# Method for Volume of Irregular Shape Pellets Estimation Using 2D Imaging Measurement
## 1 Introduction  
The rapid application of modern technologies is evident in many various industries. The increasing performance of computer equipment and the wider realization of various theoretical mathematical calculations expands the possibilities of applications of equipment. The largest volumes of production are conditioned by application of cutting edge technical and scientific solutions in various fields of industry. The chemistry industry is no exception. The increasing demand of food supplies and scarcity of cultivated land is a reason for the wider application of fertilizers. Rational fertilization of cultivated land and optimal distribution across the surface of soil or insertion into soil results in better harvests. Therefore, there are specific requirements for the size and shape of fertilizer pellets. However, it is a huge task for manufacturers to assure the quality of fertilizers. As the fertilizer pellets are quite small (2-4 mm in diameter), it is difficult to evaluate their quality by using direct methods of measuring. With increasing productivity, the best tools for quality assurance are indirect methods of measuring that allow real-time evaluation of the quality of pellets [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13]. The technique of processing digital images provides results that are very similar to the results of control equipment based on direct measurements [14; 15; 16; 17; 18; 19]. A variety of image enhancement methods assure reliability of results [20]. A high frequency of discretization of production monitoring allows for a quick reaction to any production process deviations that manifest in changes of production parameters. Applied numerical intellect solutions simplify the preparation of equipment for work [21; 22]. One of the most important qualitative parameters used for the evaluation of pellets is their distribution according to size [23]. However, other parameters are not less important, such as: distribution according to roundness, elongation, compactness, uniformity index of pellets and so on [24]. According to the international standards of sampling and the evaluation of samples [25; 26; 27], the manufacturer strictly defines qualitative parameters related to other physical parameters. Round pellets and pellets that are categorized by nondispersive size distribution are more likely to be more evenly distributed during fertilization using an automatic spreader [28; 29]. Optimal spreading conditions are achieved with higher bulk density, because it creates further throwing distance of the pellets. Various fertilization quality assessment systems are installed depending on the type of spreader used [30]. However, it must be combined with optimal distribution interval of pellets--ideally, distribution interval deviates by \(\pm\)0.8 mm (width) from the average [31]. Additionally, the more the shape of the pellet is similar to an ideal circle, the longer the distance of its flight, because of its aerodynamic properties. Hardness of the pellet prevents the disks of the pellet spreader from breaking it apart [32]. One of the relevant problems related to using indirect measuring methods is the matching of the results to those from using direct methods. It is especially difficult to evaluate the pellets of irregular shape. According to the literature analysis, many various methods are used for scanning of pellets as well as recalculation of results. The main purpose of this article is to propose a fast method for evaluating the quality parameters of fertilizer pellets, which would ensure continuous quality control. This can only be achieved through indirect measurements. Digital image analysis allows for versatile and fast output analysis. However, there are problems with the evaluation of irregularly shaped pellets in two-dimensional images. This increases the discrepancy between the actual results and the results of the indirect measurement. In this work, the proposed method of evaluation of fertilizer pellets of irregular shape is via processing and analysis of digital images.