# Testing the Effectiveness of Voxels for Structural Analysis
## 1 Introduction
### Denoising  
Converting an unstructured 3D point cloud into a coherent surface reconstruction (3D mesh) poses significant challenges, particularly in scenarios involving the digitization of architectural sites, the development of virtual environments, reverse engineering for CAD model creation, and geospatial analysis. The progress of technologies, particularly in scanning techniques, has enabled the collection of dense 3D point clouds containing millions of points. A crucial aspect of preserving cultural heritage is understanding its geometric complexity. Since the objects being detected and analyzed have experienced modifications over the centuries, such as repairs, alterations, and reconstructions, this task is inherently complex. These modifications frequently result in the formation of cracks and damage that is typically challenging to identify and understand. Accurate diagnosis, which facilitates the identification and interpretation of crack patterns in cultural heritage objects and structures, is vital for comprehending the structural behavior of these artifacts and for guiding subsequent interventions. This identification process is primarily visual but may not always be practical. Consequently, it is imperative to establish an optimal workflow that produces results that are as true to reality as possible. Another important aspect to be addressed in the upcoming sections of this research is the segmentation of the 3D models, concentrating on the key components that define the object under investigation. Three-dimensional point clouds derived from photogrammetric and laser scanning surveys frequently present noise due to various influences, such as non-collaborative materials or surfaces, insufficient lighting, intricate geometries, and the limited accuracy of the tools used. This noise not only alters the unstructured geometry of the point clouds but also introduces irrelevant information, reducing the geometric precision of the resulting mesh model and subsequently impacting the results of any analyses performed on it. Therefore, it is crucial to clean the raw data. The process of eliminating noise from point clouds has become a key area in 3D geometric data processing, as it allows for the extraction of the true ground point cloud while refining the ideal surface. This research examines the effectiveness of a current algorithm for creating various cultural heritage models intended for structural analysis. Point clouds were post-processed and evaluated compared with the original data, profiles have been extrapolated from raw and denoised data, and compared, and the 3D meshes from the denoised data have been exported to assess the algorithm's performance across different geometries and case studies. The objective was to investigate its capability to generate more accurate volumetric data from 3D meshes to support structural analysis. Bilateral filtering [25] is acknowledged as a nonlinear method for image smoothing, and its principles have been adapted for denoising point clouds [26]. Techniques employing bilateral filtering apply this method directly to point clouds, considering factors such as point position, point normal, and point color [27]. Guided filtering [28] acts as a specific image filter that can function as an edge-preserving smoothing operator [29]. Recently, numerous filter-based algorithms have utilized point normals as guiding data, iteratively refining and updating points to conform to the estimated normals. Furthermore, graph-based point cloud denoising techniques treat the input point cloud as a graph filter [30], implementing denoising through selected graph filters. Patch-based graph representations create a graph using surface patches derived from point clouds, with each patch represented as a node [31]. Optimization-driven denoising techniques aim to produce a denoised point cloud that closely resembles the original input cloud [32].