# Method for Volume of Irregular Shape Pellets Estimation Using 2D Imaging Measurement
## 5 Conclusions  
We have provided the results of experiments with the proposed method for evaluation of pellet volume using two-dimensional image processing. After completion of the first experiments it was determined that approximation of irregularly shaped pellets using circular geometric shapes presents a larger amount of error than approximation using ellipsoids. Respectively, when sphere shape approximation is used, the average absolute error is up to 1.258 cm\({}^{3}\) (\(\sigma\) = 0.687), while when using ellipsoid, 0.153 cm\({}^{3}\) (\(\sigma\) = 0.171). It is more than eight times the difference. Additionally, it must be noted that irregularly shaped pellets were evaluated.  
The standard method, which is not precise when irregular shapes are being evaluated, was evaluated according to literature sources. Evaluation of pellet volume by using its cross-section layers whose height is limited by the lowest possible height of scanning equipment provides better results of volume calculation. It was determined that the shape of an elongated ellipse is characteristic to a monoammonium phosphate pellet. Additionally, the most common met irregularities of pellet shape (notches) were evaluated. The proposed method allows for the elimination of discrepancies by evaluating the envelope line of the region limited by the pellet silhouette. After improving approximation of the cross-section using the ellipse geometric shape according to convexity of area limited by the pellet's silhouette, better results were achieved. This allowed us to reduce relative error from 10.20% to 2.50%. However, in order to achieve these results, it is very important that the more characteristic region of the scanned pellet should be evaluated. When the pellet is rotated by 90\({}^{\circ}\) from position in which this pellet limits the largest area in relation to the field of view of the video camera, the error is only up to \(<\) 2% of its average volume. The proposed method of pellets analysis makes it possible to achieve high results of indirect measurements with an error of less than 2%. This provides an opportunity for continuous monitoring of production. To ensure reliable results, they can be compared with the data of measurements performed by the direct measurement method (the latter are performed significantly less frequently). In further works it is planned to carry out experiments with pellet ducts of different shapes, which are used to transport pellet for testing.  
Conceptualization, D.A. and A.L.; methodology, A.L. and D.A.; software, A.L. and D.N.; validation, A.L., M.Z., and V.M.; formal analysis, R.S. and J.J., visualization, M.Z., D.N., and D.K.; investigation, A.V., V.M., J.J., and D.K.; resources, A.L. and A.V.; data curation, A.L.; writing--original draft preparation, D.A. and A.L.; writing--review and editing, V.M., D.K. and R.S.; supervision, D.A.; funding acquisition, A.V., M.Z., and D.N. All authors have read and agreed to the published version of the manuscript. This research received no external funding. The authors declare no conflict of interest. The authors declare no conflict of interest.