ROOT PHENOTYPING FROM X-RAY COMPUTED TOMOGRAPHY: SKELETON EXTRACTION

Breakthrough imaging technologies are a potential solution to the plant phenotyping bottleneck in marker-assisted breeding and genetic mapping. X-Ray CT (computed tomography) technology is able to acquire the digital twin of root system architecture (RSA), however, advances in computational methods to digitally model spatial disposition of root system networks are urgently required. We extracted the root skeleton of the digital twin based on 3D data from X-ray CT, which is optimized for high-throughput and robust results. Significant root architectural traits such as number, length, growth angle, elongation rate and branching map can be easily extracted from the skeleton. The curve-skeleton extraction is computed based on a constrained Laplacian smoothing algorithm. This skeletal structure drives the registration procedure in temporal series. The experiment was carried out at the Ag Alumni Seed Phenotyping Facility (AAPF) at Purdue University in West Lafayette (IN, USA). Three samples of tomato root at 2 different times and three samples of corn root at 3 different times were scanned. The skeleton is able to accurately match the shape of the RSA based on a visual inspection. The results based on a visual inspection confirm the feasibility of the proposed methodology, providing scalability to a comprehensive analysis to high throughput root phenotyping.


INTRODUCTION
Root System Architecture (RSA) is the connection between plants and soils, being the critical piece to water and nutrient extraction from (Seethepalli et al., 2020, Postma et al., 2017. The plant science community requires advanced approaches in the characterization of root system architecture (RSA) that support emerging root phenotyping technologies (Bucksch et al., 2014b). The curve-skeleton is identified as a powerful descriptor for analyzing root system networks (Bucksch, 2014a). From the literature, there are several methods to extract the curve-skeleton from a solid, usually classified into two key types: volumetric and geometric (Cornea et al, 2007). This classification relies on the solid representation, depending on using an interior representation or a surface representation. Regarding volumetric approaches, they normally used a volumetric discrete representation, either a regularly partitioned voxelized representation or a discretized function demarcated in the 3D space. The potential loss of details within the solid and numerical instability due to inappropriate discretization resolution are the general disadvantages (Au et al., 2008). In the other hand, geometric approaches directly work on the meshes or point sets. The most common used geometric methods are the Voronoi diagram (Brandt and Algazi, 1992) and medial axis (Marie et al., 2016). Furthermore, currently, reeb-graph-based methods have increased the popularity (Mohamed et Hamza, 2012). There are another group of approaches, which are not classified within the two main types.
In this paper, we propose a skeleton extraction from root digital twins obtained by X-ray CT. Thereby, values of essential root traits can be extracted as phenotypic data to quantitatively assist growth analysis and RSA description. We use a constrained Laplacian smoothing algorithm which is performed directly on the mesh domain, followed by a connectivity surgery and embedding refinement process. This skeletal structure controls the correspondences between root ramifications over time, driving the registration procedure in temporal series. This challenging process is optimized for accurate, repeatable, and robust data, allowing high-throughput root phenotyping from Xray CT systems.

Materials
X-Ray CT is an emerging 3D imaging technology able to noninvasively scan the underground root with high speed and efficiency. The digital twin of the root structure in 3D can be precisely obtained. This technology allows us to nondestructively, comprehensively and accurately monitor the exact same plant root even at different points in time under controlled conditions. Our system scans pots in less than 7 min for 20 cm in height with photon energies in the 225 keV range. The resulting voxel size will be 200 μm. The Focus-Detector distance is 800 mm. Both X-ray detector and X-ray tube are fixed within the system. A rotation stage allows 360° for measurement. There is as well a vertical translation axis to optionally extend the vertical field of

Methodology
The curve-skeleton is essentially a 1D structure that abstracts the model's volume and topological characteristics (Bucksch, 2014a). For this study, we choose a robust skeleton extraction method via Laplacian-based contraction (Au et al., 2008). The algorithm works directly on the original mesh, without a resampled volumetric representation. Thereby, it is pose-insensitive, including global rotation invariant. The method first contracts the mesh geometry into a zero-volume skeletal shape, removing details and noise by applying an iterative Laplacian smoothing that tightly moves all the vertices along their curvature normal directions. After each iteration, a connectivity process is carried out, removing all the collapsed faces from the degenerated mesh until no triangles exist. The challenge of this step is to carefully control the contraction procedure so that it leads to a collapsed mesh with sufficient skeletal nodes to The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLIII-B4-2021 XXIV ISPRS Congress (2021 edition) maintain a fine correspondence between the skeleton and the original geometry. As a consequence, the contraction does not alter the mesh connectivity and retains the key features, guarantying to be homotopic to the original mesh. Finally, to refine the skeleton's geometric embedding, we describe a process that moves each skeletal node to the center of mass of its local mesh region. The potential limitation of this skeleton extraction is that only works for closed mesh models with manifold connectivity since the Laplacian contraction algorithm operates for every individual vertex. Once we have the skeleton, significant root architectural traits as number, length, growth angle, and branching map can be easily extracted. Furthermore, this skeletal structure controls the correspondences between root ramifications over time, driving the registration procedure in temporal series. Thus, we can automatically perform a growth analysis of the diverse ramifications, quantified by the elongation rate trait. Figure 1 and 2 illustrate the skeleton extracted from tomato and corn root samples from the digital twins, respectively. Before the skeleton in relative units, a small figure is provided that represents the digital twin of the root in black with the skeleton embedded in red. Based on a visual inspection, we can affirm that the skeleton algorithm may fail when there are several narrow areas very closed. Two different errors can exist: they cannot be defined by the skeleton or the skeleton is out of the mesh. Figure 3 shows these issues in tomato (Figure 3.a) and corn (Figure 3.b).  Results are analytically being evaluated, with particular attention for the abstraction and analysis of RSA traits in particular datasets as well as in temporal series.

CONCLUSIONS
In conclusion, the proposed pipeline aims to automatically extract phenotypic data of RSA from digital twins obtained by non-invasive X-ray CT. Moreover, the ease of this workflow will potentially increase the usability to imaging technologies regarding genetic mapping and phenotypic selection for in breeding programs (Herrero-Huerta et al., 2019, Herrero-Huerta et al., 2020. This skeletal structure controls the correspondences between root ramifications over time, driving the registration procedure in temporal series. As further studies, analyzing temporal series throw the skeleton from different plant species will be needed. The root phenotypic data may serve as significant information for emerging disciplines as functional phenomics, which is poised to combat major global challenges such as climate change, environmental degradation, and food insecurity (York, 2017).