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Virtual plants are developed by digital agriculture, computer graphics, and 3D reconstruction technology; because crop morphological structure is reproduced in 3D form, virtual plants can resolve the issue of parameter extraction caused by the low resolution of 2D images2,3. Virtual plants are of great significance to crop yield prediction4, resource and environment analysis5, and crop cultivation guidance6. Additionally, virtual plants have become extremely important for precision analysis of crop phenotypes7,8, analysis of plant-type characteristics9, computer-aided design of morphological structure10,11,12, and collaborative analysis of crop growth structure and function13,14.
Soybean is an important food and oil crop worldwide, and is the main source of high-quality human protein15. It can be predicted that, with increasing human populations and land degradation, demand for soybeans will also increase. Currently, the development of high-throughput gene sequencing technology has enabled the full discovery of genes that regulate important soybean traits16. However, because of the complexity of soybean plants, there have been few studies on the extraction of phenotypic parameters and analysis of growth patterns based on virtual plant models. The most common method is still the traditional manual measurement, which is destructive.
However, research on soybean plant growth morphology plays an important guiding role for analysing the growth patterns of soybean, rational seed selection, breeding, interplanting, and improving soybean yield17. Therefore, the accurate extraction of plant dynamic phenotypic parameters using virtual plants and the realisation of the design breeding mode, which combines molecular breeding with phenotypic breeding approaches, have become key problems to improve soybean yield.
The combination of information technology and agricultural virtual reality technology provides an important method for obtaining virtual plants. Currently, the methods used to obtain virtual plants through 3D reconstruction are roughly divided into rule-based18, image-based vision19,20,21, 3D scanner22, and 3D digitiser23 methods. Using a rule-based method to conduct crop 3D reconstruction and visualisation can clearly reveal crop growth patterns. However, 3D reconstruction based on 3D scanner and 3D digitiser methods has some disadvantages, such as requiring a large amount of cloud data, time-consuming processing, and expensive equipment. However, in this paper, the low-cost 3D reconstruction technology both reconstructs and performs parameter extraction of soybean plants during the whole growth period, and can also be easily used by some breeders to promote progress in crop phenotypic breeding.
Because of the ongoing development of 3D reconstruction technology, this paper proposes 3D reconstruction and phenotype extraction technology for plants that can reconstruct plant models with 3D reconstruction technology and soybean plant morphological sequence images. The flow chart of the whole 3D reconstruction process is shown in Fig. 2a. First, the morphological sequence images of soybean plants during specific growth periods were obtained through the digital image acquisition platform. Then, the morphological sequence images were preprocessed. Finally, 3D reconstruction was performed by camera calibration, feature extraction; then, the corresponding phenotypic parameter extraction and application were completed.
In this study, a precision estimation method of camera parameters based on the RANSAC algorithm was adopted. This method has strong robustness under the conditions of substantial noise and incorrect point matches. The RANSAC algorithm, proposed by Fishler and Bolles in 1981, is simple but powerful technology that is widely used in the field of computer vision for model parameter estimation tasks35, such as camera parameter estimation36,37, motion estimation38,39, image registration40,41, projection reconstruction42, and ellipse extraction43. During camera calibration, 15 photos were taken for each group of calibration templates (with and without plants). Then, the camera was calibrated based on the RANSAC calibration algorithm proposed by Lv44 and Zhou45. Finally, the corresponding internal and external parameter matrices of the camera at different angles were obtained by detecting the feature points on the calibration template.
When the initial 3D point cloud of a soybean plant was obtained from the soybean plant pictures, it was necessary to reconstruct the surface of the 3D point cloud. In this study, octree structure was adopted to infer the spatial description of the 3D point cloud of soybean plants. From the initial node, each node extended into eight sub-nodes, and the corresponding spatial cube of the node was divided into eight parts; this was conducted until the number of layers specified in the 3D reconstruction was satisfied. The root node of the initial 3D point cloud in this paper was a boundary box around the surface that was reconstructed49,50. Therefore, octree was used to divide point clouds, and the data structure of each layer of octree nodes was established.
In the formula, \(F\) is a real or complex equation in space. In this paper, \(f\) refers to the 3D surface of soybean plants. If the \(f(x)\) of a point is equal to 0, then the point is on the surface; if \(f(x) > 0\) or \(f(x) Therefore, the main task of 3D reconstruction of soybean plants based on Poisson equation is to accurately calculate its gradient based on the sample points in the point cloud to approximate the implicit function of vector field \(\overrightarrowV\) as accurately as possible. Consequently, the Poisson equation was solved as follows:
\(NgbrD(s)\) is the eight nodes with depth D, and is the weighted coefficient of interpolation. Based on the requirement of the second-order smoothness of soybean plants in the process of 3D reconstruction, the method of cubic spline interpolation was used to calculate the weighted coefficient.
The extraction of dynamic phenotypic parameters of soybean plants based on 3D models is key for researching morphological changes of soybean plants. In this study, the parameters of soybean plant length, plant width, plant height, canopy height, canopy area, plant volume, and plant type were calibrated according to Qiu52.
To improve the accuracy of the 3D reconstruction technology, the same standards were adopted to manually measure the plant. The Pearson correlation analysis was used to analyse the accuracy of the parameters plant length, plant width, canopy height, plant height, canopy area, and plant volume. Simultaneously, the radar charts of the plants were drawn according to the phenotypic parameters, and quantitative analysis of the phenotypic parameters was carried out.
Because the phenotypic parameters of soybean during the whole growth period can be obtained based on this method, the plant growth model and growth rate model can be analysed by logistic model. Compared with other parametric growth models, a logistic growth curve analysis was conducted using a 3-parametric model in this study53. The parameter estimations of the logistic model (Eq. 19) were implemented by gradient descent (sgd package and glm function based on R language)54. The specific analysis formula was as follows:
Figure 4 shows the main view (Fig. 4a) and top view (Fig. 4b) of the 3D reconstruction models of the soybean DN252 plant. This clearly reflects the whole process of soybean development. Figure 4 shows that the 3D models obtained based on the low-cost 3D reconstruction technology truly reflected the colour and texture characteristics of soybean plants. Therefore, this method facilitates high-quality 3D reconstruction and morphological visualisation of soybean plants and can more realistically reveal the morphology and growth state of plants.
Morphological changes of soybean plants during the different growth and development stages based on the 3D model of the DN252 plant. (a) The front view. (b) The top view. V3, V4, R1, R2, R3, R5, R6, R7, and R8 refer to the stages in sequence55.
In this study, three barrels of each variety were planted and scattered in the middle of their respective test areas (see Fig. 1). These materials were used to explain whether there were significant differences between the phenotypes of barrel plants and those of other plants in the field. Figure 5a depicts the box plot and t test results of plant height differences between barrel and field planting of DN251; although the plant height of barrel-planted plants was significantly lower than that of the field-planted plants at each stage of soybean development, the overall difference was not significant. This conclusion was verified by the subsequent t-test; that is, there was no significant difference in plant height between barrel and field planting.
This result was also verified for plant height phenotype of other varieties (Fig. 5b). Analysis of differences between plant length (Fig. 5c), plant width (Fig. 5d), and canopy height (Fig. 5e) of barrel- and field-planted plants was also similar to that of plant height (in this analysis, when alpha is 0.1, the difference may be significant, but the probability of this occurring is very low). It was concluded that there was no significant difference in plant height, plant length, plant width, and canopy height between the barrel- and field-planted plants.
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