## 2 Materials and Methods
### Acquisition of Image Information and Extraction of External Characteristics  
For machine vision technology, we independently constructed a system to acquire image information (IIAS) (Figure 1). The system consists of a GigE camera (DFK 33 GP006, Imaging Source, Germany), a camera lens (M0814-MP2, F1.4, f8 mm 2/3, China), an experimental box, a tray, two ring light sources (24V/580 mA), two striped light sources (24V/580 mA), and a computer equipped with \"IC capture\" image acquisition software and MATLAB R2018a software (MathWorks Inc., Natick, MA, USA). Combined graphical programming with the MATLAB Toolbox was used to extract external characteristics of the sample image.  
The camera was calibrated using a calibration board with 110 mm squares and the Computer Vision System Toolbox 8.1 in MATLAB software. Camera intrinsics and camera extrinsics were acquired. The Image Processing Toolbox 10.2 in MATLAB was used to extract fruit characteristics of pomelo, including pixel values for length and width. Pixel values were transformed into millimeter values based on the camera intrinsics and camera extrinsics [22], and these millimeter values for length and width were used to estimate volume and mass. Thus, the external characteristics of honey pomelo were estimated based upon the image information captured by the image acquisition system [23].  
Each sample was considered a similar ellipsoid. The volume estimation formulated in Equation (2) for an ellipsoid (\(V_{ellipsoid}\)) is a modification of the volume of a sphere (\(V_{spere}\)) presented in Equation (1).  
\[V_{sphere}=\frac{4}{3}\pi r^{3}, \tag{1}\]  
\[V_{ellipsoid}=\frac{4}{3}\pi\frac{L}{2}\frac{W}{2}\frac{H}{2}\approx\pi\frac{LW ^{2}}{6}, \tag{2}\]  
For a sphere, the length (\(L\)), width (\(W\)), and height (\(H\)) are equal to the radius (\(r\)), so the volume of an ellipsoid can be calculated from \(L\), \(W\), or \(H\), as shown in Figure 2a. When the volume was estimated, each section was regarded as a cone frustum, with the top and bottom areas were considered as a standard circle, and \(W\) and \(H\) set to the same value (Figure 2b).  
Figure 1: System to acquire image information.  
As shown in Figure 2, to better approximate the shape of the samples, the volume of the ellipsoid can be estimated by summing the volumes of an individual cone frustum [24]. The volume of each individual cone frustum and ellipsoid can be calculated using the following equations [21]:  
\[V_{j}=\frac{1}{3}\pi\Delta\textbf{l}\bigg{(}(\frac{W_{bj}}{2})^{2}+\frac{W_{bj}W _{tj}}{4}+(\frac{W_{tj}}{2})^{2}\bigg{)} \tag{3}\]  
\[V=\sum_{j=1}^{n}V_{j}=\sum_{j=1}^{n}\frac{\pi\Delta L}{12}(W^{2}{}_{bj}+W_{bj}W _{tj}+W^{2}{}_{tj}), \tag{4}\]  
where \(W_{bj}\) is the diameter of the bottom circle, in mm; \(W_{tj}\) is the diameter of the top circle, in mm; \(\Delta L\) is the height of the cone frustum, in mm; \(V_{j}\) is the volume of a cone frustum, in cm\({}^{3}\); and \(V\) is the estimated volume, in cm\({}^{3}\).  
In 2005, [PERSON] and [PERSON] found a high correlation between the mass and volume of apples with a high coefficient of determination [25]. This method used Equation (5) for the linear correlation between \(M_{acc}\) and \(V_{acc}\). The calculated k and b represent the slope and the intercept, respectively, which were utilized to calculate \(M\) in Equation (6).  
\[V_{acc}=kM_{acc}+b, \tag{5}\]  
\[V=kM+b, \tag{6}\]  
where \(M\) is an estimated value of mass, in g; \(M_{acc}\) is the accurate measured value of mass, in g; and \(V_{acc}\) is the accurate measured volume, in cm\({}^{3}\).