# Method for Volume of Irregular Shape Pellets Estimation Using 2D Imaging Measurement
## 3 Results
### Estimation of Pellet Volume by Dividing Them into Elliptical Layers
The average absolute error when layers are approximated as circles is 1.191 cm\({}^{3}\) (when the pellet is evaluated rotated by 90\({}^{\circ}\) from position, in which the pellet limits the largest possible area in relation to field of view of the camera), which on average represents \(<\) 9% of average volume of a pellet. Average squared deviation respectively was 1.38. While, when approximation of layers was carried out using the ellipse geometric shape, the average absolute error was 0.314 cm\({}^{3}\) (when the pellet is evaluated rotated by 90\({}^{\circ}\) from position, in which the pellet limits the largest possible area in relation to field of view of the camera) and it represents \(<\) 2% of average volume of pellet. Figure 14: (**a**) Models of analyzed pellets; (**b**) distinguishing of shape parameters of analyzed model of pellet. To evaluate the practical value of this method, measurements in a real production line were carried out. Measuring equipment, designed, manufactured and installed in previous works, with linear video camera, LED light and automatic subsystem of sampling was used [34]. Monoammonium phosphate samples (MAP) were analyzed during the experiment. Received results were compared to results received using the sieves method and the method of processing of scanned images (where pellets were approximated using ellipse) (Figures 16-18). Same samples were compared during measuring. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & & & & & & & & & \\ \hline \multirow{2}{*}{1} & \multirow{2}{*}{ \begin{tabular}{c} Largest area 1 \\ Rotated by 90\({}^{\circ}\) \\ \end{tabular}  } & \multirow{2}{*}{12.8} & \multirow{2}{*}{14.60} & \multirow{2}{*}{1.80} & \multirow{2}{*}{14.27} & \multirow{2}{*}{1.47} & \multirow{2}{*}{20.09} & \multirow{2}{*}{7.29} & \multirow{2}{*}{19.02} & \multirow{2}{*}{6.22} \\  & & & & & & & & & \\ \hline \multirow{2}{*}{2} & \multirow{2}{*}{ \begin{tabular}{c} Largest area 1 \\ Rotated by 90\({}^{\circ}\) \\ \end{tabular}  } & \multirow{2}{*}{13.6} & \multirow{2}{*}{14.94} & \multirow{2}{*}{1.34} & \multirow{2}{*}{14.69} & \multirow{2}{*}{1.09} & \multirow{2}{*}{19.56} & \multirow{2}{*}{5.96} & \multirow{2}{*}{19.3} & \multirow{2}{*}{5.7} \\  & & & & & & & & & \\ \hline \multirow{3}{*}{3} & \multirow{2}{*}{ \begin{tabular}{c} Largest area 1 \\ Rotated by 90\({}^{\circ}\) \\ \end{tabular}  } & \multirow{2}{*}{12.4} & \multirow{2}{*}{13.67} & \multirow{2}{*}{1.27} & \multirow{2}{*}{13.40} & \multirow{2}{*}{1.00} & \multirow{2}{*}{10.61} & \multirow{2}{*}{1.79} & \multirow{2}{*}{12.29} & \multirow{2}{*}{0.11} \\ \hline \multirow{3}{*}{4} & \multirow{2}{*}{ \begin{tabular}{c} Largest area 1 \\ Rotated by 90\({}^{\circ}\) \\ \end{tabular}  } & \multirow{2}{*}{15.8} & \multirow{2}{*}{14.70} & \multirow{2}{*}{1.10} & \multirow{2}{*}{14.60} & \multirow{2}{*}{14.20} & \multirow{2}{*}{15.45} & \multirow{2}{*}{0.35} & \multirow{2}{*}{14.51} & \multirow{2}{*}{1.29} \\  & & & & & & & & & \\ \hline \multirow{3}{*}{5} & \multirow{2}{*}{ \begin{tabular}{c} Largest area 1 \\ Rotated by 90\({}^{\circ}\) \\ \end{tabular}  } & \multirow{2}{*}{13.4} & \multirow{2}{*}{13.32} & \multirow{2}{*}{0.08} & \multirow{2}{*}{13.23} & \multirow{2}{*}{0.17} & \multirow{2}{*}{15.14} & \multirow{2}{*}{1.74} & \multirow{2}{*}{14.94} & \multirow{2}{*}{15.4} \\  & & & & & & & & & \\ \hline \multirow{3}{*}{6} & \multirow{2}{*}{ \begin{tabular}{c} Largest area 1 \\ Rotated by 90\({}^{\circ}\) \\ \end{tabular}  } & \multirow{2}{*}{14.6} & \multirow{2}{*}{15.00} & \multirow{2}{*}{0.40} & \multirow{2}{*}{14.87} & \multirow{2}{*}{0.27} & \multirow{2}{*}{17.46} & \multirow{2}{*}{2.86} & \multirow{2}{*}{17.06} & \multirow{2}{*}{2.46} \\  & & & & & & & & & & \\ \hline \multirow{3}{*}{7} & \multirow{2}{*}{ \begin{tabular}{c} Largest area 1 \\ Rotated by 90\({}^{\circ}\) \\ \end{tabular}