WheatSpikeNet: an improved wheat spike segmentation model for accurate estimation from field imaging

Phenotyping is used in plant breeding to identify genotypes with desirable characteristics, such as drought tolerance, disease resistance, and high-yield potentials. It may also be used to evaluate the effect of environmental circumstances, such as drought, heat, and salt, on plant growth and development. Wheat spike density measure is one of the most important agronomic factors relating to wheat phenotyping. Nonetheless, due to the diversity of wheat field environments, fast and accurate identification for counting wheat spikes remains one of the challenges. This study proposes a meticulously curated and annotated dataset, named as SPIKE-segm, taken from the publicly accessible SPIKE dataset, and an optimal instance segmentation approach named as WheatSpikeNet for segmenting and counting wheat spikes from field imagery. The proposed method is based on the well-known Cascade Mask RCNN architecture with model enhancements and hyperparameter tuning to provide state-of-the-art detection and segmentation performance. A comprehensive ablation analysis incorporating many architectural components of the model was performed to determine the most efficient version. In addition, the model's hyperparameters were fine-tuned by conducting several empirical tests. ResNet50 with Deformable Convolution Network (DCN) as the backbone architecture for feature extraction, Generic RoI Extractor (GRoIE) for RoI pooling, and Side Aware Boundary Localization (SABL) for wheat spike localization comprises the final instance segmentation model. With bbox and mask mean average precision (mAP) scores of 0.9303 and 0.9416, respectively, on the test set, the proposed model achieved superior performance on the challenging SPIKE datasets. Furthermore, in comparison with other existing state-of-the-art methods, the proposed model achieved up to a 0.41% improvement of mAP in spike detection and a significant improvement of 3.46% of mAP in the segmentation tasks that will lead us to an appropriate yield estimation from wheat plants.

Modelling of PFAS-surface interactions: Effect of surface charge and solution ions

PER-: and poly-fluoroalkyl substances (PFAS) are a class of substances of increasing concern as environmental contaminants. The interactions between PFAS and surfaces play an important role in PFAS transport and remediation. Previous studies have found PFAS adsorption to be dependent upon properties including pH, organic matter and particle size, along with PFAS functional group and carbon chain length. It is hypothesised that a theoretical examination of PFAS-surface interactions, via Monte Carlo molecular simulation, would show differences resulting from changes in surface charge, H⁺, OH^-, Ca²⁺ concentrations and PFAS carbon chain length. Monte Carlo molecular simulations of perfluorooctane and perfluorobutane sulfonic acids interacting with a graphite surface in an aqueous medium were performed. Variations in surface charge, H⁺, OH^- and Ca²⁺ concentrations were made. The distance-dependent density of molecules from the surface was analysed as a proxy for PFAS adsorption to the surface. Simulation results showed differences in surface behaviour that depended on surface charge, H⁺, OH^- and Ca²⁺ concentrations, along with carbon chain length, with surface charge playing the most prominent role in controlling PFAS adsorption. For negatively charged surfaces, adsorption due to divalent cation bridging was observed in Ca²⁺ solutions. Modelling, such as in this study, of the thermodynamic equilibrium behaviour of low concentrations of molecules, in scenarios where both adsorption and mobility of PFAS occur, can aid in the design and testing of sorptive surfaces for amendment-based PFAS remediation.

A Whole Leaf Comparative Study of Stomatal Conductance Models

We employed a detailed whole leaf hydraulic model to study the local operation of three stomatal conductance models distributed on the scale of a whole leaf. We quantified the behavior of these models by examining the leaf-area distributions of photosynthesis, transpiration, stomatal conductance, and guard cell turgor pressure. We gauged the models' local responses to changes in environmental conditions of carbon dioxide concentration, relative humidity, and light irradiance. We found that a stomatal conductance model that includes mechanical processes dependent on local variables predicts a spatial variation of physiological activity across the leaf: the leaf functions of photosynthesis and transpiration are not uniformly operative even when external conditions are uniform. The gradient pattern of hydraulic pressure which is needed to produce transpiration from the whole leaf is derived from the gradient patterns of turgor pressures of guard cells and epidermal cells and consequently leads to nonuniform spatial distribution patterns of transpiration and photosynthesis via the mechanical stomatal model. Our simulation experiments, comparing the predictions of two versions of a mechanical stomatal conductance model, suggest that leaves exhibit a more complex spatial distribution pattern of both photosynthesis and transpiration rate and more complex dependencies on environmental conditions when a non-linear relationship between the stomatal aperture and guard cell and epidermal cell turgor pressures is implemented. Our model studies offer a deeper understanding of the mechanism of stomatal conductance and point to possible future experimental measurements seeking to quantify the spatial distributions of several physiological activities taking place over a whole leaf.

Interrogating the relationship between the microstructure of amphiphilic poly(ethylene glycol-b-caprolactone) copolymers and their colloidal assemblies using non-interfering techniques

Understanding the microstructural parameters of amphiphilic copolymers that control the formation and structure of aggregated colloids (e.g., micelles) is essential for the rational design of hierarchically structured systems for applications in nanomedicine, personal care and food formulations. Although many analytical techniques have been employed to study such systems, in this investigation we adopted an integrated approach using non-interfering techniques - diffusion nuclear magnetic resonance (NMR) spectroscopy, dynamic light scattering (DLS) and synchrotron small-angle X-ray scattering (SAXS) - to probe the relationship between the microstructure of poly(ethylene glycol-b-caprolactone) (PEG-b-PCL) copolymers [e.g., block molecular weight (MW) and the mass fraction of PCL (f_PCL)] and the structure of their aggregates. Systematic trends in the self-assembly behaviour were determined using a large family of well-defined block copolymers with variable PEG and PCL block lengths (number-average molecular weights (M_n) between 2 and 10 and 0.5-15 kDa, respectively) and narrow dispersity (Ð < 1.12). For all of the copolymers, a clear transition in the aggregate structure was observed when the hydrophobic f_PCL was increased at a constant PEG block M_n, although the nature of this transition is also dependent on the PEG block M_n. Copolymers with low M_n PEG blocks (2 kDa) were observed to transition from unimers and loosely associated unimers to metastable aggregates and finally, to cylindrical micelles as the f_PCL was increased. In comparison, copolymers with PEG block M_n of between 5 and 10 kDa transitioned from heterogenous metastable aggregates to cylindrical micelles and finally, well-defined ellipsoidal micelles (of decreasing aspect ratios) as the f_PCL was increased. In all cases, the diffusion NMR spectroscopy, DLS and synchrotron SAXS results provided complementary information and the grounds for a phase diagram relating copolymer microstructure to aggregation behaviour and structure. Importantly, the absence of commonly depicted spherical micelles has implications for applications where properties may be governed by shape, such as, cellular uptake of nanomedicine formulations.

On the Efficacy of Water Transport in Leaves. A Coupled Xylem-Phloem Model of Water and Solute Transport

In this paper, we present and use a coupled xylem/phloem mathematical model of passive water and solute transport through a reticulated vascular system of an angiosperm leaf. We evaluate the effect of leaf width-to-length proportion and orientation of second-order veins on the indexes of water transport into the leaves and sucrose transport from the leaves. We found that the most important factor affecting the steady-state pattern of hydraulic pressure distribution in the xylem and solute concentration in the phloem was leaf shape: narrower/longer leaves are less efficient in convecting xylem water and phloem solutes than wider/shorter leaves under all conditions studied. The degree of efficiency of transport is greatly influenced by the orientation of second-order veins relative to the main vein for all leaf proportions considered; the dependence is non-monotonic with efficiency maximized when the angle is approximately 45° to the main vein, although the angle of peak efficiency depends on other conditions. The sensitivity of transport efficiency to vein orientation increases with increasing vein conductivity. The vein angle at which efficiency is maximum tended to be smaller (relative to the main vein direction) in narrower leaves. The results may help to explain, or at least contribute to our understanding of, the evolution of parallel vein systems in monocot leaves.

Density functional theory of confined ionic liquids: the influence of power-law attractions on molecule distributions and surface forces

Interaction energies and density profiles for two model ionic liquids, [C₄mim⁺][BF₄⁻] and [C₄mim⁺][TFSI⁻], confined between charged planar walls are studied within a density functional theory framework. The results of these simulations are also compared with results assuming a simpler linear hexamer–monomer, cation–anion system. We focus attention on the effect on the atom site distributions and the surface forces of an additional, specific attractive potential between oppositely charged molecules. We consider both short- and long-ranged attractive potentials in order to span the degree to which the ionic counterions associate. Independent of its strength, we interpret the results found with the short-ranged potential to be a manifestation of limited molecular association. In contrast, depending on its strength, the results found with the long-ranged potential suggest a much stronger and possibly longer ranged associations of ionic groups. Both potentials are found to influence the behavior of the surface force at small separations, while the long-ranged attractive potential has the greater influence of the two on the long-ranged behavior of the surface force.

Interaction energies and density profiles for two model ionic liquids, [C₄mim⁺][BF₄⁻] and [C₄mim⁺][TFSI⁻], confined between charged planar walls are studied within a density functional theory framework.

A Comprehensive Biophysical Model of Ion and Water Transport in Plant Roots. III. Quantifying the Energy Costs of Ion Transport in Salt-Stressed Roots of Arabidopsis

Salt stress defense mechanisms in plant roots, such as active Na+ efflux and storage, require energy in the form of ATP. Understanding the energy required for these transport mechanisms is an important step toward achieving an understanding of salt tolerance. However, accurate measurements of the fluxes required to estimate these energy costs are difficult to achieve by experimental means. As a result, the magnitude of the energy costs of ion transport in salt-stressed roots relative to the available energy is unclear, as are the relative contributions of different defense mechanisms to the total cost. We used mathematical modeling to address three key questions about the energy costs of ion transport in salt-stressed Arabidopsis roots: are the energy requirements calculated on the basis of flux data feasible; which transport steps are the main contributors to the total energy costs; and which transport processes could be altered to minimize the total energy costs? Using our biophysical model of ion and water transport we calculated the energy expended in the trans-plasma membrane and trans-tonoplast transport of Na+, K+, Cl-, and H+ in different regions of a salt-stressed model Arabidopsis root. Our calculated energy costs exceeded experimental estimates of the energy supplied by root respiration for high external NaCl concentrations. We found that Na+ exclusion from, and Cl- uptake into, the outer root were the major contributors to the total energy expended. Reducing the leakage of Na+ and the active uptake of Cl- across outer root plasma membranes would lower energy costs while enhancing exclusion of these ions. The high energy cost of ion transport in roots demonstrates that the energetic consequences of altering ion transport processes should be considered when attempting to improve salt tolerance.

Energy costs of salt tolerance in crop plants

Agriculture is expanding into regions that are affected by salinity. This review considers the energetic costs of salinity tolerance in crop plants and provides a framework for a quantitative assessment of costs. Different sources of energy, and modifications of root system architecture that would maximize water vs ion uptake are addressed. Energy requirements for transport of salt (NaCl) to leaf vacuoles for osmotic adjustment could be small if there are no substantial leaks back across plasma membrane and tonoplast in root and leaf. The coupling ratio of the H⁺ -ATPase also is a critical component. One proposed leak, that of Na⁺ influx across the plasma membrane through certain aquaporin channels, might be coupled to water flow, thus conserving energy. For the tonoplast, control of two types of cation channels is required for energy efficiency. Transporters controlling the Na⁺ and Cl^- concentrations in mitochondria and chloroplasts are largely unknown and could be a major energy cost. The complexity of the system will require a sophisticated modelling approach to identify critical transporters, apoplastic barriers and root structures. This modelling approach will inform experimentation and allow a quantitative assessment of the energy costs of NaCl tolerance to guide breeding and engineering of molecular components.

An Automatic Field Plot Extraction Method From Aerial Orthomosaic Images

Unmanned aerial vehicles have an immense capacity for remote imaging of plants in agronomic field research trials. Traits extracted from the plots can explain development of the plants coverage, growth, flowering status, and related phenomenon. An important prerequisite step to obtain such information is to find the exact position of plots to extract them from an orthomosaic image. Extraction of plots using tools which assume a uniform spacing is often erroneous because the plots may neither be perfectly aligned nor equally distributed in a field. A novel approach is proposed which uses image-based optimization algorithm to find the alignment of plots. The method begins with a uniformly spaced grid of plots which is iteratively aligned with regions of high vegetation index, i.e., the underlying plots. The approach is validated and tested on two different orthomosaic images of fields containing wheat plots with simulated and real alignment problems, respectively. The result of alignment is compared to manually located ground truth position of plots and the errors are quantitatively analyzed. The effectiveness of the proposed method is confirmed in accurately estimating the phenotypic trait of canopy coverage compared to the common methods of extraction from uniform grids or trimmed grids. The software developed in this study is available from SourceForge, https://sourceforge.net/projects/phenalysis/.

High-Throughput Field Imaging and Basic Image Analysis in a Wheat Breeding Programme

Visual assessment of colour-based traits plays a key role within field-crop breeding programmes, though the process is subjective and time-consuming. Digital image analysis has previously been investigated as an objective alternative to visual assessment for a limited number of traits, showing suitability and slight improvement to throughput over visual assessment. However, easily adoptable, field-based high-throughput methods are still lacking. The aim of the current study was to produce a high-throughput digital imaging and analysis pipeline for the assessment of colour-based traits within a wheat breeding programme. This was achieved through the steps of (i) a proof-of-concept study demonstrating basic image analysis methods in a greenhouse, (ii) application of these methods to field trials using hand-held imaging, and (iii) developing a field-based high-throughput imaging infrastructure for data collection. The proof of concept study showed a strong correlation (r = 0.95) between visual and digital assessments of wheat physiological yellowing (PY) in a greenhouse environment, with both scores having similar heritability (H2 = 0.85 and 0.76, respectively). Digital assessment of hand-held field images showed strong correlations to visual scores for PY (r = 0.61 and 0.78), senescence (r = 0.74 and 0.75) and Septoria tritici blotch (STB; r = 0.76), with greater heritability of digital scores, excluding STB. Development of the high-throughput imaging infrastructure allowed for images of field plots to be collected at a rate of 7,400 plots per hour. Images of an advanced breeding trial collected with this system were analysed for canopy cover at two time-points, with digital scores correlating strongly to visual scores (r = 0.88 and 0.86) and having similar or greater heritability. This study details how high-throughput digital phenotyping can be applied to colour-based traits within field trials of a wheat breeding programme. It discusses the logistics of implementing such systems with minimal disruption to the programme, provides a detailed methodology for the basic image analysis methods utilized, and has potential for application to other field-crop breeding or research programmes.

High-Throughput Field Imaging and Basic Image Analysis in a Wheat Breeding Programme

Visual assessment of colour-based traits plays a key role within field-crop breeding programmes, though the process is subjective and time-consuming. Digital image analysis has previously been investigated as an objective alternative to visual assessment for a limited number of traits, showing suitability and slight improvement to throughput over visual assessment. However, easily adoptable, field-based high-throughput methods are still lacking. The aim of the current study was to produce a high-throughput digital imaging and analysis pipeline for the assessment of colour-based traits within a wheat breeding programme. This was achieved through the steps of (i) a proof-of-concept study demonstrating basic image analysis methods in a greenhouse, (ii) application of these methods to field trials using hand-held imaging, and (iii) developing a field-based high-throughput imaging infrastructure for data collection. The proof of concept study showed a strong correlation (r = 0.95) between visual and digital assessments of wheat physiological yellowing (PY) in a greenhouse environment, with both scores having similar heritability (H² = 0.85 and 0.76, respectively). Digital assessment of hand-held field images showed strong correlations to visual scores for PY (r = 0.61 and 0.78), senescence (r = 0.74 and 0.75) and Septoria tritici blotch (STB; r = 0.76), with greater heritability of digital scores, excluding STB. Development of the high-throughput imaging infrastructure allowed for images of field plots to be collected at a rate of 7,400 plots per hour. Images of an advanced breeding trial collected with this system were analysed for canopy cover at two time-points, with digital scores correlating strongly to visual scores (r = 0.88 and 0.86) and having similar or greater heritability. This study details how high-throughput digital phenotyping can be applied to colour-based traits within field trials of a wheat breeding programme. It discusses the logistics of implementing such systems with minimal disruption to the programme, provides a detailed methodology for the basic image analysis methods utilized, and has potential for application to other field-crop breeding or research programmes.

Correction to: Detection and analysis of wheat spikes using Convolutional Neural Networks

[This corrects the article DOI: 10.1186/s13007-018-0366-8.].

Quantifying the force between mercury and mica across an ionic liquid using white light interferometry

HYPOTHESIS

Under axisymmetric conditions, changes in the thickness of the thin film between a fluid drop and a solid revealed by white light interferometry can provide information about the interaction of the bodies. Thus, in principle one can quantify the force between the surfaces using interferometric information of film thickness profile. This is needed to quantify and analyze drop-solid interactions across complex fluids such as an ionic liquid to independently characterize new surface forces.

EXPERIMENTS

Interferometric fringes were obtained in experiments on the interaction between a mercury drop and mica across a film of room temperature ionic liquid. The data is analyzed using a novel formula giving the total force acting on the drop. The calculations are compared with two other approaches to estimating forces. Qualitative and quantitative differences are discussed.

FINDINGS

This is the first report of forces measured between mercury and mica across an ionic liquid. The system is subjected to different applied electric potentials. In each case a long ranged, exponentially decaying repulsive force is found. At small separations, the system becomes unstable and the surfaces jump into contact. The comparison of force calculation methods demonstrates the superiority of the force approach proposed here.

A Comprehensive Biophysical Model of Ion and Water Transport in Plant Roots. II. Clarifying the Roles of SOS1 in the Salt-Stress Response in Arabidopsis

SOS1 transporters play an essential role in plant salt tolerance. Although SOS1 is known to encode a plasma membrane Na⁺/H⁺ antiporter, the transport mechanisms by which these transporters contribute to salt tolerance at the level of the whole root are unclear. Gene expression and flux measurements have provided conflicting evidence for the location of SOS1 transporter activity, making it difficult to determine their function. Whether SOS1 transporters load or unload Na⁺ from the root xylem transpiration stream is also disputed. To address these areas of contention, we applied a mathematical model to answer the question: what is the function of SOS1 transporters in salt-stressed Arabidopsis roots? We used our biophysical model of ion and water transport in a salt-stressed root to simulate a wide range of SOS1 transporter locations in a model Arabidopsis root, providing a level of detail that cannot currently be achieved by experimentation. We compared our simulations with available experimental data to find reasonable parameters for the model and to determine likely locations of SOS1 transporter activity. We found that SOS1 transporters are likely to be operating in at least one tissue of the outer mature root, in the mature stele, and in the epidermis of the root apex. SOS1 transporter activity in the mature outer root cells is essential to maintain low cytosolic Na⁺ levels in the root and also restricts the uptake of Na⁺ to the shoot. SOS1 transporters in the stele actively load Na⁺ into the xylem transpiration stream, enhancing the transport of Na⁺ and water to the shoot. SOS1 transporters acting in the apex restrict cytosolic Na⁺ concentrations in the apex but are unable to maintain low cytosolic Na⁺ levels in the mature root. Our findings suggest that targeted, tissue-specific overexpression or knockout of SOS1 may lead to greater salt tolerance than has been achieved with constitutive gene changes. Tissue-specific changes to the expression of SOS1 could be used to identify the appropriate balance between limiting Na⁺ uptake to the shoot while maintaining water uptake, potentially leading to enhancements in salt tolerance.

Detection and analysis of wheat spikes using Convolutional Neural Networks

BACKGROUND

Field phenotyping by remote sensing has received increased interest in recent years with the possibility of achieving high-throughput analysis of crop fields. Along with the various technological developments, the application of machine learning methods for image analysis has enhanced the potential for quantitative assessment of a multitude of crop traits. For wheat breeding purposes, assessing the production of wheat spikes, as the grain-bearing organ, is a useful proxy measure of grain production. Thus, being able to detect and characterize spikes from images of wheat fields is an essential component in a wheat breeding pipeline for the selection of high yielding varieties.

RESULTS

We have applied a deep learning approach to accurately detect, count and analyze wheat spikes for yield estimation. We have tested the approach on a set of images of wheat field trial comprising 10 varieties subjected to three fertilizer treatments. The images have been captured over one season, using high definition RGB cameras mounted on a land-based imaging platform, and viewing the wheat plots from an oblique angle. A subset of in-field images has been accurately labeled by manually annotating all the spike regions. This annotated dataset, called SPIKE, is then used to train four region-based Convolutional Neural Networks (R-CNN) which take, as input, images of wheat plots, and accurately detect and count spike regions in each plot. The CNNs also output the spike density and a classification probability for each plot. Using the same R-CNN architecture, four different models were generated based on four different datasets of training and testing images captured at various growth stages. Despite the challenging field imaging conditions, e.g., variable illumination conditions, high spike occlusion, and complex background, the four R-CNN models achieve an average detection accuracy ranging from 88 to 94 % across different sets of test images. The most robust R-CNN model, which achieved the highest accuracy, is then selected to study the variation in spike production over 10 wheat varieties and three treatments. The SPIKE dataset and the trained CNN are the main contributions of this paper.

CONCLUSION

With the availability of good training datasets such us the SPIKE dataset proposed in this article, deep learning techniques can achieve high accuracy in detecting and counting spikes from complex wheat field images. The proposed robust R-CNN model, which has been trained on spike images captured during different growth stages, is optimized for application to a wider variety of field scenarios. It accurately quantifies the differences in yield produced by the 10 varieties we have studied, and their respective responses to fertilizer treatment. We have also observed that the other R-CNN models exhibit more specialized performances. The data set and the R-CNN model, which we make publicly available, have the potential to greatly benefit plant breeders by facilitating the high throughput selection of high yielding varieties.

Reliable and accurate extraction of Hamaker constants from surface force measurements

A simple and accurate closed-form expression for the Hamaker constant that best represents experimental surface force data is presented. Numerical comparisons are made with the current standard least squares approach, which falsely assumes error-free separation measurements, and a nonlinear version assuming independent measurements of force and separation are subject to error. The comparisons demonstrate that not only is the proposed formula easily implemented it is also considerably more accurate. This option is appropriate for any value of Hamaker constant, high or low, and certainly for any interacting system exhibiting an inverse square distance dependent van der Waals force.

Land-based crop phenotyping by image analysis: consistent canopy characterization from inconsistent field illumination

BACKGROUND

One of the main challenges associated with image-based field phenotyping is the variability of illumination. During a single day's imaging session, or between different sessions on different days, the sun moves in and out of cloud cover and has varying intensity. How is one to know from consecutive images alone if a plant has become darker over time, or if the weather conditions have simply changed from clear to overcast? This is a significant problem to address as colour is an important phenotypic trait that can be measured automatically from images.

RESULTS

In this work we use an industry standard colour checker to balance the colour in images within and across every day of a field trial conducted over four months in 2016. By ensuring that the colour checker is present in every image we are afforded a 'ground truth' to correct for varying illumination conditions across images. We employ a least squares approach to fit a quadratic model for correcting RGB values of an image in such a way that the observed values of the colour checker tiles align with their true values after the transformation.

CONCLUSIONS

The proposed method is successful in reducing the error between observed and reference colour chart values in all images. Furthermore, the standard deviation of mean canopy colour across multiple days is reduced significantly after colour correction is applied. Finally, we use a number of examples to demonstrate the usefulness of accurate colour measurements in recording phenotypic traits and analysing variation among varieties and treatments.

Land-based crop phenotyping by image analysis: Accurate estimation of canopy height distributions using stereo images

In this paper we report on an automated procedure to capture and characterize the detailed structure of a crop canopy by means of stereo imaging. We focus attention specifically on the detailed characteristic of canopy height distribution—canopy shoot area as a function of height—which can provide an elaborate picture of canopy growth and health under a given set of conditions. We apply the method to a wheat field trial involving ten Australian wheat varieties that were subjected to two different fertilizer treatments. A novel camera self-calibration approach is proposed which allows the determination of quantitative plant canopy height data (as well as other valuable phenotypic information) by stereo matching. Utilizing the canopy height distribution to provide a measure of canopy height, the results compare favourably with manual measurements of canopy height (resulting in an R² value of 0.92), and are indeed shown to be more consistent. By comparing canopy height distributions of different varieties and different treatments, the methodology shows that different varieties subjected to the same treatment, and the same variety subjected to different treatments can respond in much more distinctive and quantifiable ways within their respective canopies than can be captured by a simple trait measure such as overall canopy height.

Pre-processing by data augmentation for improved ellipse fitting

Ellipse fitting is a highly researched and mature topic. Surprisingly, however, no existing method has thus far considered the data point eccentricity in its ellipse fitting procedure. Here, we introduce the concept of eccentricity of a data point, in analogy with the idea of ellipse eccentricity. We then show empirically that, irrespective of ellipse fitting method used, the root mean square error (RMSE) of a fit increases with the eccentricity of the data point set. The main contribution of the paper is based on the hypothesis that if the data point set were pre-processed to strategically add additional data points in regions of high eccentricity, then the quality of a fit could be improved. Conditional validity of this hypothesis is demonstrated mathematically using a model scenario. Based on this confirmation we propose an algorithm that pre-processes the data so that data points with high eccentricity are replicated. The improvement of ellipse fitting is then demonstrated empirically in real-world application of 3D reconstruction of a plant root system for phenotypic analysis. The degree of improvement for different underlying ellipse fitting methods as a function of data noise level is also analysed. We show that almost every method tested, irrespective of whether it minimizes algebraic error or geometric error, shows improvement in the fit following data augmentation using the proposed pre-processing algorithm.

Estimation of vegetation indices for high-throughput phenotyping of wheat using aerial imaging

BACKGROUND

Unmanned aerial vehicles offer the opportunity for precision agriculture to efficiently monitor agricultural land. A vegetation index (VI) derived from an aerially observed multispectral image (MSI) can quantify crop health, moisture and nutrient content. However, due to the high cost of multispectral sensors, alternate, low-cost solutions have lately received great interest. We present a novel method for model-based estimation of a VI using RGB color images. The non-linear spatio-spectral relationship between the RGB image of vegetation and the index computed by its corresponding MSI is learned through deep neural networks. The learned models can be used to estimate VI of a crop segment.

RESULTS

Analysis of images obtained in wheat breeding trials show that the aerially observed VI was highly correlated with ground-measured VI. In addition, VI estimates based on RGB images were highly correlated with VI deduced from MSIs. Spatial, spectral and temporal information of images contributed to estimation of VI. Both intra-variety and inter-variety differences were preserved by estimated VI. However, VI estimates were reliable until just before significant appearance of senescence.

CONCLUSION

The proposed approach validates that it is reasonable to accurately estimate VI using deep neural networks. The results prove that RGB images contain sufficient information for VI estimation. It demonstrates that low-cost VI measurement is possible with standard RGB cameras.

Convective and diffusive effects on particle transport in asymmetric periodic capillaries

We present here results of a theoretical investigation of particle transport in longitudinally asymmetric but axially symmetric capillaries, allowing for the influence of both diffusion and convection. In this study we have focused attention primarily on characterizing the influence of tube geometry and applied hydraulic pressure on the magnitude, direction and rate of transport of particles in axi-symmetric, saw-tooth shaped tubes. Three initial value problems are considered. The first involves the evolution of a fixed number of particles initially confined to a central wave-section. The second involves the evolution of the same initial state but including an ongoing production of particles in the central wave-section. The third involves the evolution of particles a fully laden tube. Based on a physical model of convective-diffusive transport, assuming an underlying oscillatory fluid velocity field that is unaffected by the presence of the particles, we find that transport rates and even net transport directions depend critically on the design specifics, such as tube geometry, flow rate, initial particle configuration and whether or not particles are continuously introduced. The second transient scenario is qualitatively independent of the details of how particles are generated. In the third scenario there is no net transport. As the study is fundamental in nature, our findings could engender greater understanding of practical systems.

Phenotyping of plants in competitive but controlled environments: a study of drought response in transgenic wheat

In recent years, the interest in new technologies for wheat improvement has increased greatly. To screen genetically modified germplasm in conditions more realistic for a field situation we developed a phenotyping platform where transgenic wheat and barley are grown in competition. In this study, we used the platform to (1) test selected promoter and gene combinations for their capacity to increase drought tolerance, (2) test the function and power of our platform to screen the performance of transgenic plants growing in competition, and (3) develop and test an imaging and analysis process as a means of obtaining additional, non-destructive data on plant growth throughout the whole growth cycle instead of relying solely on destructive sampling at the end of the season. The results showed that several transgenic lines under well watered conditions had higher biomass and/or grain weight than the wild-type control but the advantage was significant in one case only. None of the transgenics seemed to show any grain weight advantage under drought stress and only two lines had a substantially but not significantly higher biomass weight than the wild type. However, their evaluation under drought stress was disadvantaged by their delayed flowering date, which increased the drought stress they experienced in comparison to the wild type. Continuous imaging during the season provided additional and non-destructive phenotyping information on the canopy development of mini-plots in our phenotyping platform. A correlation analysis of daily canopy coverage data with harvest metrics showed that the best predictive value from canopy coverage data for harvest metrics was achieved with observations from around heading/flowering to early ripening whereas early season observations had only a limited diagnostic value. The result that the biomass/leaf development in the early growth phase has little correlation with biomass or grain yield data questions imaging approaches concentrating only on the early development stage.

Detecting spikes of wheat plants using neural networks with Laws texture energy

BACKGROUND

The spike of a cereal plant is the grain-bearing organ whose physical characteristics are proxy measures of grain yield. The ability to detect and characterise spikes from 2D images of cereal plants, such as wheat, therefore provides vital information on tiller number and yield potential.

RESULTS

We have developed a novel spike detection method for wheat plants involving, firstly, an improved colour index method for plant segmentation and, secondly, a neural network-based method using Laws texture energy for spike detection. The spike detection step was further improved by removing noise using an area and height threshold. The evaluation results showed an accuracy of over 80% in identification of spikes. In the proposed method we also measure the area of individual spikes as well as all spikes of individual plants under different experimental conditions. The correlation between the final average grain yield and spike area is also discussed in this paper.

CONCLUSIONS

Our highly accurate yield trait phenotyping method for spike number counting and spike area estimation, is useful and reliable not only for grain yield estimation but also for detecting and quantifying subtle phenotypic variations arising from genetic or environmental differences.

A Comprehensive Biophysical Model of Ion and Water Transport in Plant Roots. I. Clarifying the Roles of Endodermal Barriers in the Salt Stress Response

In this paper, we present a detailed and comprehensive mathematical model of active and passive ion and water transport in plant roots. Two key features are the explicit consideration of the separate, but interconnected, apoplastic, and symplastic transport pathways for ions and water, and the inclusion of both active and passive ion transport mechanisms. The model is used to investigate the respective roles of the endodermal Casparian strip and suberin lamellae in the salt stress response of plant roots. While it is thought that these barriers influence different transport pathways, it has proven difficult to distinguish their separate functions experimentally. In particular, the specific role of the suberin lamellae has been unclear. A key finding based on our simulations was that the Casparian strip is essential in preventing excessive uptake of Na⁺ into the plant via apoplastic bypass, with a barrier efficiency that is reflected by a sharp gradient in the steady-state radial distribution of apoplastic Na⁺ across the barrier. Even more significantly, this function cannot be replaced by the action of membrane transporters. The simulations also demonstrated that the positive effect of the Casparian strip of controlling Na⁺ uptake, was somewhat offset by its contribution to the osmotic stress component: a more effective barrier increased the detrimental osmotic stress effect. In contrast, the suberin lamellae were found to play a relatively minor, even non-essential, role in the overall response to salt stress, with the presence of the suberin lamellae resulting in only a slight reduction in Na⁺ uptake. However, perhaps more significantly, the simulations identified a possible role of suberin lamellae in reducing plant energy requirements by acting as a physical barrier to preventing the passive leakage of Na⁺ into endodermal cells. The model results suggest that more and particular experimental attention should be paid to the properties of the Casparian strip when assessing the salt tolerance of different plant varieties and species. Indeed, the Casparian strip appears to be a more promising target for plant breeding and plant genetic engineering efforts than the suberin lamellae for the goal of improving salt tolerance.

A Hybrid Approach for Improving Image Segmentation: Application to Phenotyping of Wheat Leaves

In this article we propose a novel tool that takes an initial segmented image and returns a more accurate segmentation that accurately captures sharp features such as leaf tips, twists and axils. Our algorithm utilizes basic a-priori information about the shape of plant leaves and local image orientations to fit active contour models to important plant features that have been missed during the initial segmentation. We compare the performance of our approach with three state-of-the-art segmentation techniques, using three error metrics. The results show that leaf tips are detected with roughly one half of the original error, segmentation accuracy is almost always improved and more than half of the leaf breakages are corrected.

Obtaining T1-T2 distribution functions from 1-dimensional T1 and T2 measurements: The pseudo 2-D relaxation model

We present the pseudo 2-D relaxation model (P2DRM), a method to estimate multidimensional probability distributions of material parameters from independent 1-D measurements. We illustrate its use on 1-D T1 and T2 relaxation measurements of saturated rock and evaluate it on both simulated and experimental T1-T2 correlation measurement data sets. Results were in excellent agreement with the actual, known 2-D distribution in the case of the simulated data set. In both the simulated and experimental case, the functional relationships between T1 and T2 were in good agreement with the T1-T2 correlation maps from the 2-D inverse Laplace transform of the full 2-D data sets. When a 1-D CPMG experiment is combined with a rapid T1 measurement, the P2DRM provides a double-shot method for obtaining a T1-T2 relationship, with significantly decreased experimental time in comparison to the full T1-T2 correlation measurement.

Quantifying the Onset and Progression of Plant Senescence by Color Image Analysis for High Throughput Applications

Leaf senescence, an indicator of plant age and ill health, is an important phenotypic trait for the assessment of a plant's response to stress. Manual inspection of senescence, however, is time consuming, inaccurate and subjective. In this paper we propose an objective evaluation of plant senescence by color image analysis for use in a high throughput plant phenotyping pipeline. As high throughput phenotyping platforms are designed to capture whole-of-plant features, camera lenses and camera settings are inappropriate for the capture of fine detail. Specifically, plant colors in images may not represent true plant colors, leading to errors in senescence estimation. Our algorithm features a color distortion correction and image restoration step prior to a senescence analysis. We apply our algorithm to two time series of images of wheat and chickpea plants to quantify the onset and progression of senescence. We compare our results with senescence scores resulting from manual inspection. We demonstrate that our procedure is able to process images in an automated way for an accurate estimation of plant senescence even from color distorted and blurred images obtained under high throughput conditions.

Modeling Root Zone Effects on Preferred Pathways for the Passive Transport of Ions and Water in Plant Roots

We extend a model of ion and water transport through a root to describe transport along and through a root exhibiting a complexity of differentiation zones. Attention is focused on convective and diffusive transport, both radially and longitudinally, through different root tissue types (radial differentiation) and root developmental zones (longitudinal differentiation). Model transport parameters are selected to mimic the relative abilities of the different tissues and developmental zones to transport water and ions. For each transport scenario in this extensive simulations study, we quantify the optimal 3D flow path taken by water and ions, in response to internal barriers such as the Casparian strip and suberin lamellae. We present and discuss both transient and steady state results of ion concentrations as well as ion and water fluxes. We find that the peak in passive uptake of ions and water occurs at the start of the differentiation zone. In addition, our results show that the level of transpiration has a significant impact on the distribution of ions within the root as well as the rate of ion and water uptake in the differentiation zone, while not impacting on transport in the elongation zone. From our model results we infer information about the active transport of ions in the different developmental zones. In particular, our results suggest that any uptake measured in the elongation zone under steady state conditions is likely to be due to active transport.

RootGraph: a graphic optimization tool for automated image analysis of plant roots

This paper outlines a numerical scheme for accurate, detailed, and high-throughput image analysis of plant roots. In contrast to existing root image analysis tools that focus on root system-average traits, a novel, fully automated and robust approach for the detailed characterization of root traits, based on a graph optimization process is presented. The scheme, firstly, distinguishes primary roots from lateral roots and, secondly, quantifies a broad spectrum of root traits for each identified primary and lateral root. Thirdly, it associates lateral roots and their properties with the specific primary root from which the laterals emerge. The performance of this approach was evaluated through comparisons with other automated and semi-automated software solutions as well as against results based on manual measurements. The comparisons and subsequent application of the algorithm to an array of experimental data demonstrate that this method outperforms existing methods in terms of accuracy, robustness, and the ability to process root images under high-throughput conditions.

RootAnalyzer: A Cross-Section Image Analysis Tool for Automated Characterization of Root Cells and Tissues

The morphology of plant root anatomical features is a key factor in effective water and nutrient uptake. Existing techniques for phenotyping root anatomical traits are often based on manual or semi-automatic segmentation and annotation of microscopic images of root cross sections. In this article, we propose a fully automated tool, hereinafter referred to as RootAnalyzer, for efficiently extracting and analyzing anatomical traits from root-cross section images. Using a range of image processing techniques such as local thresholding and nearest neighbor identification, RootAnalyzer segments the plant root from the image's background, classifies and characterizes the cortex, stele, endodermis and epidermis, and subsequently produces statistics about the morphological properties of the root cells and tissues. We use RootAnalyzer to analyze 15 images of wheat plants and one maize plant image and evaluate its performance against manually-obtained ground truth data. The comparison shows that RootAnalyzer can fully characterize most root tissue regions with over 90% accuracy.

A complete system for 3D reconstruction of roots for phenotypic analysis

Here we present a complete system for 3D reconstruction of roots grown in a transparent gel medium or washed and suspended in water. The system is capable of being fully automated as it is self calibrating. The system starts with detection of root tips in root images from an image sequence generated by a turntable motion. Root tips are detected using the statistics of Zernike moments on image patches centred on high curvature points on root boundary and Bayes classification rule. The detected root tips are tracked in the image sequence using a multi-target tracking algorithm. Conics are fitted to the root tip trajectories using a novel ellipse fitting algorithm which weighs the data points by its eccentricity. The conics projected from the circular trajectory have a complex conjugate intersection which are image of the circular points. Circular points constraint the image of the absolute conics which are directly related to the internal parameters of the camera. The pose of the camera is computed from the image of the rotation axis and the horizon. The silhouettes of the roots and camera parameters are used to reconstruction the 3D voxel model of the roots. We show the results of real 3D reconstruction of roots which are detailed and realistic for phenotypic analysis.

Polyethyleneimine for copper absorption II: kinetics, selectivity and efficiency from seawater

Nano-thin coatings of glutaraldehyde cross-linked polyethyleneimine effectively and selectively accumulated copper from natural seawater.

Landmark-free statistical analysis of the shape of plant leaves

The shapes of plant leaves are important features to biologists, as they can help in distinguishing plant species, measuring their health, analyzing their growth patterns, and understanding relations between various species. Most of the methods that have been developed in the past focus on comparing the shape of individual leaves using either descriptors or finite sets of landmarks. However, descriptor-based representations are not invertible and thus it is often hard to map descriptor variability into shape variability. On the other hand, landmark-based techniques require automatic detection and registration of the landmarks, which is very challenging in the case of plant leaves that exhibit high variability within and across species. In this paper, we propose a statistical model based on the Squared Root Velocity Function (SRVF) representation and the Riemannian elastic metric of Srivastava et al. (2011) to model the observed continuous variability in the shape of plant leaves. We treat plant species as random variables on a non-linear shape manifold and thus statistical summaries, such as means and covariances, can be computed. One can then study the principal modes of variations and characterize the observed shapes using probability density models, such as Gaussians or Mixture of Gaussians. We demonstrate the usage of such statistical model for (1) efficient classification of individual leaves, (2) the exploration of the space of plant leaf shapes, which is important in the study of population-specific variations, and (3) comparing entire plant species, which is fundamental to the study of evolutionary relationships in plants. Our approach does not require descriptors or landmarks but automatically solves for the optimal registration that aligns a pair of shapes. We evaluate the performance of the proposed framework on publicly available benchmarks such as the Flavia, the Swedish, and the ImageCLEF2011 plant leaf datasets.

Mathematically modelling competitive ion absorption in a polymer matrix

In the competition for ion absorption in PEI, the short-term win by faster diffusing zinc is overshadowed by long-term win by slower copper due to more stable binding resulting from conformational changes in PEI.

On the competitive uptake and transport of ions through differentiated root tissues

We simulate the competitive uptake and transport of a mixed salt system in the differentiated tissues of plant roots. The results are based on a physical model that includes both forced diffusion and convection by the transpiration stream. The influence of the Casparian strip on regulating apoplastic flow, the focus of the paper, is modelled by varying ion diffusive permeabilities, hydraulic reflection coefficients and water permeability for transport across the endodermis-pericycle interface. We find that reducing diffusive permeabilities leads to significantly altered ion concentration profiles in the pericycle and vascular cylinder regions, while increased convective reflectivities affect predominantly ion concentrations in the cortex and endodermis tissues. The self-consistent electric field arising from ion separation is a major influence on predicted ion fluxes and accumulation rates.

Mathematical modelling of the uptake and transport of salt in plant roots

In this paper, we present and discuss a mathematical model of ion uptake and transport in roots of plants. The underlying physical model of transport is based on the mechanisms of forced diffusion and convection. The model can take account of local variations in effective ion and water permeabilities across the major tissue regions of plant roots, represented through a discretized coupled system of governing equations including mass balance, forced diffusion, convection and electric potential. We present simulation results of an exploration of the consequent enormous parameter space. Among our findings we identify the electric potential as a major factor affecting ion transport across, and accumulation in, root tissues. We also find that under conditions of a constant but realistic level of bulk soil salt concentration and plant-soil hydraulic pressure, diffusion plays a significant role even when convection by the water transpiration stream is operating.

The actual dielectric response function for a colloidal suspension of spherical particles

In this paper, we present a theoretical analysis of the dielectric response of a dense suspension of spherical colloidal particles based on a self-consistent cell model. Particular attention is paid to (a) the relationship between the dielectric response and the conductivity response and (b) the connection between the real and imaginary parts of these responses based on the Kramers-Kronig relations. We have thus clarified the analysis of Carrique et al. (Carrique, F.; Criado, C.; Delgado, A. V. J. Colloid Interface Sci. 1993, 156, 117). We have shown that both the conduction and displacement current components are complex quantities with both real and imaginary parts being frequency dependent. The dielectric response exhibits characteristics of two relaxation phenomena: the Maxwell-Wagner and the alpha-relaxations, with the imaginary part being the more sensitive instrument. The inverse Fourier transform of the simulated dielectric response is compared with a phenomenological, two-exponential response function with good agreement obtained. The two fitted decay times also compare well with times extracted from the explicit simulations.

High-frequency behavior of the dynamic mobility and dielectric response of concentrated colloidal dispersions

A matched asymptotic analysis of the system of equations governing the electrokinetic cell model of ref 4 (Ahualli, S.; Delgado, A.; Miklavcic, S.; White, L. R. Langmuir 2006, 22, 7041) is performed. Asymptotic expressions are obtained for the dynamic mobility and complex conductivity response of a dense suspension of charged spherical particles to an applied electric field. The asymptotic expressions are compared with full numerical calculations of the linear response functions as a function of surface (zeta) potential, electrolyte strength, and particle density. We find that the numerical procedure used is robust and highly accurate at a very high frequency under a wide range of double-layer conditions. The asymptotic form for the dielectric response of the system is accurate to megahertz frequencies. The asymptotic formulas for the other response functions have limited viability as predictive tools within the current range of experimentally accessible frequencies but are useful as checks on numerical calculations.

Dynamic dielectric response of concentrated colloidal dispersions: comparison between theory and experiment

The cell-model electrokinetic theory of Ahualli et al. Langmuir 2006, 22, 7041; Ahualli et al. J. Colloid Interface Sci. 2007, 309, 342; and Bradshaw-Hajek et al. Langmuir 2008, 24, 4512 is applied to a dense suspension of charged spherical particles, to exhibit the system's dielectric response to an applied electric field as a function of solids volume fraction. The model's predictions of effective permittivity and complex conductivity are favorably compared with published theoretical calculations and experimental measurements on dense colloidal systems. Physical factors governing the volume fraction dependence of the dielectric response are discussed.

Frequency-dependent electrical conductivity of concentrated dispersions of spherical colloidal particles

This paper outlines the application of a self-consistent cell-model theory of electrokinetics to the problem of determining the electrical conductivity of a dense suspension of spherical colloidal particles. Numerical solutions of the standard electrokinetic equations, subject to self-consistent boundary conditions, are implemented in formulas for the electrical conductivity appropriate to the particle-averaged cell model of the suspension. Results of calculations as a function of frequency, zeta potential, volume fraction, and electrolyte composition, are presented and discussed.

Use of a cell model for the evaluation of the dynamic mobility of spherical silica suspensions

In this paper we evaluate the validity of a cell model for the calculation of the dynamic mobility of concentrated suspensions of spheres. The key point is the consideration of the boundary conditions (electrical and hydrodynamic) at the boundary of the fluid cell surrounding a single probe particle. The model proposed is based on a universal criterion for the averages of fluid velocity, electric potential, pressure field or electrochemical properties in the cell. The calculations are checked against a wide set of experimental data on the dynamic mobility of silica suspensions with two different radii, several ionic strengths, and two particle concentrations. The comparison reveals an excellent agreement between theory and experiment, and the model appears to be extremely suitable for correctly predicting the behavior of the dynamic mobility, including the changes in the zeta potential, zeta, with ionic strength, the frequency and amplitude of the Maxwell-Wagner-O'Konski relaxation, and the inertial relaxation occurring at the top of the frequency range accessible to our experimental device.

Electrostatic potential and double layer force in a semiconductor-electrolyte-semiconductor heterojunction

This paper reports a theoretical study of the electrostatic potential within a so-called pen-heterojunction made up of two semi-infinite, doped semiconductor media separated by an electrolyte region. An external potential is then applied across the entire system. Both the electrostatic potentials and double layer surface forces are studied as functions of the usual double layer system properties, semiconductor properties such as doping concentrations of acceptor and donator atoms, as well as applied potential. We find that both attractive and repulsive forces are possible depending on the surface charges on the electrolyte-semiconductor interfaces, and that these forces can be significantly modified by the applied potential and by the doping levels in the semiconductors.

Dynamic electrophoretic mobility of concentrated dispersions of spherical colloidal particles. On the consistent use of the cell model

This paper outlines a complete and self-consistent cell model theory of the electrokinetics of dense spherical colloidal suspensions for general electrolyte composition, frequency of applied field, zeta potential, and particle size. The standard electrokinetic equations, first introduced for any given particle configuration, are made tractable to computation by averaging over particle configurations. The focus of this paper is on the systematic development of suitable boundary conditions at the outer cell boundary obtained from global constraints on the suspension. The approach is discussed in relation to previously published boundary conditions that have often been introduced in an ad hoc manner. Results of a robust numerical calculation of high-frequency colloidal transport properties, such as dynamic mobility, using the present model are presented and compared with some existing dense suspension models.

Stable van der Waals-induced deformations of the air-water interface. Theoretical predictions and a suggestion for an experiment

This article concerns the stability of the air-water interface subjected to a 2D attractive van der Waals stress. The physical problem models the setup of a Wilhelmy plate experiment prior to three-phase contact line formation. We present and employ an unambiguous condition to quantify the stability limit in terms of the distance of closest approach of a solid cylindrical plate of parabolic cross section to the fluid surface as a function of the strength of the van der Waals surface force and plate geometry. A numerical study spanning 4 orders of magnitude of the Hamaker constant and nearly 6 orders of magnitude of solid geometry characterizes the dependence of the stability limit on these physical parameters. Comparisons are also made with a previously published analytical condition guaranteeing a stable deformation of the fluid interface. A possible experiment for testing the theory is also described. Used together with the theory, the technique could be used as an independent means of determining system properties such as the surface tension or Hamaker constant.