## 3 Results and Discussion: Qualitative and Quantitative Tool Comparison
### Design of a Synthetic Quality Metric for Software Selection  
In order to establish a unique metric for software evaluation, a synthetic metric was designed to qualify and model the quality of the software. Taking into account the mean values and standard deviations of the metrics previously evaluated (shown in Figures 4-8), we obtained the coefficient of variation as \(\Delta metric_{i}/metric_{i}\) and designed the synthetic metric as a function of this coefficient of variation (CV) for each metric, considered as the standard deviation (\(\Delta metric_{i}\)) divided by the mean value (\(\overline{metric_{i}}\)). This is shown in Equation (1):  
\[\frac{\Delta x}{x}=f(\frac{\Delta Sph}{Sph},\frac{\Delta Fla}{Pla},\frac{ \Delta Lin}{Lin},\frac{\Delta Anti}{Ani},\frac{\Delta Cur}{Cur}) \tag{1}\]  
where \(Sph\) stands for sphericity, \(Pla\) stands for planarity (or flatness), \(Lin\) stands for linearity, \(Anti\) stands for anisotropy, and \(Cur\) is curvature. The results of the relative values for each metric are in Table 3. Figure 10 shows the correlation among the CVs of the point cloud quality metrics. Here, we can see that anisotropy is one of the outlier metrics in this set. Figure 9: Visual comparison of a detailed colored point cloud with the different selected tools. We propose the design of the synthetic metric as a multilinear composed variable in the form exposed in Equation (1). In a first approach, we used the summation of all of these CV values. Furthermore, we used Table 1 considering as weighting factors whether the software did not have an API (85%) and whether it was not free software (85%). After using this procedure with the coefficients of variation, we developed a multilinear model taking the synthetic quality (SynthQ) metric as the dependent variable. In RStudio, we used the linear modeling (lm) function to compute this multilinear model. The result of that model is shown in Equation (2). Furthermore, Table 4 shows a summary of the whole multilinear regression study. \[SynthQ=1.243+1.450\cdot Sph-0.241\cdot Pla-0.141\cdot Cur \tag{2}\]  
As indicated in the explanation of the features, we can see that the Agisoft Metashape tool was the one that provided the best quality (as it provided a high number of points in Table 2), followed by DJI Terra and finally Pix4D Mapper, which was the one that obtained the worst result on that test. In this case, all these options required a license fee and here, we applied a payload. With our model, OpenDroneMap (ODM) appeared as the best option in terms of cost-benefit relationship, as shown in Table 5. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Software** & **Sph** & **Pla** & **Lin** & **Ani** & **Cur** \\ \hline Agisoft & 0.6219 & 0.5399 & 0.3951 & 0.1663 & 0.5087 \\ Pix4 DMapper & 1.3013 & 0.3427 & 0.4877 & 0.0968 & 1.2058 \\ ODM & 1.1353 & 0.3411 & 0.4440 & 0.1195 & 1.0314 \\ DJI Terra & 0.5373 & 0.4220 & 0.4314 & 0.1249 & 0.9475 \\ Meshroom & 1.0000 & 0.3006 & 0.4242 & 1.0000 & 1.0000 \\ Regard3D & 1.1324 & 0.3070 & 0.4261 & 0.0547 & 1.0644 \\ RealityCapture & 1.0639 & 0.5025 & 0.3620 & 0.0804 & 0.9373 \\
3 DF Zephyr & 1.2219 & 0.2856 & 0.4333 & 0.0725 & 1.1512 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Coefficients of variation (CV) for every metric and software tool. Figure 10: Correlation-graphic for all the CV values of the quality metrics. After conducting a comprehensive review of related works, we identified only one relevant paper [32]. This paper initiated a comparison of tools for agronomy point cloud representation, providing a foundational reference point for our research. To extend beyond the existing state of the art, we expanded and enriched this comparative analysis. Unlike the previous work, we incorporated additional tools and introduced quality metrics for a more nuanced evaluation of point clouds. Our dataset, acquired using a DJI Mavic 3M drone in the agricultural fields of El Puig, Valencia, Spain, offers a rich foundation for a meticulous assessment of software tools.