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- Open Access

# A method to calculate the number of wheat seedlings in the 1st to the 3rd leaf growth stages

- Tao Liu
^{1}View ORCID ID profile, - Tianle Yang
^{1}, - Chunyan Li
^{1}, - Rui Li
^{1}, - Wei Wu
^{1}, - Xiaochun Zhong
^{2}, - Chengming Sun
^{1}Email author and - Wenshan Guo
^{1}Email author

**Received:**12 November 2017**Accepted:**12 November 2018**Published:**16 November 2018

## Abstract

### Background

The number of cultivated wheat seedlings per unit area allows calculation of plant density. Wheat seedling density provides emergence data and this is useful for improving crop management. The number of wheat seedlings is typically determined by visual counts but this is time-consuming and laborious.

### Results

We obtained field digital images of 1st to 3rd leaf stage wheat seedlings. The seedlings were extracted using an image analysis technique that calculated the coverage degree of the seedlings and the number of angular points of overlapping leaves. The wheat seedling quantity estimation model was constructed using multivariate regression analysis. The model parameters included coverage degree, number of angular points, variety coefficient, and leaf age. Introduction of the number of angular points increased the accuracy of the single coverage degree model. The R^{2} value was consistently > 0.95 when the model was applied to different varieties, indicating that the model was adaptable for different varieties. As the leaf stage or density increased, the accuracy of the model declined, but the minimum R^{2} remained > 0.87, indicating good adaptability of the model to seedlings with different leaf ages and densities.

### Conclusions

This method is an effective means for counting wheat seedlings in the 1st to the 3rd leaf stages.

## Keywords

- Wheat seedling numbers
- 1st to the 3rd leaf stages
- Image processing
- Models
- Multivariate analysis

## Background

Wheat yield and quality are affected by planting density [1, 2]. An optimal density of wheat seedlings provides the best canopy structure and yield. Determining the number of wheat seedlings per unit area provides information on seedling emergence and is the basis for subsequent cultivation and management [3]. The number of seedlings is usually determined manually but manual count is laborious.

Image analysis techniques have been applied to several aspects of plant production. Common applications include estimation of crop biomass [4], diagnosis of nutritional status [5], analysis of growth [6], monitoring of fertility processes [7], analysis of crop structure [8], and monitoring of diseases, insects, pests, and weeds [9, 10]. Image analysis has also been used to study plant quantitative traits [11, 12], such as fruit counts [13, 14], crop grain counts [15], and pest counts [16]. For the wheat crop, some researchers analyzed the phenotypic traits by image processing technology [17, 18]. There are, however, few reports on the use of image analysis for wheat seedling counts. Recently, researchers have proposed a method for wheat plant counting at the emergence stage based on high spatial resolution RGB images taken from the ground level either from a rover system or from hand held cameras [19]. For reaching the high throughput required for field phenotyping, Jin et al. [20]. proposed a plant counting method from very low altitude unmanned aerial vehicle (UAV) imagery. Although these studies are very useful at the emergence stage of wheat crops, it may be unable to count plants at other leaf stages. Wheat seedlings are not as regular in shape as crop grains or fruits. As a result, overlapping objects are difficult to separate. For the reason of curled leaves, the posture of seedlings are diverse. It also add to the difficulty of segmentation. Finally, there are differences between different varieties of wheat seedlings. Therefore, the image segmentation and counting methods used in previous studies are not useful for counting wheat seedlings.

We optimized the skeleton structure of wheat seedlings using the freeman chain code [21]. Wheat seedlings in the 1st leaf stage were reconstructed into segments to accurately identify each wheat seedling and to complete counting [22]. However, this counting method was restricted to wheat at the 1st leaf stage, the individuals of which can be easily overlooked. Studies on seedling emergence are generally performed during the 1st to the 3rd leaf stages. This provides knowledge of the areas where seedlings are at low density and facilitates additional seeding. In this study, an image analysis technique was used to study methods for rapidly assessing seedling quantity during the 1st–3rd leaf stages, and to analyze differences in the counting of wheat seedlings of different varieties, different leaf ages, and different planting density. We used these data to construct a model for estimating the number of wheat seedlings.

## Methods

### Field experiment and image acquisition

^{−1}. Here, 50%, 10%, 20%, and 20% total nitrogen treatments were applied at the sowing, tillering, jointing, and booting stages, respectively. As noted in Table 1, three common seedling types were selected for the experiments. Coverage of these wheat varieties with different seedling types is different. Coverage of lax seedlings is more than the half erect seedlings when the numbers of leaves are the same, and coverage of erect seedlings is the minimum among these three seedling types [23]. So, the variety parameters (

*Va*) were selected to reduce the impact of the coverage difference among varieties.

Basic information of the experiments

Cultivars | Seedlings type | Density (10 |
---|---|---|

YM23 | Half erect | 75 |

150 | ||

225 | ||

300 | ||

HM7 | Lax | 75 |

150 | ||

225 | ||

300 | ||

YF4 | Erect | 75 |

150 | ||

225 | ||

300 |

### Extraction of target area

- (1)The white quadrangles in the original images were extracted using Eq. 1. With F(x, y) as the white quadrangle, the color components of red, green, and blue in the RGB images are represented by r, g, and b, respectively. The parameters in Eq. 1 were got by color Features of white quadrangles, wheat seedlings, soil and straws.$${\text{F}}\left( {{\text{x}},{\text{y}}} \right) = \left\{ {\begin{array}{*{20}l} {r\left( {x,y} \right) + g\left( {x,y} \right) + b\left( {x,y} \right) > 2.1} \hfill \\ {r\left( {x,y} \right) - b\left( {x,y} \right) < 0.05} \hfill \\ \end{array} } \right\}$$(1)
- (2)Four inflection points of the white quadrangle were extracted. The curvature of the boundary points of the white quadrangle were calculated using Eq. 2, and the 4 angular points were acquired through the variations of the curvature.
*C*_{(k,i)}represents the k neighborhood chain code at the boundary point I;*θi*is the difference of the tangent inclination at the boundary point; and*φ*_{i}is the preliminary curvature at the boundary point i. The preliminary curvature value*φ*_{i}of the inflection point and its nearby points were relatively large. For this reason, the curvature value*e*_{i}represents the inflection point. k is the chain code of the pixel.$$\left\{ {\begin{array}{*{20}l} {\uptheta_{i} = \left| {C_{{\left( {k, i + \frac{k}{8}} \right)}} - C_{{\left( {k,i} \right)}} } \right|} \hfill \\ {\varphi_{i} = \left\{ {\begin{array}{*{20}l} {\uptheta_{i} } \hfill & {\uptheta_{i} \le k /2} \hfill \\ {k -\uptheta_{i} } \hfill & {\uptheta_{i} > k /2} \hfill \\ \end{array} } \right.} \hfill \\ {e_{i} = \varphi_{i} \mathop \sum \limits_{j = - 1}^{1} \varphi_{i + j} } \hfill \\ \end{array} } \right.$$(2) - (3)For the image perspective transformation, the different imaging positions distorted the white-quadrangle area which could influence post-processing. Therefore, a perspective transformation was applied to the images using Eq. 3. The point
*u*,*v*was at the right side of the original image. The coordinates after transformation were*x*=*x*′*/w*′,*y*=*y*′*/w*′. The matrix indicates linear transformation and translation. Equation coefficients were solved using the 4 known points.$$\left[ {x^{\prime } ,y^{\prime } ,w^{\prime } } \right] = \left[ {u,v,w} \right]\left[ {\begin{array}{*{20}c} {a_{11} } & {a_{12} } & {a_{13} } \\ {a_{21} } & {a_{22} } & {a_{23} } \\ {a_{31} } & {a_{32} } & {a_{33} } \\ \end{array} } \right]$$(3) - (4)
For image cutting, the original white quadrangle was converted to a square in the transformed image. The target area is the inside of the white quadrangle. All the target areas were changed to 800 × 800 pixels.

The extraction results of measurement region are shown in Fig. 2. The white quadrangles in the original images (Fig. 2a) were extracted successfully (Fig. 2b), and four inflection points of the white quadrangle were extracted successfully by the boundary curvature (Fig. 2b). Perspective transformation was solved by 4 known points in Fig. 2b, and the transformative image is shown in Fig. 2c. A 1-m^{2} region was obtained after cutting processing (Fig. 2d). The distortion of the image caused during the photography could be eliminated properly. The results showed that a normative 1-m^{2} region could be obtained accurately by the white squares and image processing methods in Sect. 2.2.

### Extraction of wheat seedlings

### Extraction of characteristic values

*Ix*,

*Iy*is the grayscale value of the image; w(x, y) is the window function; and R is the response function of angular points [25]. When the displacements of the window along x and y direction were

*u*and

*v*, respectively, the grayscale change can be given by Eqs. (6, 7).

*E*(

*u*,

*v*) will change significantly how regardless of the (

*u*,

*v*) do change, these points are corner points. The value of

*M*is the determining factor in corner point detection. Hence, the function of corner can be expressed as

*det*(

*M*) is the determinant of

*M*,

*trace*(

*M*) is the trace of

*M. k*is constant, and it takes 0.04 here.

*k*is and empirical constant, it takes 0.04–0.06. It depends on the size of the image.

### Influence of leaf morphology on coverage degree and the number of angular points

Normally, the accuracy of wheat seedling estimation is not high when only use coverage alone to model. This is mainly due to the overlapped and curled leaves. Leaves in the images are either independent or overlapping. As shown in Fig. 4, when four identical leaves were present in the same area in the form of non-overlapped, slightly overlapped, and highly overlapped, the coverage degree decreased, and the number of angular points increased. For a given number of leaves, the coverage degree and the number of angular points were negatively correlated. Curling of leaf blades affects the degree of coverage. Because of leaf curling, the number of angular points increased while the coverage degree decreased (Fig. 5). Thus, the number of angular points is an important parameter reflecting the overlap of wheat seedlings and the curling of leaves. Combining the number of angular points with coverage degree can improve the accuracy of wheat seedling estimation.

### Model construction

The datasets (images) were separated into two sub-datasets for model training (720 observations in Huaian) and model validation (720 observations in Yangzhou). As the first step for model calibration, correlation analysis was performed between coverage degree (*Co*) and the number of wheat seedlings. The number of angular points (*Ha*) was also increased with the number of wheat seedlings. As the relationship between *Co* and seedlings number was found to be significantly different among leaf stages and varieties, the parameters of leaf age (La) and variety (Va) should be considered to count seedlings number more correctly. Thus, the stepwise multiple linear regression (SMLR) analysis was adopted to calibrate models to count the number of wheat seedlings by using *Co*, *Ha*, La and Va as predictor variables. SMLR method is based on the assumption that linear relationship exists between the number of wheat seedlings and Co. The performance of model equations derived from SMLR analysis was evaluated by the coefficients of determination (R^{2}), adjusted R^{2} (A-R^{2}), the root mean square error in prediction (RMSE), and the relative error in prediction (REP). R^{2} and RMSE were used to describe the stability of the model and the mean deviation between the measured value and the true value. Adjusted R^{2} and REP were used to evaluate the prediction accuracy of the model. In addition, variety, leaf age, and density were verified.

## Results and analysis

### Extraction of wheat seedlings

### Single-factor coverage degree model

^{2}of the estimation model reached a peak at the 1st stage, but declined with an increase in density or leaf age. R

^{2}ranged from 0.57 to 0.89. Even though the coverage degree can be used to predict trends in the number of wheat seedlings, the accuracy was relatively low, especially during the late growth stage and under conditions of high seedling density. The results indicate that there are large differences among the estimation models at different leaf ages when only the coverage degree is used to construct the model. These differences will complicate applications.

### Multi-factor comprehensive model

*Ha*) with the coverage degree (

*Co*), and using the data of 3 varieties at the 1st, 2nd, and 3rd stages, an estimation model was constructed for wheat seedlings of different varieties and with different leaf ages (

*La*) using SMLR (Table 2). Compared with estimation using only

*Co*, the introduction of Ha significantly increased the R

^{2}value and lowered the RMSE and Rep values. The models in Table 2 could get high R

^{2}(more than 0.95) and low RMSE (less than 18) when all the data of sowing densities was pooled together to calibrate and validate the model. The results showed that the proposed angular points could reduce the influences of overlapped leaves and distorted leaves when estimating seedling numbers by the coverage degree. However, the estimation model of different varieties and leaf ages varied, which does not support its application.

Model equations for estimating seedling number (SN) of different leaf ages using coverage degree and angular points

Varieties | La | Models | R | Adjusted-R | RMSE | Rep (%) |
---|---|---|---|---|---|---|

YM23 | 1 | SN | 0.9867 | 0.9864 | 10.31 | 7.72 |

2 | SN | 0.9781 | 0.9775 | 12.16 | 8.79 | |

3 | SN | 0.9706 | 0.9698 | 12.98 | 8.91 | |

HM7 | 1 | SN | 0.9765 | 0.9759 | 11.86 | 9.22 |

2 | SN | 0.9611 | 0.9601 | 13.13 | 10.63 | |

3 | SN | 0.9508 | 0.9495 | 17.32 | 12.49 | |

YF4 | 1 | SN | 0.9806 | 0.9801 | 9.67 | 8.12 |

2 | SN | 0.9713 | 0.9705 | 12.59 | 9.19 | |

3 | SN | 0.9549 | 0.9537 | 16.39 | 11.31 |

*Ha*and

*Co*coefficients declined with increasing leaf age. To normalize the model, the model transition from the 1st to the 3rd stage was transformed into

*Va*is the variety coefficient,

*Ha*is the overlap degree of leaves,

*La*is leaf age,

*a*,

*b*and

*c*are the coefficient. The value of

*La*should be confirmed after investigating the proportion of different leaf stages seedlings, and it’s a non-integer. Based on the wheat seedling data of different varieties and leaf ages,

*a*= 0.44,

*b*= 110.43,

*c*= 3.35, and

*d*= 1.11, which were obtained by regression analysis. The modeling and validation results of the different varieties are shown in Table 3. The R

^{2}value was always > 0.95, and RMSE remained in a small range in both the modeling process and validation process. Adjustment of the variety parameter

*Va*made the difference insignificant when the model was applied to different varieties. Compared with separate modeling, the accuracy of the overall model declined slightly, but its application scope and period increased.

Calibration and validation results of the seedling number estimation model (Eq. 9)

Varieties |
| Training | Validation | ||||||
---|---|---|---|---|---|---|---|---|---|

R | A-R | RMSE | Rep (%) | R | A-R | RMSE | Rep (%) | ||

YM23 | 1.05 | 0.9626 | 0.9620 | 18.4 | 8.17 | 0.9386 | 0.9370 | 20.27 | 9.72 |

HM7 | 0.86 | 0.9533 | 0.9525 | 21.84 | 12.31 | 0.9183 | 0.9162 | 22.23 | 12.79 |

YF4 | 1.12 | 0.9537 | 0.9529 | 23.06 | 14.25 | 0.9129 | 0.9106 | 22.99 | 15.01 |

### Validation of leaf ages and densities

^{2}of 75 × 10

^{4}density was always > 0.95, while the R

^{2}of 300 × 10

^{4}density was approximately 0.9 (Fig. 8). The accuracy in the 1st leaf stage was the highest, and its mean value was > 0.95. Accuracy was lowest in the 3rd leaf stage, with a mean R

^{2}value of 0.91, and the R

^{2}values of 225 × 10

^{4}and 300 × 10

^{4}were < 0.9. The above R

^{2}values were very high and the value of RMSE was small, indicating the reliability and high precision of the results. These results indicate that it is best to get images at the 1st or 2nd leaf stages, especially when plant densities are high.

## Discussion

A multivariate model consisting of coverage degree, angular points, leaf age and variety coefficients was used to estimate the quantity of wheat seedling (Eq. 9). The coverage degree was selected as the main parameter of this model because it is highly correlated with the number of wheat seedlings. The changes in the quantity can be reflected to some extent by solely using coverage degree, which is similar to previous results where coverage degree was used to estimate agronomic parameters [6, 26]. However, the overlap and degree of leaf curl were not considered in those studies. In the present study, the number of angular points strongly reflected the overlap and degree of leaf curl thereby improving the accuracy of estimation compared to a system that solely uses the coverage degree.

*Ha*) proposed in this study attenuate the increase in errors caused by plant density. As presented in Fig. 9, the effect of Ha on improving the accuracy increases with plant density. Although the accuracy of the proposed model decreased slightly with plant density, a low RMSE was maintained to ensure the reliability of the estimation results.

^{2}increases consistently when Ha is used to count seedlings. The effect of Ha on improving the accuracy increases with leaf age. Although the accuracy of the proposed model decreased slightly with leaf age, a low RMSE could be maintained to ensure the reliability of the estimation results. Thus, the model can be applied to the quantity estimation of wheat seedlings of different varieties from the 1st to the 3rd leaf stages.

^{2}white square and an image capturing device (digital camera, smart phone, and surveillance camera are all practicable) can be used when original images are needed.

## Conclusion

A wheat seedling estimation model was constructed based on coverage degree and angular points. Its application scope was expanded, and the application period was prolonged using a variety coefficient and leaf age coefficient. The new model explained the unsatisfactory accuracy of a previous estimation model that only used degree of coverage. The new model was improved by the introduction of angular points. The new model could be used to estimate the quantity of wheat seedlings in the 1st to the 3rd stages, and it provides a basis for timely seedling supplements and subsequent crop management.

## Declarations

### Authors’ contributions

TL and WG performed all experiments and analyzed the data. TY, XZ and RL performed some experiments and analyzed the data. WW and CL contributed the conceptual design and provided supervision. LT and CS wrote the main manuscript text and prepared all figures. All authors were involved in preparing and revising the manuscript. All authors read and approved the final manuscript.

### Acknowledgements

We thank LetPub (www.letpub.com) for linguistic assistance during manuscript preparation.

### Competing interests

The authors declare that they have no competing interests.

### Availability of data and materials

All data analyzed during this study are presented in this published article.

### Consent for publication

Yes. All authors have seen the manuscript and approved to submit to your journal. All authors agree to publish.

### Ethics approval and consent to participate

Not applicable.

### Funding

This research was mainly supported by the National Key Research and Development Program of China (2016YFD0300107), the National Natural Science Foundation of China (31701355, 31771711, 31671615), China Postdoctoral Science Foundation (2016M600448), the Yangzhou Science Foundation for Excellent Youths (YZ2017098) and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

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## Authors’ Affiliations

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