# Determination of Seed Volume Based on Selected Seed Dimensions
## 1 Introduction  
Seeds constitute a large group of products that are processed and handled in agriculture and forestry, and in the food and transport industries. The physical properties of seeds influence operations such as sowing, harvest, storage, and transport. A thorough knowledge of the properties of the processed material is required to design technological and industrial operations [1, 2]. Seed volume is one such property, and it is used to divide seed batches into size classes. Seed volume plays a very important role in planning seed drying [3, 4], coating, dressing, and scarification operations [5, 6]. The characteristics of the processed granular material, including the volume of individual particles, have to be reliably determined before planning a research study. Particle volume affects the behavior of the entire batch of granular material. Three groups of methods are generally used to determine the volume of particles, including the seeds of crops, forest trees, and shrubs. In the first method, seed dimensions are measured, and seed shape is described with the use of simple geometric figures, such as a sphere, a spheroid, or a cylinder [6, 7, 8, 9]. The measured dimensions are substituted into general mathematical equations to calculate seed volume. The volume of seeds with a complex shape is determined with the use of parametric equations. A model of the corresponding geometric figure is built and used to calculate the seed parameters [10, 11, 12, 13]. The second group of methods relieson digital images and image-processing software to elicit information about the geometric properties of seeds [14; 15; 16; 17; 18; 19; 20]. An image provides two-dimensional information about the examined particle. To calculate the third dimension, the seed is rotated by 90\({}^{\circ}\) and an additional image is captured, or a system of mirrors is used to acquire two projections in an image. Multiple cross-sections of the analyzed particle embedded in a fixing material can also be photographed, and the resulting images can be used to build a 3D model [21; 22] to determine the particle volume. In the third group of methods, 3D scanners are used to generate a 3D model of the examined object [23; 24; 25; 26]. The model can be used to measure the geometric parameters of a particle, including its external dimensions and volume. However, this approach is laborious and time-consuming, and it requires specialist equipment and image processing software. The scanned object has to be fixed to a rotating stage with the use of glue or a pin. In a virtual model, glue and pins have to be removed, and the surface of the object at the point of attachment has to be modified. Most research studies rely on the first method, which is the easiest to use. In this approach, the basic geometric parameters of seeds have to be determined. The shape of the analyzed seed cannot always be described with a simple geometric figure, which is why the volume coefficient \(k\) is often calculated [8]. The volume coefficient is determined with the use of a glass pycnometer based on the relationship between the volume of liquid displaced by seeds and the reference volume of seeds. The reference volume of seeds is determined on the assumption that individual seeds are cuboids whose size is described by the measured parameters. Depending on the number of the measured dimensions, seed volume \(V\) can be calculated with one of the below equations:  
\[V=k\!\cdot\!a\!\cdot\!b\!\cdot\!c \tag{1}\]  
\[V=k\!\cdot\!a\!\cdot\!b^{2} \tag{2}\]  
\[V=k\!\cdot\!a^{3} \tag{3}\]  
where \(a\), \(b\), and \(c\) are the basic dimensions of a seed, measured perpendicular to each other, and the volume coefficient \(k\) has a different value in each equation. In this formula, seed shape does not have to be determined, and a corresponding geometric figure for mathematical calculations does not have to be selected.