We used the model ArchiSimple, which was shown to allow the generation of a large diversity of root systems with a minimal amount of parameters (Pagès et al., 2013). To produce a large library of root systems, we ran the model 10,000 times, each time with a random set of parameters (Figure 2A). For each simulation, the growth and development of the root system were constrained in two dimensions.

The simulations were divided into two main groups: fibrous and tap-rooted. For the fibrous simulations, the model generated a random number of root axes and secondary (radial) growth was disabled. For tap-root simulations, only one root axis was produced and secondary growth was enabled (the extent of which was determined by a random parameter).

The root system created in each simulation was stored in a Root System Markup Language (RSML) file. Each RSML file was then read by the RSML Reader plugin from ImageJ to extract ground-truth data for the library (Lobet et al., 2015). These ground-truth data included geometrical and morphological parameters (Table 1). For each RSML data file, the RSML Reader plugin also created three JPEG images (at a resolution of 300 DPI) for each root system. To simulate one type of image degradation, we added different levels of noise to the images (using the Salt and Pepper Filter in ImageJ) (Figure 2D). For each root system, we computed overlapping index as the number of root segments having an overlap with other root segments over the total number of root segments.

Each generated image was analyzed using a custom-made ImageJ plugin, Root Image Analysis-J (or RIA-J). For each image, we extracted a set of classical root image descriptors, such as the total root length, the projected area, and the number of visible root tips (Figure 2E). In addition, we included shape descriptors such as the convex-hull area or the exploration ratio (see Supplemental File 1 for details of RIA-J). The list of traits and algorithms used by our pipeline is listed in Table 2. Distribution of the different descriptors is given in the Supplemental Figure 2.

Data analysis was performed in R (R Core Team)¹. Plots were created using ggplot2 (Wickham, 2009) and lattice (Sarkar, 2008).

The Mean Relative Errors (MRE) were estimated using the equation:

where n is the number of observations, y¯i is the ground-truth and y_i is the estimated ground-truth.

A random forest is a state-of-the-art machine learning algorithm typically used for making new predictions (in both classification and regression tasks). Random Forests can perform non-linear predictions and, thus, often outperform linear models. Since its introduction by Breiman (2001), Random Forests have been widely used in many fields from gene regulatory network inference to generic image classification (Huynh-Thu et al., 2013; Marée et al., 2016). Random Forest relies on growing a multitude of decision trees, a prediction algorithm that has shown good performances by itself but, when combined with other decision trees (hence the name forest), returns predictions that are much more robust to outliers and noisy data (see bootstrap aggregating, Breiman, 1996).

In a machine learning setting one is given a set D = {(x₁, y₁), (x₂, y₂), …, (x_n, y_n)},

where xi=(xi1,xi2…,xis) is an element of a s−dimensional feature space X,

and yi=(yi1,yi2,…,yit) an element of a t−dimensional response space Y.

The learning task is to find a model

that predicts the data in a good way, where goodness is measured with regard to an error function L.

A decision tree T_D is a machine learning method that, for a dataset D, constructs a binary tree with each node representing a binary question and each leaf a value of the response space. In other words, a prediction can be made from an input value by looking at the set of binary questions that leads to a leaf (e.g., is the first-order root bigger than q1 and if yes is the number of second-order roots smaller than q2 and if no, …).

Each decision is based upon exactly one feature and is used for deciding which branch of the tree a given input value must take. Hence a decision tree splits successively the set D into smaller subsets and assigns them a value y_i = T_D(x_i) of the response space.

The choice of the feature used for splitting depends on a relevance criterion. In our setting, the default relevance criterion from the randomForest R package (CRAN randomForest, 2015), namely the Gini index, has been used.

A Random Forest

consists of l decision trees T_{D, k}, where several key parameters such as the feature space, are chosen randomly (hence the word Random in the algorithm name). While using a random subspace strongly accelerates the growth of a single tree, it can also decrease its accuracy. However, the use of large number of trees counterbalance advantageously those two effects. The final prediction for each input value x_i corresponds to the majority vote of all the decision trees of the forest T_{D, k}(x_i) in a classification setting while an average of all predicted values is used in a regression task.

All data used in this paper (including the image and RSML libraries) are available at the address http://doi.org/10.5281/zenodo.208214

An archived version of the codes used in this paper is available at the address http://doi.org/10.5281/zenodo.208499

An archived version of the machine learning framework is available at the address https://github.com/FaustFrankenstein/RandomForestFramework/releases/tag/v1.0

We combined existing tools into a single pipeline to produce a large library of ground-truth root system images. The pipeline combines a root model (ArchiSimple, Pagès et al., 2013), the Root System Markup Language (RSML) and the RSML Reader plugin from ImageJ (Lobet et al., 2015). In short, ArchiSimple was used to create a large number of root systems, based on random input parameter sets. Each output was stored as an RSML file (Figure 2A), which was then used by the RSML Reader plugin to create a graphical representation of the root system (as a. jpeg file) and a ground-truth dataset (Figure 2B). Details about the different steps are presented in the Materials and Methods section.

We used the pipeline to create a library of 10,000 root system images, separated into fibrous (multiple first order roots and no secondary growth) and tap-root systems (one first order root and secondary growth). The ranges of the different ground-truth data are shown in Table 3 and their distribution is shown in the Supplemental Figure 1.

We started by evaluating whether fibrous and tap-root systems should be separated during the analysis. We performed a Principal Component Analysis on the ground-truth dataset to reduce its dimensionality and assess if the type grouping influenced the overall dataset structure (Figure 3A). Fibrous and tap-root systems formed distinct groups (MANOVA p < 0.001), with limited overlap. The first principal component, which represented 30.9% of the variation within the dataset, was mostly influenced by the number of first-order axes. The second principal component (19.1% of the variation) was influenced, in part, by the root diameters. These two effects were consistent with the clear root system type grouping, since they expressed the main difference between the two groups of root-system types. Therefore, since the type grouping had such a strong effect on the overall structure, we decided to separate them for the following analyses.

To demonstrate the utility of a synthetic library of ground-truth root systems, we analyzed every image of the library using a custom-built root image analysis tool, RIA-J. We decided to do so since our purpose was to test the usefulness of the synthetic analysis and not to assess the accuracy of existing tools. Nonetheless, RIA-J was designed using known and published algorithms, often used in root system quantification. A detailed description of RIA-J can be found in the Materials and Methods section and Supplemental File 1.

We extracted 10 descriptors from each root system image (Table 2) and compared them with the ground-truth data. For each pair of descriptor-data, we performed a linear regression and computed its r-squared value. Different types of information are highlighted in Figure 4. First, using a ground-truth image library allows for a quick and systematic analysis of all the descriptors extracted by the image analysis pipeline. Second, it allows researchers to identify which traits can be accurately evaluated (or not) and by which descriptors. Third, for some ground-truth data, such as the mean length of second order roots or the number of first order roots, it shows that none of the classical descriptors gave a good estimation (Figure 4, highlighted with arrows). Finally, the figure highlights that some correlations were different for fibrous- and tap-root systems. As an example, the correlation found between the mean_2+_order_diameter and diam_mean estimators was better for fibrous roots than within the tap-root dataset. Consequently, validation of the different image analysis algorithms should be performed, at least, for each group. An algorithm giving good results for a fibrous root system might fail when applied to tap-rooted ones.

In addition to being related to the species of study, estimation errors are likely to increase with the root system size. As the root system grows and develops, the number of crossing and overlapping segments increases (Figure 5A), making the subsequent image analysis potentially more difficult and prone to error. However, a systematic analysis of such error is seldom performed.

Estimation errors are also likely to increase as the image quality decreases. Here we artificially added one type of noise (random “salt and pepper” particles) to the images, with two intensity levels. It should be noted that virtually any type of image degradation could be added to the original images using custom image filters (e.g., using ImageJ). Different types of degradation are expected to generate different levels of estimation errors.

Figure 5 shows the relationship between the ground-truth and descriptor values for three parameters: the total root length (Figure 5B), the number of roots (Figure 5C), and the root system depth (Figure 5D). For each of these variables, we quantified the Mean Relative Error (see Materials and Methods for details) as a function of the overlap index. This was done for three levels of noise added to the images (“null,” “medium,” and “high”). We can observe that for the estimation of both the total root length and the number of lateral roots, the Mean Relative Error increased with the size of the root system (Figures 5B–C). As stated above, such increase of the error was somehow expected with increasing complexity. Moreover, depending on the metric of interest, such as the number of root tips, low image quality can result in high level of error. For other traits, such as the root system depth, no errors were expected (depth is supposedly an error-less variable) and the Mean Relative Error was close to 0 whatever the size of the root system and image quality.

The results presented here are tightly dependent on the specific algorithms used for image analysis and hence might be different for other published tools. However, they are a call for caution when analyzing root images: unexpected errors in ground-truth estimation can arise. Our image library can be used to better identify the errors generated by other analysis tools, current or future.

To improve the calibration and validation of future root image analysis tools, we propose the following procedure:

Develop the new root image analysis pipeline;

The main advantage of creating a synthetic library is to generate paired datasets of image descriptors and their corresponding ground-truth values. Having information on both can, in theory, be used to either calibrate the image analysis pipeline or to identify the best descriptors for the ground-truth traits of interest. Here, we explored the second approach and used a Random Forest algorithm to find which combination of descriptors would best describe each ground-truth data (see Material and Methods for details). In short, we randomly divided the whole dataset into training (3/4) and testing subsets (1/4). The training set was used to create a Random Forest model for each ground-truth data, which was then we applied to the test set. The accuracy of these new predictions was then compared to the accuracy of the direct method (single descriptors) (Figure 2C).

Figure 6 shows the comparison of the accuracy (both the r-squared values from linear regressions and the Mean Relative Error, MRE) of both methods for each ground-truth data. We can clearly see that the Random Forest approach performed always better (sometimes substantially) than the direct approach, even for images with high level of noise. In addition, for most traits, the r-squared and MRE values were above 0.9 and below 0.1 respectively, which is very good, especially for such a wide range of images. In addition, the Random Forest approach allowed the correct estimation of traits that were difficult to estimate with the direct approach (such as the number of first-order axes or the mean second-order root density).

Figure 7 shows the detailed comparison of both methods for the estimation of the total root length. Again, a clear improvement was visible with the Random Forest method, leading to small errors, even with large root systems and noisy images.

Here we presented how machine learning algorithms (Random Forest), could be used in combination with a synthetic image library to improve the estimation of root system traits. Although both the training and test datasets used were made of synthetic images, we believe this approach presents an interesting perspective for the analysis of experimental images.

Indeed, a root architectural model can be used to build a custom library of synthetic images from a set of parameters evaluated on a small number of plants from the experimental dataset. Such library could then be used to train the machine learning model which, in turn, will enable the automatic evaluation of root traits from the remaining experimental images. Alternatively, the algorithm could be directly trained on a subset of experimental data obtained by manual or semi-automatic analyses to be then automatically applied to the rest of the dataset. One must keep in mind that the output of the machine learning strongly depends upon the quality of the dataset used for its training and hence must be analyzed carefully.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.