## 3 Evaluation of Budding Rate
### Identification of Cotton Plants  
To count the germination rate correctly, the cotton plants should be identified and extracted from the classification images correctly. A problem in counting (one isolated polygon composed of cotton pixels was consider as one cotton plant) the number of cotton plants is the overlap of leaves, which decreases the germination rate of cotton. The overlapping of leaves is a common scenario in observation, for codons present different growth status even if they have the same sowing date. Figure 2, a zoomed-in image subset from Figure 4, is presented to illustrate this problem. Figure 2a is the true-color image and 2b is the corresponding classification result. As shown in Figure 2a, the cotton plants can be clearly seen in the true-color image with a resolution of 5.2 mm, and the classification results are reasonable, as most of the cotton plants were correctly distinguished from the background objects. However, as the blue circles show in Figure 2b, some of the cotton plants are contiguous, meaning that a set of isolated points is recognized as one cotton plant; thus, the number of cotton plants is underestimated. Hence, before counting the number of the cotton plants, this problem should be fixed. If we consider the shape of the cotton plant to be a circle, with \(r\) as the radius of the circle., when two cotton plants with a radius of \(r\) are connected (not exactly overlapping), the maximal axis length of the shape composed by these two cotton plants is less than \(4r\), and the minimal axis length of the shape for the composed shape should be less than \(2r\). However, in practice, the ratio of overlapping is not fixed, and it is very difficult to describe it using a fixed formula. This study considers that for the cotton plant shape in the classified image, when the maximum axial length \(max\) is greater than \(3r\) and the minimum axial length \(max\) is less than \(\sqrt{3}/2\times r\), an overlap between the two cotton plants is identified. Equation (1) describes this further. \[\text{Cotton}_{\text{overlap}}=\left\{ \begin{array}{cc}\text{True},&L_{ max}>3r_{mean}\text{ and }L_{min}<\sqrt{3}/2\times r_{mean}\\ &\text{False},&\text{else}\end{array} \right. \tag{1}\]  
Figure 2: A zoomed-in image of the study region, the true color image (**a**) and classification results of cotton plants (**b**). \[r_{mean}=\sqrt{s_{max}/\pi} \tag{2}\]  
In Equation (1), \(L_{max}\) is the maximal axis length of the shape, \(L_{min}\) is the minimal axis length, \(r_{mean}\) is the mean radius of the cotton plant, and in Equation (2), \(S_{mean}\) is the mean area of the cotton plant. Determining the mean area of the cotton plant is difficult, because the size of the plant varies with growth time. Obviously, a fixed value should not be used. The cotton images from the validation areas shown in Figure 4 were selected. The pixel number of each cotton plant was counted, and cotton plants having a pixel number less than 3 were removed. Then, the frequency distribution chart of the number of pixels of the cotton plant was composed, as shown in Figure 3.  
As shown in Figure 3, the pixel distribution is similar to a gamma distribution; most of the cotton plants had a pixel number of less than 200, and no more than 10% of cotton plants had a pixel number greater than 200. Considering the fact that most of the cotton plants should not overlapping each other during the unearthed stage of germination, the area of cotton plants with the maximum possibility can be used as the mean area of the total cotton plant. Equation (3) depicts this point. \[S_{mean}=\frac{\sum_{p=P_{max}-10\%}^{P_{max}}{Num_{p}}}{N_{total}}*S_{GSD} \tag{3}\]  
In Equation (3), \(p\) is the frequency of the pixel number, \(P_{max}\) is the maximal frequency of the pixel number, \(Num_{p}\) is the number of pixels appearing \(p\) times, \(N_{total}\) is the total number of bins which meet the conditions.