-organogenesis and microengineering-driven geometrical cell confinement allow to envision the bioengineering of a functional biomimetic intrahepatic biliary tract. Approach: three-dimensional (3D) bile ducts were built in vitro by restricting cell adhesion to two-dimensional (2D) patterns to guide cell self-organization. Tree shapes mimicking the configuration of the human biliary system were micropatterned on glass slides, restricting cell attachment to these areas. Different tree geometries and culture conditions were explored to stimulate self-organogenesis of normal rat cholangiocytes (NRCs) used as a biliary cell model, either alone or in co-culture with human umbilical endothelial cells (HUVECs). Results: Pre-seeding the micropatterns with HUVECs promoted luminogenesis with higher efficiency to yield functional branched biliary tubes. Lumen formation, apico-basal polarity, and preservation of the cholangiocyte phenotype were confirmed. Moreover, intact and functional biliary structures were detached from the micropatterns for further manipulation. Conclusion: This study presents physiologically relevant 3D biliary duct networks built in vitro from 2D micropatterns. This opens opportunities for investigating bile duct organogenesis, physiopathology, and drug testing.

Correlation of coronary artery geometry with the complexity and severity of coronary atherosclerosis: rationale and design of the GEOMETRY-CTA study

Abstract Funding Acknowledgements Type of funding sources: Public grant(s) – EU funding. Main funding source(s): This research is co-financed by Greece and the European Union (European Social Fund-ESF) through the Operational Programme «Human Resources Development, Education and Lifelong Learning 2014-2020» in the context of the project “Correlation of coronary artery tree geometry and clinical parameters with the distribution, complexity and severity of coronary artery disease: a pilot study using multislice CT coronary angiography” (MIS 5047882) Background Development and progression of coronary atherosclerosis is complex and not yet fully understood. Accumulative evidence supports the notion that coronary artery disease (CAD) results from an interaction of systemic factors, such as dyslipidemia, with local hemodynamic factors that regulate the site-specific predilection of atherosclerosis, particularly low endothelial shear stress (ESS). Since low ESS develops in geometrically irregular regions of the coronary tree for a given arterial blood flow, geometrical factors affect atherosclerotic plaque distribution and vulnerability. However, the correlation of coronary geometric features with the complexity and severity of CAD has not been fully elucidated. Purpose GEOMETRY-CTA is a prospective, non-randomized, observational study that aims to investigate the correlation of coronary artery geometrical features with the complexity and severity of CAD using Coronary Computed Tomography Angiography (CCTA). The prognostic value of a CCTA-derived geometric risk score will also be assessed. Methods The study aims to recruit 100 consecutive patients with suspected CAD and low/intermediate pre-test probability. Coronary geometrical characteristics such as angulation of coronary bifurcations, tortuosity, coronary artery volume index (CAVi) and vessel-length will be assessed with multi-planar reformation and volume rendering techniques, and integrated into a single geometric risk score. The extent and vulnerability of plaque burden will be calculated using several anatomical scoring systems such as the Leiden CTA risk score, CT-SYNTAX score, and CT-adapted Gensini score. Patients will be prospectively followed for 12 months after enrollment. Results The primary objective of the study is to evaluate the correlation of the geometric risk score with CAD severity and plaque vulnerability. We also hypothesize that wider bifurcation angles and lower CAVi augmenting the atherosclerosis-prone environment and predict higher CAD extent and complexity. Conclusion The present study aims to introduce a quantitative, non-invasive imaging biomarker expressing CAD severity and investigate its prognostic value in regards to adverse cardiovascular events. The derived index will be available for incorporation in larger national prospective studies for further cardiovascular risk stratification.

Estimation of coronary stenosis severity based on flow distribution ratios

We suggest improving minimally-invasive stenosis severity estimation, using a combination of existing geometry-based methods with Transluminal Attenuation Gradient measurements. Instead of local flow values, the method uses flow distribution ratios along the entire tree. The tree geometry is used to derive a lumped model and predict the ‘theoretical’ ratios in each bifurcation, while attenuation measurements are used for extracting ‘actual’ ratios. The discrepancies between the measured and the theoretical values are utilized to assess a functional degree of stenosis. Our experimental and numerical analyses show that the quantitative value of discrepancy is proportional to stenosis severity, regardless of boundary conditions.

Bending the Bruhat-Tits tree. Part I. Tensor network and emergent Einstein equations

As an extended companion paper to [1], we elaborate in detail how the tensor network construction of a p-adic CFT encodes geometric information of a dual geometry even as we deform the CFT away from the fixed point by finding a way to assign distances to the tensor network. In fact we demonstrate that a unique (up to normalizations) emergent graph Einstein equation is satisfied by the geometric data encoded in the tensor network, and the graph Einstein tensor automatically recovers the known proposal in the mathematics literature, at least perturbatively order by order in the deformation away from the pure Bruhat-Tits Tree geometry dual to pure CFTs. Once the dust settles, it becomes apparent that the assigned distance indeed corresponds to some Fisher metric between quantum states encoding expectation values of bulk fields in one higher dimension. This is perhaps a first quantitative demonstration that a concrete Einstein equation can be extracted directly from the tensor network, albeit in the simplified setting of the p-adic AdS/CFT.

Impartial achievement games on convex geometries

We study a game where two players take turns selecting points of a convex geometry until the convex closure of the jointly selected points contains all the points of a given winning set. The winner of the game is the last player able to move. We develop a structure theory for these games and use it to determine the nim number for several classes of convex geometries, including one-dimensional affine geometries, vertex geometries of trees, and games with a winning set consisting of extreme points.

Patient-specific fluid–structure interaction model of bile flow: comparison between 1-way and 2-way algorithms

Gallbladder disease is one of the most spread pathologies in the world. Despite the number of operations dealing with biliary surgery increases, the number of postoperative complications is also high. The aim of this study is to show the influence of the biliary system pathology on bile flow character and to numerically assess the effect of surgical operation (cholecystectomy) on the fluid dynamics in the extrahepatic biliary tree, and also to reveal the difference between 1-way and 2-way FSI algorithms on the results. Moreover, the bile viscosity and biliary tree geometry influence on the choledynamics were evaluated. Bile velocity, pressure, wall shear stress (WSS), displacements and von Mises stress distributions in the extrahepatic biliary tree are presented, and comparison is made between a healthy and a lithogenic bile. The patient-specific biliary tree model is created using magnetic resonance imaging (MRI) and imported in a commercial finite element analysis software. It is found that in the case of lithogenic bile, velocities have lower magnitude while pressures are higher. Furthermore, stress analysis of the bile ducts shows that the WSS distribution is found mostly prevailing in the common hepatic duct and common bile duct areas. It is shown that when it is necessary to evaluate the bile flow dynamics in urgent medical situations, 1-way analysis is acceptable. Nevertheless, 2-way FSI provides more accurate data, if necessary to evaluate the stress–strain state of bile ducts. The proposed model can be applied to medical practice to reduce the number of post-operative complications.

UNSUPERVISED CLUSTERING OF AIRWAY TREE STRUCTURES ON HIGH-RESOLUTION CT: THE MESA LUNG STUDY.

The morphology of the proximal human airway tree is highly variable in the general population, and known variants in airway branching patterns are associated with increased risk of COPD and with polymorphisms in growth factors involved in pulmonary development. Variation in the geometry and topology of the airway tree remains incompletely characterized, and their clinical implications are not yet understood. In this work, we present an approach to unsupervised clustering of airway tree structures in Billera-Holmes-Vogtmann tree-space. We validate our pipeline on synthetic airway tree data, and apply our algorithm to identify reproducible and morphologically distinct airway tree subtypes in the MESA Lung CT cohort.

Three-dimensional quantification of tree architecture from mobile laser scanning and geometry analysis

Key messageMobile laser scanning and geometrical analysis revealed relationships between tree geometry and seed dispersal mechanism, latitude of origin, as well as growth.The structure and dynamics of a forest are defined by the architecture and growth patterns of its individual trees. In turn, tree architecture and growth result from the interplay between the genetic building plans and environmental factors. We set out to investigate whether (1) latitudinal adaptations of the crown shape occur due to characteristic solar elevation angles at a species’ origin, (2) architectural differences in trees are related to seed dispersal strategies, and (3) tree architecture relates to tree growth performance. We used mobile laser scanning (MLS) to scan 473 trees and generated three-dimensional data of each tree. Tree architectural complexity was then characterized by fractal analysis using the box-dimension approach along with a topological measure of the top heaviness of a tree. The tree species studied originated from various latitudinal ranges, but were grown in the same environmental settings in the arboretum. We found that trees originating from higher latitudes had significantly less top-heavy geometries than those from lower latitudes. Therefore, to a certain degree, the crown shape of tree species seems to be determined by their original habitat. We also found that tree species with wind-dispersed seeds had a higher structural complexity than those with animal-dispersed seeds (p < 0.001). Furthermore, tree architectural complexity was positively related to the growth performance of the trees (p < 0.001). We conclude that the use of 3D data from MLS in combination with geometrical analysis, including fractal analysis, is a promising tool to investigate tree architecture.

Spatial architecture of biliary tree in mammals: Fractal and Euclidean geometric features.

The study of the fractal architecture of various organs and structures expanded the possibilities for determining the ranges of their functioning and structural arrangement, which, as a result, was reflected in the development of new approaches to diagnostics and therapeutic impacts. The architecture of the excretory duct systems, similar to the hemo- and lymph- circulatory beds and the bronchial tree, is considered fractal. At the same time, information about hitherto unknown structures of the biliary tree continues to appear in the literature. We aimed to study the features of the spatial geometry of the biliary tree and assess the significance of both its fractal and Euclidean characteristics for the development of approaches that facilitate comprehensive description of intrahepatic biliary tract architecture. We investigated the architecture of the biliary trees of six men, seven male canines, and seven male Wistar rats using the corrosion casting method. Corrosion casts were prepared by injecting solidifying latexes into the bile ducts. The preparations were studied using a light stereomicroscope and a scanning electron microscope. Biliary tree branching is of various types. In addition, the correlation between variations in the caliber and length of the bile ducts and their order is not significant. Therefore, the biliary tree should not be considered as a classical fractal and it consists of the main modules, represented by the network of the bile canaliculi (first nonfractal module) and a biliary tree with a fractal branching (second module) that drains the bile canaliculi mesh and the additional modules represented by the mucosal biliary glands (in mammals with the gallbladder) or the periportal biliary plexus (in mammals without a gallbladder) and the aberrant biliary ducts. Such a configuration of the biliary bed should optimally ensure the smooth implementation of the physiological function of the liver, as well as its adaptation to different pathologies accompanied by biliary hypertension. It also might be considered in the diagnosis and assessment of ductular reaction, biliary regeneration, and/or carcinogenesis.

Impact of Tree Crown Transmittance on Surface Reflectance Retrieval in the Shade for High Spatial Resolution Imaging Spectroscopy: A Simulation Analysis Based on Tree Modeling Scenarios

With the advancement of high spatial resolution imaging spectroscopy, an accurate surface reflectance retrieval is needed to derive relevant physical variables for land cover mapping, soil, and vegetation monitoring. One challenge is to deal with tree shadows using atmospheric correction models if the tree crown transmittance Tc is not properly taken into account. This requires knowledge of the complex radiation mechanisms that occur in tree crowns, which can be provided by coupling the physical modeling of canopy radiative transfer codes (here DART) and the 3D representations of trees. First in this study, a sensitivity analysis carried out on DART simulations with an empirical 3D tree model led to a statistical regression predicting Tc from the tree leaf area index (LAI) and the solar zenith angle with good performances (RMSE ≤ 4.3% and R2 ≥ 0.91 for LAI ≤ 4 m2.m−2). Secondly, more realistic 3D voxel-grid tree models derived from terrestrial LiDAR measurements over two trees were considered. The comparison of DART-simulated Tc from these models with the previous predicted Tc over 0.4–2.5 µm showed three main sources of inaccuracy quoted in order of importance: (1) the global tree geometry shape (mean bias up to 21.5%), (2) the transmittance fraction associated to multiple scattering, Tscat (maximum bias up to 13%), and (3) the degree of realism of the tree representation (mean bias up to 7.5%). Results showed that neglecting Tc leads to very inaccurate reflectance retrieval (mean bias &gt; 0.04), particularly if the background reflectance is high, and in the near and shortwave infrared – NIR and SWIR – due to Tscat. The transmittance fraction associated to the non-intercepted transmitted light, Tdir, can reach up to 95% in the SWIR, and Tscat up to 20% in the NIR. Their spatial contributions computed in the tree shadow have a maximum dispersion of 27% and 8% respectively. Investigating how to approximate Tdir and Tscat spectral and spatial variability along with the most appropriate tree 3D modeling is crucial to improve reflectance retrieval in tree shadows when using atmospheric correction models.

Tree crown geometry and its performances on human thermal comfort adjustment

Trees play an important part in landscaping as well as thermal environment adjustment. This study selected a satellite city of Sichuan Province in China, Xindu, for field measurement about tree’s crown characteristics on their cooling performances on five sunny summer days during August 2019. There were several parameters showing tree characteristics used, including tree canopying size (tree crown radius, TCR), tree geometry (the ratio of TCR to trunk height, R/TH), site openness (sky view factor, SVF), and leaf density (leaf area index, LAI). It was found that R/TH had the most significant thermal adjusting effects than others. The increase of R/TH by 1 can reduce physiological equivalent temperature by approximately 2.5 ​°C (R2 ​= ​0.8932) and 2.65 ​°C (R2 ​= ​0.8424) in the morning and afternoon respectively. SVF and LAI had less significant cooling effect due to the fact of dense-leaf season. This result provided good direction for future landscape design towards microclimate adjustment.

Fractal dimension of tree crowns explains species functional-trait responses to urban environments at different scales.

The evolution of form and function of trees of diverse species has taken place over hundreds of millions of years, while urban environments are relatively new on an evolutionary time scale, representing a novel set of environmental constraints for trees to respond to. It is important to understand how trees of different species, planted in these anthropogenically-structured urban ecosystems, are responding to them. Many theories have been advanced to understand tree form and function, including several that suggest the fractal-like geometry of trees is a direct reflection of inherent and plastic morphological and physiological traits that govern tree growth and survival. In this research, we analyzed the "fractal dimension" of thousands of tree crowns of many different tree species, growing in different urban environments across the United States, to learn more about the nature of trees and their responses to urban environments at different scales. Our results provide new insights regarding how tree crown fractal dimension relates to balances between hydraulic- and light-capture-related functions (e.g., drought and shade tolerance). Our findings indicate that trees exhibit reduced crown fractal dimension primarily to reduce water loss in hotter cities. More specifically, the intrinsic drought tolerance of the studied species arises from lower surface to volume ratios at both whole-crown and leaf scales, preadapting them to drought stress in urban ecosystems. Needle-leaved species showed a clear trade-off between optimizing the fractal dimension of their crowns for drought vs. shade tolerance. Broad-leaved species showed a fractal crown architecture that responded principally to inherent drought tolerance. Adjusting for the temperature of cities and intrinsic species effects, the fractal dimension of tree crowns was lower in more heavily urbanized areas (with greater paved area or buildings) and due to crowns conflicting with utility wires. With expectations for more urbanization and generally hotter future climates, worldwide, our results add new insights into the physiological ecology of trees in urban environments, which may help humans to provide more hospitable habitats for trees in urbanized areas and to make better decisions about tree selection in urban forest management.

Mechanical behavior of trees with structural defects under lateral load: A numerical modeling approach

Tree structural defects are a common cause of tree failure. These structural defects often result from progressive wood decay over time. Therefore, special attention is required to study the changes in the lateral responses of trees as defects are introduced. This can show how, using these changes, significant tree defects that can ultimately disrupt tree stability be detected. In this study, a three-dimensional (3D) numerical model was proposed to investigate the mechanical behavior of trees with structural defects under lateral load. The 3D numerical model was verified by non-destructive tree pulling tests with the incorporation of the overall stiffness of the tested trees. Then, trees with structural defects were simulated with different tree geometries and defect sizes. In addition, to examine the effect of decay volume extents and deterioration in elastic modulus due to decay, a simplified two-dimensional (2D) numerical simulation was performed. Through comparison with the results of the tree pulling tests, the 3D numerical model was found to be appropriate and applicable for the evaluation of the tree’s lateral response as well as the effects on tree stability. Numerical analysis results, therefore, confirmed the fact that the mechanical behavior of the tree under lateral load is strongly dependent on the presence of significant decay that can cause whole tree failure.

AdQSM: A New Method for Estimating Above-Ground Biomass from TLS Point Clouds

Forest above-ground biomass (AGB) can be estimated based on light detection and ranging (LiDAR) point clouds. This paper introduces an accurate and detailed quantitative structure model (AdQSM), which can estimate the AGB of large tropical trees. AdQSM is based on the reconstruction of 3D tree models from terrestrial laser scanning (TLS) point clouds. It represents a tree as a set of closed and complete convex polyhedra. We use AdQSM to model 29 trees of various species (total 18 species) scanned by TLS from three study sites (the dense tropical forests of Peru, Indonesia, and Guyana). The destructively sampled tree geometry measurement data is used as reference values to evaluate the accuracy of diameter at breast height (DBH), tree height, tree volume, branch volume, and AGB estimated from AdQSM. After AdQSM reconstructs the structure and volume of each tree, AGB is derived by combining the wood density of the specific tree species from destructive sampling. The AGB estimation from AdQSM and the post-harvest reference measurement data show a satisfying agreement. The coefficient of variation of root mean square error (CV-RMSE) and the concordance correlation coefficient (CCC) are 20.37% and 0.97, respectively. AdQSM provides accurate tree volume estimation, regardless of the characteristics of the tree structure, without major systematic deviations. We compared the accuracy of AdQSM and TreeQSM in modeling the volume of 29 trees. The tree volume from AdQSM is compared with the reference value, and the determination coefficient (R2), relative bias (rBias), and CV-RMSE of tree volume are 0.96, 6.98%, and 22.62%, respectively. The tree volume from TreeQSM is compared with the reference value, and the R2, relative Bias (rBias), and CV-RMSE of tree volume are 0.94, −9.69%, and 23.20%, respectively. The CCCs between the volume estimates based on AdQSM, TreeQSM, and the reference values are 0.97 and 0.96. AdQSM also models the branches in detail. The volume of branches from AdQSM is compared with the destructive measurement reference data. The R2, rBias, and CV-RMSE of the branches volume are 0.97, 12.38%, and 36.86%, respectively. The DBH and height of the harvested trees were used as reference values to test the accuracy of AdQSM’s estimation of DBH and tree height. The R2, rBias, and CV-RMSE of DBH are 0.94, −5.01%, and 9.06%, respectively. The R2, rBias, and CV-RMSE of the tree height were 0.95, 1.88%, and 5.79%, respectively. This paper provides not only a new QSM method for estimating AGB based on TLS point clouds but also the potential for further development and testing of allometric equations.

COMPRESSION OF HIGH-RESOLUTION VOXEL PHANTOMS BY MEANS OF B+ TREE

Data structures are chosen to save space and to grant fast access to data by it’s key for a particular structural representation. The data structures surveyed are linear lists, hierarchical structures, graph structures. B+ tree is an expansion of a B tree data structure which allows efficient insertions, deletions and search operations. It is used to store a large amount of data that cannot be stored in the main memory. B+ tree leaf nodes are connected together in the form of a singly linked list to make search queries more efficient and effective. The drawback of binary tree geometry is that the decrease in memory use comes at the expense of more frequent memory access, might slow down simulation in which frequent memory access constitutes a significant part of the execution time. Processing and compression of voxel phantoms without loss of quality. Voxels are often utilized in the visualization and analysis of medical and scientific (logical) information. Voxel phantoms which comprise a set of small volume components appeared towards the end of the 1980s and improved on the first scientific models. These are the models of the human body. These phantoms are an extremely exact representation. Fetching of records in the equal number of disk accesses and to reduce the access time by reducing the height of the tree and increasing the number of branches in the node.

The influence of changing location of trees in urban green spaces on insolation mitigation

Urban areas are often overheated, which potentially results in a range of negative effects on the urban microclimate. One way to mitigate urban overheating is to provide shading by tall vegetation (trees). Simulations of insolation with different tree locations were used for insolation mitigation in previous research. However, in urban green spaces potential tree locations can be selected with greater freedom. Therefore, the method for selecting tree locations has to rely on optimization, as there are many possible combinations of locations.The aim of this paper is to devise an approach for insolation mitigation by changing the location of trees in urban green spaces. The approach uses input data that describe the geometry of the built environment and the geometry of trees, as well as climate and weather data (direct radiation, diffuse radiation and cloud cover). The algorithm is applicable to any location and urban environment. The approach uses the Evolutionary algorithm, a method based on natural selection suitable for solving optimization problems. The evolutionary approach is compared to the simulation of average insolation values and the simulations and selection of random tree locations. It is also applied to a real-world example. The results indicate that the proposed approach can be used to mitigate insolation in urban green spaces.

The Adaptive Geometry of Trees Revisited.

The Adaptive Geometry of Trees had an important conceptual influence on plant ecology and helped inspire many new approaches to understanding succession, plant adaptation, and plant competition. Its central model provided an elegant potential explanation for how optimal canopy form should shift with ecological conditions, change those conditions through time, and thus help drive succession and be a consequence of it. Yet on close examination, this deeply inspirational model does not lead to the predictions for which it is widely known. Here I show that the Horn model actually favors monolayer canopies over multilayers under all light conditions if relative growth rate (growth per unit investment) is maximized. Horn's conclusion that multilayers would be favored over monolayers in brighter sites is an artifact. I propose that self-shading multilayers might gain an advantage in brightly lit sites by reducing water loss, reducing the costs of branch construction and maintenance, reducing photoinhibition, increasing light capture in sidelit microsites, and increasing water and nutrient supplies (or leaf longevity) when combined with one or more of the previous potential advantages. I conclude with a brief discussion connecting Horn's model to other conceptual frameworks in plant ecology and outlining possible future extensions.

Multispectral Mapping on 3D Models and Multi-Temporal Monitoring for Individual Characterization of Olive Trees

3D plant structure observation and characterization to get a comprehensive knowledge about the plant status still poses a challenge in Precision Agriculture (PA). The complex branching and self-hidden geometry in the plant canopy are some of the existing problems for the 3D reconstruction of vegetation. In this paper, we propose a novel application for the fusion of multispectral images and high-resolution point clouds of an olive orchard. Our methodology is based on a multi-temporal approach to study the evolution of olive trees. This process is fully automated and no human intervention is required to characterize the point cloud with the reflectance captured by multiple multispectral images. The main objective of this work is twofold: (1) the multispectral image mapping on a high-resolution point cloud and (2) the multi-temporal analysis of morphological and spectral traits in two flight campaigns. Initially, the study area is modeled by taking multiple overlapping RGB images with a high-resolution camera from an unmanned aerial vehicle (UAV). In addition, a UAV-based multispectral sensor is used to capture the reflectance for some narrow-bands (green, near-infrared, red, and red-edge). Then, the RGB point cloud with a high detailed geometry of olive trees is enriched by mapping the reflectance maps, which are generated for every multispectral image. Therefore, each 3D point is related to its corresponding pixel of the multispectral image, in which it is visible. As a result, the 3D models of olive trees are characterized by the observed reflectance in the plant canopy. These reflectance values are also combined to calculate several vegetation indices (NDVI, RVI, GRVI, and NDRE). According to the spectral and spatial relationships in the olive plantation, segmentation of individual olive trees is performed. On the one hand, plant morphology is studied by a voxel-based decomposition of its 3D structure to estimate the height and volume. On the other hand, the plant health is studied by the detection of meaningful spectral traits of olive trees. Moreover, the proposed methodology also allows the processing of multi-temporal data to study the variability of the studied features. Consequently, some relevant changes are detected and the development of each olive tree is analyzed by a visual-based and statistical approach. The interactive visualization and analysis of the enriched 3D plant structure with different spectral layers is an innovative method to inspect the plant health and ensure adequate plantation sustainability.