The advent of next-generation sequenc20170028ing technology has had a major impact on genomics, and the genomic analysis has become routine for most agricultural crop species [1], [2], [3], [4]. Due to the increased availability of high-throughput genotyping platforms, there are many economically important crop varieties that have since been sequenced and annotated. It has significantly contributed to the increase in agricultural productivity. However, satisfying the demand of a growing world population still presents a tremendous challenge for crop improvement [5]. Although genomics techniques have been advancing rapidly, conventional plant phenotyping lags far behind compared to current genotyping systems. To relieve this bottleneck, various research institutes have been established or many plant research laboratories are planning to establish their own phenotyping system. They employ robotics, automation and use various imaging techniques [6], [7], [8], [9], [10]. This advanced phenotyping aims at a quantification of photosynthesis, development, architecture, growth or biomass productivity of single plants by accelerating plant breeding programs [10], [11]. Automated, high-throughput phenotyping facilities have enabled to grow hundreds to thousands of plants maintained in a controlled environment and automatically photographed each day from the standard position. This image data is analysed via image analysis algorithm and software to extract phenotypic traits.

To characterize plant architecture and performance, image analysis methods have become more popular. This method has the capacity to measure many dynamically morphological and physiological traits of a given individual [12]. Plant phenotyping is the quantitative or qualitative study of these traits at any organizational level, in a particular genomic expression state and environment [13]. Generally, plant phenotypic traits of interest can be classified as physiological, structural, or performance-related. Performance-related traits are defined by the complex traits (such as shoot fresh/dry weight, yield) which eventually determine plant performance in terms of biomass and yield. Plant biomass is a vital trait in the study of functional plant biology and growth analysis. Second, repeated measurements of plant biomass are the source for the calculation of growth rates and net primary production [14], [15]. Thus, plant biomass analysis is a basis for unraveling a number of complex questions of plant growth, development and response to the environment.

There are several techniques to measure plant biomass depending on the available budget, required accuracy, structure and composition of the vegetation, and also numerous disciplines of plant biology [16], [17]. However, it is difficult to make a generally applicable statement regarding the best technique for biomass estimation. The standard method for biomass determination of individual plant is defined to measure shoot fresh (SFW) biomass or the oven-dried shoot dry (SDW) biomass [14], [18]. For the dry shoot biomass, the plant is harvested and oven-dried at the end of the experiment. It is considered one of the widely acceptable measures for studying the biomass of an individual plant [17]. These customary plant biomass measuring methods are destructive. Consequently, they require many individuals to be cultivated for repeated measurements that are labor-intensive and time-consuming. Imaging-based phenotyping has enabled the non-destructive assessment of plant responses to the environment over time, and allows determination of plant biomass without having to harvest the whole plant [19], [20], [21], [22].

A non-destructive method based on digital image analysis addresses not only above-ground fresh and oven-dried biomass. It has also been applied for estimating above-ground forest and canopy biomass for remote sensing, satellite, and airborne images [23], [24], [25], [26], [27], [28], [29], [30], [31], [32]. For that reason, imaging techniques are now the most commonly used method for estimating biomass in ecology and agriculture.

A number of linear and non-linear functions are used to model biomass accumulations [15], [17], [32], [33], [34], [35]. However, non-linear models are complicated due to the fact that higher order model coefficients are insignificant [17]. The models predominantly cited in literature to estimate the biomass of a plant were generated by destructively measured parameters as response variables, and parameters derived from image analysis as predictor variables [15], [17], [34].

Several image-based biomass studies considered linear methods for estimating the biomass as a linear function of plant area [17], [36] which perform better than non-linear models, such as quadratic, cubic and power methods [15], [17], [27]. However, the estimation error from this model is large, prohibiting accurate estimation of the biomass of plants. Color pixel-based traits and a mixed variable (area × days) were also used in the image-based biomass model as predictor variables, where the response variable SDW was destructively measured [15], [17]. For the accurate inference of biomass and to bridge the genotype to phenotype gap, it is crucial to recognize more significant traits, particularly for the stressed plants. Plant compactness is an important phenotypic trait that reflects plant density and architecture [9]. Thus, there is a need to develop such a method for estimating biomass that takes into consideration plant compactness as well. Although, Yang et al. [9] used biomass models by considering plant compactness; however, the response variable of those models was destructively measured.

The objective of the present study is to develop a generalized linear model to estimate accurate plant biomass without using destructively measured parameters. We attempt to develop a linear biomass estimation model to estimate plant biomass based on image-derived phenotypic traits. We have demonstrated our model that uses mixed variables of plant area and their age and plant compactness, which significantly reduces estimation errors. This model can be used to acquire more insights by accurately estimating the plant biomass using the non-destructive approach from high-throughput phenotype images.

A schematic workflow for development of the biomass model based on high-throughput plant imaging is shown in Figure 1. It shows the image-based biomass model construction steps ranging from the experiment to the model to be developed.

We have considered a linear model

(1)\documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document}$${D_b} = {a_0} + {a_1} \times A + {e_0}$$\end{document}Db=a0+a1×A+e0

where we defined D_b as digital volume (response variable), A as projected shoot area (predictor variable), a₀ as model intercept, a₁ as model coefficient and e₀ as model error. The biomass estimation error of this model is large, unable to explain observed variances, and moreover there is a big difference between actual and estimated biomass. To improve the model [1], Golzarian et al. [17] proposed a linear predictive model based on the concept of plant specific weight (PSW), defined as the plant weight per total projected shoot area.

We have generalized this linear biomass model based on plant compactness. This phenotypic trait provides meaningful information on plant architecture in addition to the commonly recognized agronomic traits such as plant height, tiller number and green leaf area [9]. This is the reason why we chose plant compactness as a predictor to improve the biomass model. Plant compactness was calculated as the square of plant border length divided by the projected side or top area [39].

We extended equation (1) by including trait (predictor) plant compactness, compactness × days, and area × days. Then the associated equations with our proposed predictive biomass models can be written as,

\documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document}$${\text{Model 1: }}{D_b}{\rm{ = }}{a_{\rm{0}}}{\rm{ + }}{a_{\rm{1}}}{\rm{ \times }}A{\rm{ + }}{a_{\rm{2}}}{\rm{ \times PC + }}{e_{\rm{0}}}$$\end{document}Model 1: Db=a0+a1×A+a2×PC+e0

\documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document}$${\text{Model 2: }}{D_b}{\rm{ = }}{a_{\rm{0}}}{\rm{ + }}{a_{\rm{1}}}{\rm{ \times }}A{\rm{ + }}{a_{\rm{2}}}{\rm{ \times PC}} \times \text{HD}{\rm{ + }}{e_{\rm{0}}}$$\end{document}Model 2: Db=a0+a1×A+a2×PC×HD+e0

\documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document}$${\text{Model 3: }}{D_b}{\rm{ = }}{a_{\rm{0}}}{\rm{ + }}{a_{\rm{1}}}{\rm{ \times }}A{\rm{ + }}{a_{\rm{2}}}{\rm{ \times }}A{\rm{ \times }}\text{HD} + {a_3} \times {\rm{PC + }}{e_{\rm{0}}}$$\end{document}Model 3: Db=a0+a1×A+a2×A×HD+a3×PC+e0

Where PC and HD are plant compactness and plant age in days after planting, respectively.

The performance of these models was assessed through five-fold cross-validation technique [9], [17]. For comparison of model fitting and model superiority, we used the following model assessment criteria:

The models in this study were developed using a barley plant phenotype data set collected in the experiment explained earlier. We constructed three models, where digital volume is a function of inputs of area and compactness; area and compactness × HD; and area, area × HD and compactness. The coefficients of each model were estimated using regression analysis. All of these coefficients contribute significantly to the predicted value of digital biomass (Table 1). The average PCC, R², and RMSRE with standard error (SE) of two treatment categories are given in Table 2.

According to Table 2, Model 1 and Model 2 provide almost the same resulting PCC (0.97 ± 0.0001) and R² (0.94 ± 0.0001) value, and the PCC and R² value of Model 3 is 0.99 ± 0.0001 and 0.98 ± 0.0001 for control data set on average. For the stress dataset resulting values, Model 1 provides the PCC (0.98 ± 0.0002) and R² (0.96 ± 0.0004), Model 2 provides the PCC (0.97 ± 0.0002) and R² (0.94 ± 0.0004) and Model 3 provides the PCC (0.99 ± 0.0002) and R² (0.98 ± 0.0004). The estimation error (RMSRE) of Model 2 is 0.0067 ± 0.0003, where Model 1 and Model 2 RMSRE are 0.0061 ± 0.0003 for the control dataset. In stress datasets, Model 3 produces smaller RMSRE (0.0064 ± 0.0006) than Model 1 and Model 2 (Table 2).

Among these three proposed models, Model 3 performed better, when area, area × HD and compactness are considered as predictors in the biomass model. However, we found that Model 1 and Model 2 provide almost similar results, but still less superior than Model 3 according to the estimation error. Therefore, we propose to use Model 3, which looks like an integrated biomass model of Yang et al. [9] and Golzarian et al. [17] for digital biomass estimation.

Plant growth and development studies demonstrated that automated digital imaging is a powerful tool to relieve the plant phenotyping bottleneck [2], [9], [22], [35], [46], [47], [48], [49], [50]. Plant reveal complex phenotypic traits, and thus the main challenge is to analyze and model phenotypic traits that bridge the genotype-phenotype gap [22], [51].

In the emerging period of plant phenomics there is a need to improve existing methods or develop new ones to resolve this analytical bottleneck [10], [12], [35], [52]. It has been realized that estimation of plant biomass is important from phenotype images of cereal plants. Therefore, a practical analysis framework or approach for the estimation of biomass using image-derived traits is needed. Image-based biomass estimation methods developed so far include total harvesting of plants or harvesting sample during measurement SFW and SDW as well [15], [17].

We proposed a framework to estimate plant biomass in terms of digital image analysis. Since, most protocols of the traditional methods for biomass determination of individual plants are destructive [9], [14], [15], [17], [18]. There are difficulties with that method in measuring dynamic responses of plant growth under environment, and to collect seed from the individuals being measured [21]. We designed image-based non-destructive approach which allows determination of biomass without harvesting the whole plant.

We have used the digital volume which is highly correlated with destructively measured plant complex traits [9], [21], [22], [35]. Based on a proof of concept from the recent non-destructive biomass study, we constructed a linear model for biomass determination [21], [22], [34], [35]. For digital biomass prediction, the noticeable improvement was achieved by adding plant compactness into the model. It has significantly reduced bias in biomass estimation of cereal plants, which is the major reason of the estimation error. By contrast, other biomass estimation models resulted in large estimation error. From the analysis of results, we found that plant compactness has a good impact on digital biomass prediction.

The digital biomass predicted using our proposed model is highly correlated with the real biomass (SFW/SDW). Comparing our proposed model with the existing models, it is evident that the analyzed results confirmed the proposed model which performed well in all cases, and the model improvement is consistent and significant.

Overall, analysis results confirmed the idea that the plant compactness, which was used as an additional input for the proposed model, plays a significant role in reducing the error for estimating digital biomass. Our proposed approach provides a practical method for estimating digital biomass as a substitute method for the conventional methods. Finally, the proposed model performed better than a conventional model with smaller prediction errors. The overall performance of the new model was superior to that of the traditional model, and there were significant differences between the traditional and new model during digital biomass analysis.

In this study, we focus on a method for the accurate inference of digital biomass from high-throughput phenotype images. Our proposed model employs information obtained from image-derived traits of plants and their age. It enables the high-throughput non-destructive estimation of biomass for cereal plants regardless of whether or not plants are stressed. The method has been tested using imaged barley data sets under drought stress treatment. Comparing the obtained results from our model with the results of the existing models, we conclude that the proposed model in most cases performs better than the existing ones. The obtained results based on the presented approach demonstrated that the proposed biomass model is robust and accurate. This would be useful to advance our views for the accurate estimation of digital biomass in high-throughput image analysis.