A Pathway to Assess Genetic Variation of Wheat Germplasm by Multidimensional Traits with Digital Images

In this paper, a new pathway was proposed to assess the germplasm genetic variation by multidimensional traits of wheat seeds generated from digital images. A machine vision platform was first established to reconstruct wheat germplasm 3D model from omnidirectional image sequences of wheat seeds. Then, multidimensional traits were conducted from the wheat germplasm 3D model, including seed length, width, thickness, surface area, volume, maximum projection area, roundness, and 2 new defined traits called cardioid-derived area and the index of adjustment (J index). To assess genetic variation of wheat germplasm, phenotypic coefficients of variation (PCVs), analysis of variance (ANOVA), clustering, and the defined genetic variation factor (GVF) were calculated using the extracted morphological traits of 15 wheat accessions comprising 13 offspring and 2 parents. The measurement accuracy of 3D reconstruction model is demonstrated by the correlation coefficient (R) and root mean square errors (RMSEs). Results of PCVs among all the traits show importance of multidimensional traits, as seed volume (22.4%), cardioid-derived area (16.97%), and maximum projection area (14.67%). ANOVA shows a highly significance difference among all accessions. The results of GVF innovatively reflect the connection between genotypic variance and phenotypic traits from parents to offspring. Our results confirmed that extracting multidimensional traits from digital images is a promising high-throughput and cost-efficient pathway that can be included as a valuable approach in genetic variation assessment, and it can provide useful information for genetic improvement, preservation, and evaluation of wheat germplasm.


Introduction
Germplasm resources represent a critical foundation for crop breeding [1,2].The assessment of genetic variation in crop germ plasm has long been a significant topic in agricultural research [3][4][5].Wheat, as one of the world's principal cereal crops, holds a pivotal role in agricultural breeding.Evaluating the genetic variation of wheat germplasm offers invaluable insights for agricultural researchers, aiding them in better understanding and harnessing these resources.
The genetic variation in crop germplasm is shaped by both natural genetic drift and humandirected selection, endowing crops with the capacity to adapt to diverse environmental con ditions [6,7].Phenomics, as a potent research tool, delves deeply into and harnesses these genetic variations, paving the way for more efficacious precision breeding [8].This domain typically involves the utilization of an array of sensors to capture phe notypic data, followed by phenotypic analysis.While it presents a challenging research landscape, it is also replete with oppor tunities.Through the lens of phenomics, we can discern the intricate relationships between crop traits and genetic factors with heightened precision [9].
Phenomics has made significant strides in the study of genetic variation in crop germplasm in recent years.He et al. [10] delved into traits such as thousandgrain weight, grain length, and grain width in germplasm and elucidated key genes influencing millet yield attributes. Varshney et al. [11] constructed a genetic varia tion map from a global collection of 3,366 chickpea germplasms, unveiling superior haplotypes conferring climate adaptability in chickpeas.Chen et al. [12] harnessed natural genetic variations in a leguminous plant to identify genes modulating seed traits and conducted a genomewide association study on 32 seed related traits, focusing on seed size and composition.Despite the laudable achievements from these and numerous other studies [13][14][15][16][17][18] on germplasm genetic variation, challenges such as the intensive labor, extended duration, and potential subjectivity in phenotypic data acquisition persist.To cater to rapid and accurate evaluations of germplasm genetic variation, there is a pressing need to explore novel methodologies that enhance the efficiency and precision of research into wheat germplasm variation.
With the evolution of digital imaging methodologies, phe nomics has entered a new phase in the study of genetic variation.Image analysis can be considered a measurement tool, where automated image processing techniques allow for higher through put, reliability, and repeatability at various scales, ranging from microscopic to field levels.Typically, 2dimensional (2D) images are used to calculate parameters such as width, length, and area [19][20][21][22], while other mathematical operators are employed to derive more intricate morphological traits [23].For cereal crops, measuring detailed 3D morphological information (e.g., volume, surface area, and furrow) remains a formidable task, even though they are associated with nutrient translocation capabilities and crop growth processes.Pinpointing these pivotal phenotypes necessitates intricate measurement techniques and data process ing methods.While digital imaging offers a rapid, highthrough put, and costeffective means for seed genetic variation studies, its primary focus is on 2D traits, limiting the detectable traits for minuscule seeds.The limitations of image processing on multidimensional traits considerably constrain its applicability in wheat germplasm genetic variation research.
3D reconstruction technology, with its capability to capture an expansive range of multidimensional traits, has heralded a new revolution in agricultural breeding research.Methods based on active light, employing tools like xray computed tomography (CT) and laser scanners, boast high precision but come at a greater cost and complexity.Studies by Li [24], Huang et al. [25], and Yang and colleagues [26,27] have adeptly harnessed these tools for examining rice grain features, while Zhu et al. [28] demonstrated the efficacy of oblique photography as a more efficient alternative.However, the steep costs and intricate oper ation of these devices remain inherent challenges.Imagebased reconstruction techniques such as structure from motion (SFM) [29] and multiview stereo (MVS) [30,31] are promising, but their deployment on seeds with uniform textures, like wheat seeds, poses challenges.An innovative approach introduced by Roussel et al. [32] utilized voxel space carving with digital images for seed reconstruction, unveiling several multidimensional fea tures.The author hoped that this research would pique increased interest in voxel reconstruction methodologies.Nevertheless, seeds reconstructed using this technique exhibited discernible cut marks, and there was a lack of subsequent analysis on the role of the measured traits in genetic variation.These prior inves tigations illuminate the potential and the challenges of 3D recon struction in wheat seed phenotypic trait research, especially when digital images are the medium for 3D reconstruction.To fully capitalize on this approach and navigate its limitations, it is imperative to further refine 3D reconstruction techniques and delve deeper into the implications of measuring multidimen sional seed traits.
This research presents a pathway for assessing genetic variation in wheat germplasm using multidimensional traits derived from digital images.The specific objectives were to (a) construct a machine vision platform to acquire images of wheat seeds; (b) perform a 3D reconstruction of wheat seeds within the modeling of the rotational axis, using a voxel reconstruction method that requires only one calibration for highprecision 3D reconstruction; (c) extract multidimensional phenotypic traits from the recon structed model; and (d) evaluate genetic variation using phenotypic coefficients of variation (PCVs), analysis of variance (ANOVA), and the defined genetic variation factor (GVF).This research aims to provide useful information for the genetic improvement, pres ervation, and evaluation of wheat germplasm.

Experimental design
The evaluation of genetic variation in wheat germplasm was comprehensively assessed using a combination of phenotypic coefficient of variation (PCV), variance analysis (ANOVA), clustering, and a newly defined GVF.The validity of these results was contingent upon the accuracy of the extracted phe notypic traits.To obtain multidimensional phenotypic traits of wheat seeds, a phenotyping system utilizing omnidirectional images was developed, as shown in Fig. 1.This system con sisted of 2 steps: • Construction of a machine vision platform: Composing with a nozzle to attach wheat seeds and a checkerboard, a highprecision rotation step motor, and a control sys tem to capture images, allowing us to obtain images of the wheat seeds and checkerboard from different angles.

Materials and image acquirement
Fifteen wheat seed varieties were selected for the assessment of genetic variation.The chosen varieties comprise 2 parental strains, Xinmai 26 and Xinong 294, and 13 offspring varieties derived from them.The parental strains, cultivated over sev eral years, are excellent varieties that cover a broad spectrum of seed traits.Their hybrid offspring bear significance for the study of genetic variation.The offspring varieties are divided into 2 batches.The first batch contains 6 varieties derived from a crossbreed between Xinmai 26 and Xinong 294.The second batch consists of 7 varieties, which were obtained by first cross breeding Xinong 20 and 02Ta, followed by a crossbreed with Xinong 585.A total of 450 wheat seeds, with 30 seeds ran domly selected from each variety, were subjected to the exper iment.The detailed information of the varieties is shown in Extended Table 1.
The assessment of genetic variation was based solely on digital images.Prior to the experiment, 8 to 12 checkerboard images were acquired and utilized to calibrate the camera poses in the system.A 9 × 9 checkerboard was utilized with a cornertocorner distance of 0.5 mm, and the camera pose calibration was per formed only once.During the experiment, omnidirectional image sequences of 450 wheat seeds were acquired at 9degree intervals, totaling 40 images per seed.The acquired calibrated images and 450 × 40 images of the wheat seeds were analyzed and processed to assess the genetic variation in wheat germ plasm.The data from these images served as the sole input for the entire method.

Construction of a machine vision platform
To obtain a complete sequence of wheat seed images, a machine vision platform has been constructed that incorporates a preci sion rotating mechanism and a clever suction device, as shown in Fig. 2. The platform consists of several key components, includ ing an industrial charge coupled device (CCD) camera, a suction nozzle, a connecting shaft, a vacuum pump, and a stepper motor.The industrial camera is composed of a microscope camera (model KUY NICECM1000, 4,912 × 3,684 pixels, Shenzhen Kuy Nice Microscope Co. Ltd., China) and a fixedfocus industrial lens (model WP2M2514C, 25 mm focal length, 20 × 16.8 mm field of view, Shenzhen Work Power Technology Co. Ltd., China), which is fixed by the camera bracket to capture highresolution images of the checkerboard or wheat seeds.The camera faces the area below the suction nozzle of the device to ensure that the object to be photographed is completely within the camera's view.The suction nozzle is directly inserted into the nozzle seat and attached to the connecting shaft, with a small vacuum pump con nected to the side of the seat.The top of the connecting shaft is connected to the stepper motor.
Wheat seeds or a checkerboard were stably adsorbed on the suction nozzle after activating the air pump.The stepper motor drove the suction nozzle to rotate in 9° increments, collecting a total of 40 omnidirectional image sequences of the wheat seed at different angles.The contact surface between the suction nozzle and wheat seed was minimal, ensuring the completeness of the captured images.Before capturing wheat seed images, images of a checkerboard were also obtained for calculating the virtual angle of views.It was ensured that the interval between each rotation was 9° or 4.5°, and 9 checkerboard image sequences were collected.Accordingly, software was designed to automate this process.After fixing the machine vision platform, it was only necessary to capture images once with the checkerboard attached to the suction.Then, the number was input and the first wheat seed was placed onto the machine vision platform.
Once it was finished, the next one was placed on.These were all the operations that needed to be performed manually.Each time the nozzle rotated, the CCD camera took a picture and saved it, which was all executed automatically by the software.

Establishment of a 3D seed model
In order to study the genetic variation more thoroughly in wheat germplasm, it is necessary to comprehensively and multidimen sionally characterize the traits of wheat seeds.However, due to the small size of wheat seeds, manual nondestructive measure ment methods and image processingbased methods are prone to large errors.Therefore, this study proposes a method to build 3D models of wheat seeds considering the machine vision plat form.The method is based on IBVH [33], which constructs 3D models from multiple digital images.Also, an axisbased way was proposed to calculate the virtual views, ensuring the high precision of the 3D model.Leveraging the wheat seed model, multidimensional phenotypic traits can be extracted.
MATLAB R2018b is used to calculate the virtual view, C++ OpenCV library is used to process digital images, and C++ PCL (Point Cloud Library) [34] and VTK (Visualization Toolkit) are used to build, display 3D models, and extract phenotypic traits.The C++ development software is Microsoft Visual Studio 2017.In addition, MeshLab software is used to facilitate the viewing and display of the point cloud results.

3D model reconstruction of wheat seed
A method was proposed for building 3D models of wheat seeds using a machine vision platform.The 3D reconstruction pro cess involved 3 main steps: image processing, projection matrix calculation, and face slice reconstruction.
First, images obtained from the vision platform were pro cessed using image binarization, background removal, and silhouette extraction to get highquality contour images of wheat seeds from 40 different viewpoints.Background removal is a crucial step in the contour extraction process.A method was utilized that segments the suction nozzle background by identifying the horizontal intersection line between the suction nozzle and the wheat seeds when the total number of white pixel points in the same row changes more than a certain per centage compared to the previous view.Additionally, an algo rithm based on a localized Radon transform [35] was employed to extract the 81 corner points of the checkerboard image under each viewpoint.This information is then used to obtain the spatial position information of the corner points in the set world coordinate system under 9 different camera views.
Second, the calculation of the projection matrix, as shown in Eq. 1, was performed.This involves determining the camera's internal and external parameters using the classical linear cam era model (the pinhole model) for the conversion of the world coordinate system to the pixel coordinate system.The camera internal parameters are represented by the matrix K, which includes 5 parameters: f (effective focal length), dx and dy (object size of each pixel in the image horizontal and vertical directions), α u and α v (image horizontal and vertical scaling factors), and s uv (distortion factor).The rotation matrix R and the translation vector T are used to describe the rigid body transformation relationship between the camera coordinate system and the world coordinate system, forming a 4 × 4 matrix to determine the camera's pose, which are the external param eters of the camera.These internal and external parameters are then combined to form a 3 × 4 projection matrix P, which rep resents the geometric relationship between a 3D point in space and its projection to a 2D point in the imaging plane.A cali bration method based on the rotation axis model was proposed to calculate the camera's external parameters. (1)

Fig. 2. (A and B)
The machine vision platform for digital images of wheat seed and checkerboard.The entire platform is composed of 5 parts: (1) absorption mechanism (absorbs the sample and rotates it 360 degrees), ( 2) sample (wheat seed or checkerboard), (3) CCD camera (captures images throughout the rotation), ( 4) ring light (provides consistent lighting), and ( 5) vacuum pump (creates suction, enabling the sample to be absorbed).The absorption mechanism consists of 4 parts: (6) stepper motor (provides torque, allowing the sample to rotate at specific angles), ( 7) connecting shaft (links the motor and the suction nozzle), ( 8) air tube (connects to the vacuum pump, for creating suction so the wheat seed can be absorbed), and (9) suction nozzle (used for absorbing the wheat seed).
Finally, the 3D model of wheat seed was reconstructed by applying the face slice reconstruction method.The projection matrix calculates the projection of voxel points in space under each viewpoint, which enables the classification of spatial voxel points into 3 states: points on the seed 3D model, points inside the seed 3D model, and points outside the seed 3D model.The MC (Marching Cubes) algorithm [36] was utilized to recon struct the 3D faceted model of wheat seeds based on the states of voxel points in space.

Modeling of the rotational axis
Based on the constructed rotational visual platform, an accu rate method for modeling the rotational axis has been designed.
In the whole process of virtual view construction, the calcula tion of camera internal parameters and the establishment of the final projection matrix are the basic steps in the 3D recon struction process.In the middle, the calculation method of the rotation axis is the key of the experiment, and its accuracy directly affects the accuracy of the reconstruction results.
According to the spatial arc coordinates of each corner point in the camera coordinate system O C X C Y C Z C extracted, the circle centers of space are solved.These circle centers are located on different positions of the rotation axis.The 3D spatial straight line where the set of circle center points is located is fitted, which is the requested rotation axis.In order to obtain more robust calculation results, multiple corner points are used to participate in the estimation.The corner points P i were set to constitute the data set P, and the circle center O and radius R were obtained by fitting the spatial sphere, that is, to find Based on the linear regression of principal component analysis to fit the rotation axis, the centers of these circles Oi, i = 1, …N.The average value of N is: Finally, calculate the covariance matrix for the centers of these circles O i , as shown in Eq. 4.
The eigenvector n corresponding to the largest eigenvalue of λ is obtained, namely, the rotation axis.
Parameter extracted from the model of the seed By referring to the related research on wheat seed phenotypic identification [25], we determined 9 wheat phenotypic traits based on 3D reconstruction data, as shown in Table 1.Among them, length, width, and thickness are the maximum distances in the 3 axial directions of the reconstructed contour envelope, respectively.The surface area is obtained by combining a series of gridbased triangular patches based on the boundary voxels and the isosurface.By slicing the grain contour boundary at equal intervals along the longitudinal direction and sufficiently small intervals, the volume can be calculated by integrating and accumulating each slice.The projection area is determined by the slice with the maximum area.Additionally, 2 new pheno typic traits were proposed to respond to the ventral groove trait of wheat seeds: the cardioidderived area and J index.Since the groove is a relatively obvious trait but difficult to analyze, the groove face was oriented upward and projected onto a heart shaped curve.The resulting area, called the cardioidderived area, provides a more accurate representation of the groove than traditional methods.To normalize measurements for seeds of different sizes, J index was calculated by dividing the cardioid derived area by the square area of the seed.These 2 traits were designed to offer more detailed information about the shape and size of wheat seeds.
Following the extraction of phenotypic traits, a comparison between manual measurements and 3D reconstruction mea surements was conducted.The coefficient of determination (R 2 ) was employed to reflect the regression relationship between manual and 3D reconstruction measurements, while the root mean square error (RMSE) was used to quantify the errors.In the manual measurements, a vernier caliper was utilized

Cardioid area
to hold the wheat seeds, providing precise length measure ments.However, it should be noted that the measurements for width and thickness may exhibit slight deviations at the mil limeter scale.

Assessment of the genetic variation
A 3step process (PCV calculation, ANOVA, and GVF calcu lation) was employed to assess the genetic variation in wheat seeds, using the 3D model derived from images taken at differ ent angles, as shown in Fig. 3. Through PCV calculation, the effectiveness of multidimensional traits in expressing genetic diversity in wheat seeds was verified.ANOVA allowed for the analysis of the variance in phenotypic traits between different generations, providing insights into genetic variation in wheat.
Finally, in the GVF calculation step, genetic variation was esti mated by considering environmental factors that may affect the inheritance process.This study highlights the importance of taking into account environmental factors in the estimation of genetic variation, and the potential of using multidimensional traits to better express genetic diversity in wheat seeds.

Genetic variation for multidimensional traits
The coefficient of variation (CV) is a useful metric for quanti fying data dispersion, controlling for measurement scale and dimension.In the agricultural sector, the use of phenotypic coefficient of variation (PCV), genetic coefficient of variation (GCV), and environmental coefficient of variation (ECV) is commonplace in the assessment of crop character diversity in response to various factors [37,38].When environmental con ditions are controlled, the PCV of each character in parents and offspring can provide insights into the diversity of germ plasm for a particular variety, as shown in Eq. 5.
where δ j(i) is the effective value of the jth individual of the ith germplasm and σ P is the standard deviation (SD) of phenotypic traits.
To gain a deeper understanding of genetic variation in mul tidimensional traits, it is imperative to accurately determine the CV (PCV) for each trait within the germplasm.This process involves calculating the SD of the phenotypic traits and then dividing that value by the average effective value of each sample in the germplasm set.Through this methodology, we can assess the degree to which diversity in each germplasm variety is influ enced by elements like genetics and environmental factors.A lower PCV indicates that a trait is relatively stable, with only subtle differences between seeds or varieties.Conversely, when PCV is higher, it signifies that there is a notable variance in trait expression.Such traits are of higher value in genetic research since they can be more effectively associated and analyzed.This foundational step is essential for understanding the genetic variability in wheat and other crops.
Statistical measures were calculated for all wheat grain samples from 15 varieties, including the mean, minimum, maximum, SD, and phenotypic CV for nine traits.Following the calculation of SD, PCVs for each trait were computed.These PCVs were then ranked to identify traits exhibiting the greatest variability.Finally, to further analyze the genetic variation of traits based on pheno typic data, violin plots [39] were drawn for the 3 traits with larger variation coefficients.Data for the statistical measures were directly calculated using Excel spreadsheets.Visualization results were generated using MATLAB R2018b software, and the Violinplot Matlab master library was employed for creating violin plots.

Variance and clustering between different offspring
ANOVA and cluster were utilized to analysis genetic variation between different offspring.The ANOVA analysis was used to assess the variation between 2 groups of progeny, including those produced via binary hybridization between Xinmai 26 and Xinong 294, and those resulting from ternary hybridization between Xinong 2002Ta and Xinong 585.Individual ANOVAs were conducted for both within and across germplasm, evalu ating the differences among the 6 variants of the first progeny, as well as comparing both the first and second progeny to the parental plants.Analysis focused on the F value, calculated for each ANOVA, and the differences observed between groups.
Subsequently, clustering was employed to classify the data into distinct groups.Three different clustering methods, namely K means, hierarchical, and DBSCAN (densitybased spatial clustering of applications with noise) were utilized to categorize 390 wheat germplasm into 2 classes.Varieties derived from binary hybridization (Xinmai 26 and Xinong 294) were designated as category 0, while those from ternary hybridization (Xinong 20, 02Ta, and Xinong 585) were classified as category 1.The clus tering analysis took place after measuring wheat seed trait parameters using a 3D reconstruction method.The purpose of this analysis was to assess the reliability of the clusteringbased variety analysis approach by comparing the outcomes yielded through clustering.
The final results of the ANOVA and clustering are presented in the form of graphs and charts.The ANOVA is conducted using R programming language for data processing, with the ultimate results presented in tabular format.The outcomes of clustering are visualized through scatter plots generated in 3 different ways, accompanied by histograms that display the various evaluation metrics of the clusters.MATLAB R2018b software is employed for the clustering analysis and plotting, incorporating the Statistics and Machine Learning Toolbox.

GVF from parent to offspring
The calculation of the PCV among parents and offspring, as well as the difference analysis between varieties of parents and offspring, can reflect the genetic variety to a certain extent.However, the changes of phenotypic traits not only include the value of genetic variation but also environmental variation to a large extent.In fact, the calculation of the former cannot exclude the influence of environment on the phenotypic var iation.In order to reduce the interference of environmental error variance as much as possible and evaluate the genetic variation of the traits from parent to offspring, a method of calculating genetic coefficient is proposed.
Calculating the GVF, which reflects genetic diversity from parent to offspring, assists in understanding trait inheritance and species or population genetic makeup.The complexity of this cal culation arises from the influence of both genetic and environ mental factors on phenotypic traits.Truncation error estimation helps mitigate the impact of environmental variables.
Cumulative mean values of parent varieties are computed, and differences between offspring varieties are determined.The square root of the parent-offspring difference is calculated using the principle of covariance, obtaining the change value of the trait under the response gene's influence.Dividing the change value by the mathematical expectation value of the par ent traits yields the genetic coefficient.This coefficient indicates genetic variation from parent to offspring and the extent to which offspring traits resemble those of the parent.Considering both genetic and environmental factors provides a comprehen sive understanding of species or population genetic makeup.Equation 6 presents the genetic coefficient calculation, with P 1 and P 2 denoting parent varieties and F i referring to the ith off spring variety resulting from parental breeding.

3D model accuracy and cycle-time efficiency
Fifteen wheat varieties were employed to reconstruct 3D mod els, comprising 2 parental and 13 offspring lines.A total of 450 seed samples were collected by randomly selecting 30 seeds from each variety.These samples facilitated the successful reconstruction of the wheat grain's complete 3D shape and extraction of 9 desired phenotypic traits.
The duration was measured across 3 phases of the 3D mod eling process: image capturing, 3D modeling, and trait measure ment.During image capturing, photographs were taken at intervals of 9 degrees, each followed by a pause of 300 ms to facilitate camera shooting.This phase, which involved manual placement and image capturing of the seeds, took an average of 40 s per seed.3D reconstruction, facilitated by CUDA on a GTX 1650, allowed the reconstruction of approximately 450 wheat seeds at a voxel resolution of 128 × 128 × 128 within roughly 13 h.During trait measurement, calculation of surface area and volume through meshing required 40 to 60 s per seed, while other traits could be calculated in less than 1 s per seed.Given that these 3 processes can be executed simultaneously on a sin gle computer, the average time for complete trait measurement of wheat seeds was approximately 100 s per seed.The method, which necessitates only a lowcost industrial camera, turntable, and stepper motor, facilitates multidimensional trait measure ment of wheat seeds.It presents a significantly more costeffective solution than active light reconstruction technologies, such as CT and laser scanners, and outperforms CT reconstruction and manual mea surement in terms of time efficiency.Further com parison of results can be found in Extended Table 3.Thus, this method offers an effective blend of high throughput and low cost.
To verify the reliability of the experimental results, 120 seed samples from 4 varieties (S77, S78, S79, and S80) underwent analysis.Several manually measurable phenotypic traits were assessed and compared to the modelderived values.Out of the 9 traits, only length, thickness, and width could be easily measured manually.An electronic caliper with a precision of 0.01 mm was employed for these measurements.For wheat grain length, the top and bottom of the seed were clamped, yielding a relatively accurate value.Each seed's length was measured thrice, with the average value recorded.Given the potential for larger inaccuracies in manual measurements of wheat seed thickness and width, RMSEs are used to reflect measurement discrepancies.The seed surface is uneven and the thickness is nonuniform, necessitating the division of each wheat grain into 3 groups.Each group was measured thrice, with the maximum value selected.The average of these 3 mea surements provided the final manual measurement result.To effectively compare manual measurements with 3D model results, a scatter plot was constructed and a line was fitted, as depicted in Fig. 4A.
The RMSE for length, thickness, and width was 0.15, 0.19, and 0.26, respectively, all falling within 0.3, as depicted in Extended Fig. 3. Since measurements of width and thickness can be easily influenced by subjective factors during the mea surement process, we employed the residual plot and relative error histogram to capture these measurement errors, as illus trated in Fig. 4B to D. Most measurement points are concen trated within an absolute error of 0.5 mm and a relative error range of 10%.This observation indicates that the measurements derived from the 3D model of the wheat seed are largely con sistent with the real values, providing a reasonably accurate representation of the seed's attributes.

Genetic variation expressed from multidimensional traits
Table 2 showcases the outcomes of various statistical analyses.The 9 traits are divided into 3 categories: 1D traits (length, thickness, width), 2D traits (maximum projection area, cardi oid area), and 3D traits (surface area, volume, roundness, J index).Among these, PCV reveals interesting insights.While there may be significant variations in the volumes of wheat grains, certain traits show more consistent and limited variations.For instance, the J index, despite being a 3D trait, demonstrates limited disparities, suggesting that differences in furrow traits are minimal compared to other traits.In terms of PCV values, the traits are ranked from highest to lowest as follows: volume, cardioid area, projection area, surface area, width, thickness, roundness, length, and J index.The findings from PCV calculations highlight that 2D and 3D traits, notably volume, heartshaped projection area, and surface area, tend to have larger PCV values.In contrast, the three 1D traits con sistently show smaller PCV values.Furthermore, regarding the furrow phenotype of the wheat grain, 2 associated traits have been identified: the heartshaped area and the heartshaped derivative index.Among the 9 traits, the heartshaped area's PCV ranks second, suggesting its poten tial significance in genetic variation research, while the J index has the smallest PCV, indicating its stability across different grain varieties.
Three traits with the highest PCV rankings were selected, and the resulting violin plots are presented.As depicted in Fig. 5A to C, comparisons were made within the second category of offspring, revealing differences in the distribution of various varieties within the same batch.Notably, the distributions of the 3 traits for S76 and S82 were relatively small.Agricultural breeding experts may consider excluding these 2 grain varieties from future breeding endeavors.Figure 5D to F display com parisons between the 2 offspring batches.Although the distri bution values indicate similarities between the 2 batches, the first batch exhibited slightly larger corresponding traits than the second.Furthermore, the data concentration degree reveals a more concentrated distribution for the second batch.These violin plot results can serve as a preliminary reference for breeding experts.

Variance and clustering among diverse offspring
ANOVA revealed significant differences in both intraspecific and intermediate traits, with interspecific differences being more substantial than intraspecific differences, as displayed in Table 3.All traits exhibited significant differences, as indicated by a P value less than 0.01, which applied to both within and among germplasm.Nevertheless, the extent of these differences varied, as demonstrated by the F values.Excluding the 3 traits of length, surface area, and volume, F values for the remaining 6 traits were higher among germplasm than within germplasm.Consequently, ANOVA results suggest that variability among different offspring is somewhat greater than within the same offspring.However, these results cannot directly determine the classification of seeds originating from distinct offspring.According to the ANOVA results, various methods can effectively cluster wheat seeds into 2 categories, as illustrated in Fig. 6.It is well established that seed morphological char acteristics are subject to considerable random variations due to environmental influences.The ANOVA findings also suggested that variability among germplasm was not sub stantially greater than within germplasm.As a result, direct classification of categories based on phenotypic traits is not feasible.However, unsupervised clustering can be conducted using phenotypic variation in wheat seed traits.In Fig. 6A to C, it is evident that wheat seeds can be clustered into 2 categories reasonably well.Last, a comparison of the clus tering outcomes with actual label values revealed that the precision score of Kmeans clusterer is 70%, as demonstrated in Fig. 6D.

GVF from parent to offspring
The devised GVF quantitatively reflects genetic changes from parent to offspring.The "Genetic variation expressed from multidimensional traits" and "Variance and clustering among diverse offspring" sections demonstrate that seed phenotypic traits can respond to genetic variation to a certain degree, albeit heavily influenced by environmental factors.GVF calculations aim to minimize the impact of environmental errors.GVF val ues for 9 traits of the second offspring variety, corresponding to the 2 parents, were computed and are presented in Table 4.It is evident that surface area values significantly decreased in this offspring variety.The 4 traits with the highest GVF values are volume, cardioid area, width, and projection area.GVF results innovatively reveal the relationship between genotypic variance and phenotypic traits from parents to offspring.
In the "Genetic variation expressed from multidimensional traits" section, the coefficient of phenotypic variation was calculated, and it was hypothesized that multidimensionality might better reflect genetic variation.However, since pheno typic variation encompasses both genetic variation and envi ronmental error, minor environmental errors may be amplified in multidimensional traits.Consequently, it is not possible to directly confirm that topranked traits possess larger genetic variations through the coefficient of phenotypic variation.Never theless, GVF effectively mitigates the influence of environmen tal error through straightforward differential analysis, under the assumption of an unchanging environment, and thereby illustrates the relationship between multidimensional pheno typic traits and genetic variation.Results indicate that the aver age coefficient of genetic variation for the 9 traits of these 7 offspring is as follows: volume, cardioid area, thickness, largest area, surface area, roundness, width, J index, and length.Except for thickness, 2D and 3D trait values remain larger.This out come provides stronger evidence that the 3D model better represents and evaluates genetic variation.Finally, the average GVFs corresponding to all traits of 7 varieties were calculated.The ranked GVFs for each variety, from largest to smallest, are F 1 , F 2 , F 7 , F 4 , F 5 , F 3 , F 6 .Accordingly, F 1 , F 2 , and F 7 exhibit supe rior genetic variations and can be utilized in agricultural breed ing hybrid experiments.Thus, the GVF definition could impact breeding processes.

Establishment of a voxel reconstruction method adapted to seeds
In recent years, 3D reconstruction methods, such as SFM and MVSbased algorithms, have gained popularity due to their reliance on multiview feature extraction and matching [40][41][42].However, for wheat seed accessions characterized by small size, overall color similarity, and extremely similar texture, these mainstream 3D reconstruction algorithms pose challenges [43,44].The difficulty in extracting phenotypic features of wheat seeds has led researchers to seek alternative methods, such as employing convolutional neural networks (CNNs) to increase the number of feature points extracted or strengthen the association between a few feature points [45,46].In pursu ing these alternatives, researchers often circumvent the time consuming and errorprone calibration tasks typically associated with traditional methods.However, it all became easier when a set of adsorption, rota tion, and image capture platforms for wheat seeds was built.With the platform completely fixed, it was only necessary to capture a set of calibration chessboard images, eliminating the need for additional work.A custom rotation model based on platform rotation was designed, ensuring accurate calibration.A critical aspect of the 3D reconstruction process is the fitting of the rotation axis, as illustrated in Fig. 7.The procedure involves 4 steps: (a) generating a rotation trajectory for the same corner, (b) fitting the rotating space circle, (c) calculating the center of the space circle, and (d) fitting the axis of rotation using the center of rotation at various points.This concise and systematic approach ensures accurate alignment of the rotation axis, which is paramount for reliable seed phenotyping and analysis.The smooth morphology and yellow phenotypic color of wheat seeds, which pose challenges for conventional 3D reconstruction algorithms [32], have become the strength of the proposed method.Owing to the completely enclosed morphological characteristics of wheat seeds, the surface can be easily reconstructed with a sophisticated calibration algo rithm.This approach overcomes the limitations of existing 3D reconstruction methods and provides a promising alternative for seed phenotyping applications.

Definition of a new access to gain genetic variation
It is well established that phenotypic variance can be decom posed into genetic variance and environmental error vari ance.The goal of this study is to obtain a concise formula that captures a factor of genetic variance associated with the presence of parent and offspring while excluding environ mental error variance.By applying an engineering treatment of truncation error, the mean phenotypic variance of the 2 parents was calculated and subsequently subtracted from the phenotypic variance of the offspring.The resulting value represents the difference that can be observed from parents to offspring.To eliminate the effects of measurement units, the result was further divided by the mean value of the 2 parents.
Existing parameters that respond to genetic characteristics, such as heritability and combining ability, are available but often require integration with molecular marker techniques for analyzing genotypically distinctive features [47,48].In order to examine genetic changes more closely from parents to offspring, this study focused on phenotypic data and sought to eliminate the interference of environmental variation by proposing the GVF.One limitation of this approach, however, is the insuffi cient research on genetics within the scope of this study.This investigation has provided an enlightening pathway for exam ining genetic variation based on engineering ideas, but further research on genetic correlations is necessary, utilizing the mul tidimensional phenotypic traits extracted.

More reasonable approach to genetic variation through diverse traits
Wheat seeds are small, and their phenotypic traits are not easily accessible, resulting in limited measurable traits through man ual methods.Traditionally, grain traits were assessed by mea suring protein content after crushing, which is a destructive and irreversible measurement.In recent years, valid traits have been obtained through spectroscopic analysis, though these methods entail high costs and require extensive analysis or training of spectral data [49,50].In contrast, the present study utilizes a set of digital images to model wheat seeds compre hensively and accurately.The low cost and nondestructive nature of this method serve as notable advantages.Furthermore, this approach emphasizes the provision of multidimensional traits that are difficult to obtain via manual measurement.When breeders examine wheat seeds, they may make genetic judg ments based on seed head size and ventral groove morphology, which are challenging to measure accurately and easily.This study proposes a method for assessing genetic variation based on multidimensional traits, enabling a more comprehensive and quantitative analysis of wheat seeds using phenotypic traits such as volume, surface area, and the J index.
Undoubtedly, the accuracy of multidimensional traits mea surement is directly related to the assessment of genetic varia tion.Nonetheless, due to the difficulty in measuring phenotypic traits of wheat seeds, the accuracy assessment of the model poses a challenge.In this study, manual measurements of length, width, and thickness were employed to evaluate model preci sion.Given the substantial error associated with manual mea surements, only the R value for length (as calipers can easily grip both ends of the wheat) and the RMSE for length, width, and thickness hold referential significance.The results corrob orate the feasibility of the 3D reconstruction model.In the future, more precise yet timeconsuming and costly 3D mea surement methods, such as CT scanning, can be used for accu rate evaluation of the multidimensional traits of wheat seeds, thereby serving as a basis for comparison with the model  outcomes developed in this study.It is believed that multidi mensional traits will play an increasingly prominent role in the assessment of seed genetic variation.

Conclusion
A reference pathway was presented that uses imagebased 3D reconstruction for multidimensional traits measurement and genetic variation assessment with 40 wheat seed image sequences and less than 12 checkerboard images.Rotary axis calibration algorithm was used for seed 3D reconstruction, and 9 traits includ ing length, width, thickness, roundness, surface area, volume, projection area, cardioid area, and J index, were extracted from the 3D model.For accuracy assessment, the correlation coefficient of length is 0.91, and the RMSEs of length, width, and thickness are all less than 0.3 mm.For genetic variation assessment, PCVs among all the traits show significance of multidimensional traits, as seed volume (22.4%), cardioid derived area (16.97%), and max imum projection area (14.67%).ANOVA shows a highly sig nificance difference among all accessions.The results of GVF innovatively reflect the connection between genotypic variance and phenotypic traits from parents to offspring.These results demonstrate the feasibility of imagebased reconstruction for measuring multidimensional traits and assessing genetic variation for wheat seeds without any manual intervention or environmental error.Future studies can apply imagebased 3D reconstruction algorithms to genetic variation analysis of other crops and traits, and combine them with genotyping studies to better serve agri cultural breeding.

Fig. 1 .
Fig. 1.General schematic diagram of the 3D construction.The figure presents the 3D model reconstruction process in order of the experiment, which is divided into 3 parts.

Fig. 3 .
Fig. 3. Diagram of assessment of the genetic variation.The assessment methods for genetic variation can be mainly divided into 3 parts in a progressive relationship: PCV calculation, ANOVA (including variance analysis and clustering), and defined GVF calculation.

Fig. 4 .
Fig. 4. (A to D) Comparison of wheat kernel morphologies between reconstruction and manual measurement.

Fig. 5 .
Fig. 5. (A to F) Violin plots of the 3 traits with the highest PCV values.Based on the ranking of phenotypic coefficient of variation, the traits with the highest values for volume, projection area, and cardioid area were selected.Violin plots were then generated for these traits for 7 identical progenies and 2 different groups of progenies.

Fig. 6 .
Fig. 6. (A to D)Clustering scatter plots and evaluation of 3 different clusterers: K-means, hierarchical, and DBSCAN.Both K-means and hierarchical approaches exhibit favorable clustering performance.

Fig. 7 .
Fig.7.Results of the rotational axis modeling.A total of 28 corner points were randomly selected, and the rotation axis was fitted according to the trajectory of the corner points' rotations.

Table 2 .
Statistical characteristics of the quantitative traits

Table 3 .
Statistical characteristics of the quantitative traits

Table 4 .
Statistical characteristics of the quantitative traits feasibility of the 3D reconstructionNote: F 1 to F 7 represent 7 different varieties of the studied plant.The percentages indicate the coefficient of genetic variation for each quantitative trait in each variety. the