# Testing the Effectiveness of Voxels for Structural Analysis
## 3 Results
### Denoising
The images are fundamental to highlight the trend of the Gaussian distribution of the point in the comparison. In probability theory and statistics, **Gaussian distribution** (or a normal distribution) is a type of continuous probability distribution for a real-valued random variable. The Gaussian distribution represents a real-valued random variable with unknown distribution. Its importance is based on, among other things, the central limit theorem. This states that, under certain conditions, the average of many samples (observations) of a random variable with a finite mean and a finite variance is itself a random variable--its distribution converges to a normal distribution as the number of samples increases. Therefore, physical quantities that may be the sum of many independent processes (e.g., measurement errors) often have an almost normal distribution. The graph of the Gaussian distribution depends on two factors--the mean and the standard deviation. The mean of the distribution determines the location of the center of the graph, and the standard deviation determines the height and width of the graph. The height is determined by the scaling factor and the width is determined by the factor in the power of the exponential. When the standard deviation is large, the curve is short and wide; when the standard deviation is small, the curve is tall and narrow. All Gaussian distributions look like symmetric, bell-shaped curves. Even with a standard deviation of less than one centimeter, the profile arrangement uncovers inaccuracies where the geometric distribution of points appears disordered and erratic (Figure 2). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Object** & **Mean (mm)** & \
\begin{tabular}{c} **Standard** \\ **Deviation (mm)** \\ \end{tabular} &
\begin{tabular}{c} **Profiles Max** \\ **Distance (mm)** \\ \end{tabular} \\ \hline [PERSON] & 0.072848 & 0.034495 & 0.841 \\ \hline Masonry pillar & 0.002318 & 0.001413 & 18,530 \\ \hline [PERSON] & 0.0002883 & 0.000284 & 316,764 \\ \hline Samnitte tomb & 0.002230 & 0.011759 & 115,324 \\ \hline Chair & 0.0007 & 0.004 & 59 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean and standard deviation of each point cloud analyzed after the denoising. Figure 2: _Cont._  
These inconsistencies contribute to errors in the geometric reconstruction of the 3D mesh. The algorithm exhibits interesting performance with point clouds derived from objects made of non-cooperative materials or those featuring intricate geometries. Nevertheless, the restricted acquisition baseline presents a challenge, as inaccuracies or insufficient overlap led to excessively dense noise, topological inaccuracies, and overlapping areas. For the [PERSON] statue, a 3D mesh was constructed utilizing the Poisson surface reconstruction method in Meshlab 2023.12. Initially, normals for each point were calculated using default parameters prior to executing the reconstruction without any post-processing, preserving all settings at their defaults. This approach enabled a direct evaluation of comparison outcomes based on the raw data. The original and denoised point cloud meshes were analyzed under consistent conditions, focusing primarily on the influence of denoising on the geometric approximation during the meshing process and whether improving the geometric precision of the point cloud enhances the overall workflow. The initial phase involved examining topological inaccuracies within the meshes using Meshmixer 3.5 software. The mesh generated from raw data exhibited numerous topological issues, whereas the denoised mesh presented none, signifying a notable enhancement in geometric accuracy attributable to denoising. Following the meshing process, the models were simplified through retopology using the free software InstantMeshes and subsequently transformed into NURBS utilizing the \"MeshToNURBS\" tools in Rhinoceros 6. An analysis of the results indicated that both mesh types displayed negligible topological inaccuracies, with the denoised mesh demonstrating superior performance.