Linel2D-Net: A deep learning approach to solving 2D linear elastic boundary value problems on image domains.

Efficient solution of physical boundary value problems (BVPs) remains a challenging task demanded in many applications. Conventional numerical methods require time-consuming domain discretization and solving techniques that have limited throughput capabilities. Here, we present an efficient data-driven DNN approach to non-iterative solving arbitrary 2D linear elastic BVPs. Our results show that a U-Net-based surrogate model trained on a representative set of reference FDM solutions can accurately emulate linear elastic material behavior with manifold applications in deformable modeling and simulation.

FDM data driven U-Net as a 2D Laplace PINN solver.

Efficient solution of partial differential equations (PDEs) of physical laws is of interest for manifold applications in computer science and image analysis. However, conventional domain discretization techniques for numerical solving PDEs such as Finite Difference (FDM), Finite Element (FEM) methods are unsuitable for real-time applications and are also quite laborious in adaptation to new applications, especially for non-experts in numerical mathematics and computational modeling. More recently, alternative approaches to solving PDEs using the so-called Physically Informed Neural Networks (PINNs) received increasing attention because of their straightforward application to new data and potentially more efficient performance. In this work, we present a novel data-driven approach to solve 2D Laplace PDE with arbitrary boundary conditions using deep learning models trained on a large set of reference FDM solutions. Our experimental results show that both forward and inverse 2D Laplace problems can efficiently be solved using the proposed PINN approach with nearly real-time performance and average accuracy of 94% for different types of boundary value problems compared to FDM. In summary, our deep learning based PINN PDE solver provides an efficient tool with various applications in image analysis and computational simulation of image-based physical boundary value problems.

Awn Image Analysis and Phenotyping Using BarbNet.

Consideration of the properties of awns is important for the phenotypic description of grain crops. Awns have a number of important functions in grasses, including assimilation, mechanical protection, and seed dispersal and burial. An important feature of the awn is the presence or absence of barbs-tiny hook-like single-celled trichomes on the outer awn surface that can be visualized using microscopic imaging. There are, however, no suitable software tools for the automated analysis of these small, semi-transparent structures in a high-throughput manner. Furthermore, automated analysis of barbs using conventional methods of pattern detection and segmentation is hampered by high variability of their optical appearance including size, shape, and surface density. In this work, we present a software tool for automated detection and phenotyping of barbs in microscopic images of awns, which is based on a dedicated deep learning model (BarbNet). Our experimental results show that BarbNet is capable of detecting barb structures in different awn phenotypes with an average accuracy of 90%. Furthermore, we demonstrate that phenotypic traits derived from BarbNet-segmented images enable a quite robust categorization of 4 contrasting awn phenotypes with an accuracy of >85%. Based on the promising results of this work, we see that the proposed model has potential applications in the automation of barley awns sorting for plant developmental analysis.

Deep Learning Based Greenhouse Image Segmentation and Shoot Phenotyping (DeepShoot).

Background: Automated analysis of large image data is highly demanded in high-throughput plant phenotyping. Due to large variability in optical plant appearance and experimental setups, advanced machine and deep learning techniques are required for automated detection and segmentation of plant structures in complex optical scenes. Methods: Here, we present a GUI-based software tool (DeepShoot) for efficient, fully automated segmentation and quantitative analysis of greenhouse-grown shoots which is based on pre-trained U-net deep learning models of arabidopsis, maize, and wheat plant appearance in different rotational side- and top-views. Results: Our experimental results show that the developed algorithmic framework performs automated segmentation of side- and top-view images of different shoots acquired at different developmental stages using different phenotyping facilities with an average accuracy of more than 90% and outperforms shallow as well as conventional and encoder backbone networks in cross-validation tests with respect to both precision and performance time. Conclusion: The DeepShoot tool presented in this study provides an efficient solution for automated segmentation and phenotypic characterization of greenhouse-grown plant shoots suitable also for end-users without advanced IT skills. Primarily trained on images of three selected plants, this tool can be applied to images of other plant species exhibiting similar optical properties.

Towards Automated Analysis of Grain Spikes in Greenhouse Images Using Neural Network Approaches: A Comparative Investigation of Six Methods.

Automated analysis of small and optically variable plant organs, such as grain spikes, is highly demanded in quantitative plant science and breeding. Previous works primarily focused on the detection of prominently visible spikes emerging on the top of the grain plants growing in field conditions. However, accurate and automated analysis of all fully and partially visible spikes in greenhouse images renders a more challenging task, which was rarely addressed in the past. A particular difficulty for image analysis is represented by leaf-covered, occluded but also matured spikes of bushy crop cultivars that can hardly be differentiated from the remaining plant biomass. To address the challenge of automated analysis of arbitrary spike phenotypes in different grain crops and optical setups, here, we performed a comparative investigation of six neural network methods for pattern detection and segmentation in RGB images, including five deep and one shallow neural network. Our experimental results demonstrate that advanced deep learning methods show superior performance, achieving over 90% accuracy by detection and segmentation of spikes in wheat, barley and rye images. However, spike detection in new crop phenotypes can be performed more accurately than segmentation. Furthermore, the detection and segmentation of matured, partially visible and occluded spikes, for which phenotypes substantially deviate from the training set of regular spikes, still represent a challenge to neural network models trained on a limited set of a few hundreds of manually labeled ground truth images. Limitations and further potential improvements of the presented algorithmic frameworks for spike image analysis are discussed. Besides theoretical and experimental investigations, we provide a GUI-based tool (SpikeApp), which shows the application of pre-trained neural networks to fully automate spike detection, segmentation and phenotyping in images of greenhouse-grown plants.

Fully-automated root image analysis (faRIA).

High-throughput root phenotyping in the soil became an indispensable quantitative tool for the assessment of effects of climatic factors and molecular perturbation on plant root morphology, development and function. To efficiently analyse a large amount of structurally complex soil-root images advanced methods for automated image segmentation are required. Due to often unavoidable overlap between the intensity of fore- and background regions simple thresholding methods are, generally, not suitable for the segmentation of root regions. Higher-level cognitive models such as convolutional neural networks (CNN) provide capabilities for segmenting roots from heterogeneous and noisy background structures, however, they require a representative set of manually segmented (ground truth) images. Here, we present a GUI-based tool for fully automated quantitative analysis of root images using a pre-trained CNN model, which relies on an extension of the U-Net architecture. The developed CNN framework was designed to efficiently segment root structures of different size, shape and optical contrast using low budget hardware systems. The CNN model was trained on a set of 6465 masks derived from 182 manually segmented near-infrared (NIR) maize root images. Our experimental results show that the proposed approach achieves a Dice coefficient of 0.87 and outperforms existing tools (e.g., SegRoot) with Dice coefficient of 0.67 by application not only to NIR but also to other imaging modalities and plant species such as barley and arabidopsis soil-root images from LED-rhizotron and UV imaging systems, respectively. In summary, the developed software framework enables users to efficiently analyse soil-root images in an automated manner (i.e. without manual interaction with data and/or parameter tuning) providing quantitative plant scientists with a powerful analytical tool.

Automated Spike Detection in Diverse European Wheat Plants Using Textural Features and the Frangi Filter in 2D Greenhouse Images.

Spike is one of the crop yield organs in wheat plants. Determination of the phenological stages, including heading time point (HTP), and area of spike from non-invasive phenotyping images provides the necessary information for the inference of growth-related traits. The algorithm previously developed by Qiongyan et al. for spike detection in 2-D images turns out to be less accurate when applied to the European cultivars that produce many more leaves. Therefore, we here present an improved and extended method where (i) wavelet amplitude is used as an input to the Laws texture energy-based neural network instead of original grayscale images and (ii) non-spike structures (e.g., leaves) are subsequently suppressed by combining the result of the neural network prediction with a Frangi-filtered image. Using this two-step approach, a 98.6% overall accuracy of neural network segmentation based on direct comparison with ground-truth data could be achieved. Moreover, the comparative error rate in spike HTP detection and growth correlation among the ground truth, the algorithm developed by Qiongyan et al., and the proposed algorithm are discussed in this paper. The proposed algorithm was also capable of significantly reducing the error rate of the HTP detection by 75% and improving the accuracy of spike area estimation by 50% in comparison with the Qionagyan et al. method. With these algorithmic improvements, HTP detection on a diverse set of 369 plants was performed in a high-throughput manner. This analysis demonstrated that the HTP of 104 plants (comprises of 57 genotypes) with lower biomass and tillering range (e.g., earlier-heading types) were correctly determined. However, fine-tuning or extension of the developed method is required for high biomass plants where spike emerges within green bushes. In conclusion, our proposed method allows significantly more reliable results for HTP detection and spike growth analysis to be achieved in application to European cultivars with earlier-heading types.

Semi-automated Root Image Analysis (saRIA).

Quantitative characterization of root system architecture and its development is important for the assessment of a complete plant phenotype. To enable high-throughput phenotyping of plant roots efficient solutions for automated image analysis are required. Since plants naturally grow in an opaque soil environment, automated analysis of optically heterogeneous and noisy soil-root images represents a challenging task. Here, we present a user-friendly GUI-based tool for semi-automated analysis of soil-root images which allows to perform an efficient image segmentation using a combination of adaptive thresholding and morphological filtering and to derive various quantitative descriptors of the root system architecture including total length, local width, projection area, volume, spatial distribution and orientation. The results of our semi-automated root image segmentation are in good conformity with the reference ground-truth data (mean dice coefficient = 0.82) compared to IJ_Rhizo and GiAroots. Root biomass values calculated with our tool within a few seconds show a high correlation (Pearson coefficient = 0.8) with the results obtained using conventional, pure manual segmentation approaches. Equipped with a number of adjustable parameters and optional correction tools our software is capable of significantly accelerating quantitative analysis and phenotyping of soil-, agar- and washed root images.