# Non-Contact Tilapia Mass Estimation Method Based on Underwater Binocular Vision
## 3 Results
### Tilapia Mass Estimation  
To further validate the stability of the model, we used the body lengths of the acquired tilapia to input directly into the model. Different mass groups can be interpreted as tilapia at different growth stages. Comparisons were made by selecting the linear, power function, and quadratic term models. The estimated values of the corresponding mass groups for the three models are shown in Table 6. The evaluation metrics were root mean square error  
Figure 13: Quadratic term fit plots for different mass groups of tilapia. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Name**} & \multicolumn{2}{c}{**M1**} & \multicolumn{2}{c}{**M2**} & \multicolumn{2}{c}{**M3**} \\ \cline{2-6}  & **Equation (M=)** & \(\mathbf{R^{2}}\) & **Equation (M=)** & \(\mathbf{R^{2}}\) & **Equation (M=)** & \(\mathbf{R^{2}}\) \\ \hline Linear & \(1.427\times-99.372\) & 0.89 & \(2.565\times-260.41\) & 0.90 & \(6.939\times-1261.2\) & 0.89 \\ Exponential & \(1.639\times e^{0.028\times}\) & 0.99 & \(47.527\times e^{0.008\times}\) & 0.91 & \(27.002\times e^{0.012\times}\) & 0.86 \\ Logarithmic & \(142.08\ln(x)-603.06\) & 0.78 & \(558.96\ln(x)-2709.1\) & 0.89 & \(1886.9\ln(x)-9947.3\) & 0.90 \\ Power & \(3\times 10^{-5}\)x\({}^{2.966}\) & 0.99 & \(0.016\times^{1828}\) & 0.91 & \(2\times 10^{-5}\)x\({}^{1.124}\) & 0.87 \\ Quadratic & \(0.014\times^{2}-1.861\times+71.347\) & 0.99 & \(0.047\times^{2}-18.075\times+1991.7\) & 0.93 & \(-0.072\times^{2}+46.135\times-6564.2\) & 0.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of fittings of different models for tilapia mass. (RMSE), mean absolute error (MAE), and mean relative error (MRE), and their equations are as follows:  
\[\text{RMSE}=\sqrt{\frac{1}{n}{\sum_{i=1}^{n}{\left({y_{i}}-{\hat{y}_{i}}\right)}^{ 2}}} \tag{11}\]  
\[\text{MAE}=\frac{1}{n}{\sum_{i=1}^{n}{\left|{y_{i}}-{\hat{y}_{i}}\right|}} \tag{12}\]  
\[\text{MRE}=\frac{1}{n}{\sum_{i=1}^{n}{\left|{\frac{{y_{i}}-{\hat{y}_{i}}}{{y_{ i}}}}\right|}} \tag{13}\]  
In the above equation, \(n\) is the number of samples. \(y_{i}\) denotes the true value. \({\hat{y}_{i}}\) denotes the estimated value. Comparing the three tilapia mass estimation models, the RMSE ranged from 6.62 to 60.99 g. The lowest of these was the quadratic term model estimation results in M1, and the highest was the linear model estimation results in M3, with MAE ranging from 4.97 to 54.90 g. The lowest was still the quadratic term model estimation result in M1 and the highest was still the linear model estimation result in M3. It is not difficult to find that the linear model had poorer estimation results with \(R^{2}\) ranging from 0.89 to 0.90. Removing the group with the smallest mass, the MRE ranged from 5.74% to 9.40%. And the power function model performed better than the linear model in the small mass estimation group. The \(R^{2}\) was 0.87 to 0.99 and the MRE was 6.06% to 8.90%. The best prediction was made by the quadratic term model with an \(R^{2}\) of 0.91 to 0.99, and the MRE was also minimized to 5.34% to 7.25%. Finally, in this study, the mass of 10 tilapia whose images were acquired was estimated. After image enhancement, stereo matching, body length estimation, and mass fitting, we calculated the mass of tilapia. The results of the comparison between the manual measurements and the estimated mass of the final tilapia are shown in Figure 14. The \(R^{2}\) was 0.99, and the MRE was 5.90%. No significant difference was found between the artificially measured mass and the estimated mass, so the test proved that the method can be used for the mass estimation of tilapia. Although the experiments are affected by the water body environment with some differences in the results, we compared them with some existing methods in order to show the superiority of our approach. The methods we compared are the area- and area-squared-based mass estimation model [13] and the deep learning method using YOLOv4 DLN [6].