# Real-Time DTM Generation with Sequential Estimation and OptD Method
## 2 Materials and Methods
### Data Reduction with the OptD Method  
Reduction in datasets refers to techniques used to reduce the amount of data in a point cloud while preserving the essential features and structures that are important for visualization, analysis, or further processing. The approaches to data reduction with different sensors are similar because users are always interested in keeping the characteristic observations, for example extremum values, and the ability to save points in areas with a complex structure. It is also important that the reduction algorithm works quickly, which means that it must be computationally simple. The most commonly used reduction methods include [18; 19]:  
* uniform grid sampling, which involves dividing the point cloud space into a 3D grid of voxels and selecting one representative point from each voxel;
* voxel grid filtering, where a voxel (3D pixel) is created, and one point (usually the centroid) is chosen to represent all points within that voxel;
* random sampling, which selects a subset of points from the point cloud, though this might not preserve structure well;
* octree-based down-sampling by designing an octree data structure to subdivide the point cloud into hierarchical levels, selecting points based on resolution. To better illustrate the types of reduction method, Table 1 is presented, which compares reduction methods in terms of data retention, computational efficiency, and impact on accuracy. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reduction Method** & **Principle** & **Data Retention** & \begin{tabular}{c} **Computational** \\ **Efficiency** \\ \end{tabular} & **Impact on Accuracy** \\ \hline Uniform grid sampling [20] & \begin{tabular}{c} Divides the space into a \\ 3D grid and selects one \\ representative point \\ per voxel. \\ \end{tabular} & \begin{tabular}{c} Moderate \\ (depends on \\ grid resolution) \\ \end{tabular} & \begin{tabular}{c} High \\ (fast processing) \\ \end{tabular} & \begin{tabular}{c} Moderate \\ (loss of fine details in \\ high-density areas) \\ \end{tabular} \\ \hline Voxel grid filtering [21] & \begin{tabular}{c} Averages points within \\ a voxel to reduce \\ redundancy. \\ \end{tabular} & \begin{tabular}{c} High \\ (preserves general \\ structure) \\ \end{tabular} & \begin{tabular}{c} High \\ (efficient for large \\ datasets) \\ \end{tabular} & \begin{tabular}{c} Moderate \\ (smooths surfaces \\ but may remove \\ small features) \\ \end{tabular} \\ \hline Random sampling [18] & \begin{tabular}{c} Randomly selects a \\ subset of points. \\ \end{tabular} & \begin{tabular}{c} Low \\ (risk of missing \\ key features) \\ \end{tabular} & \
\begin{tabular}{c} Very high \\ (minimal \\ computation \\ required) \\ \end{tabular} &
\begin{tabular}{c} High \\ (loss of critical \\ terrain details) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of data reduction methods. The disadvantage of these of these computationally simple methods is that they lead to the loss of important details, especially in regions of interest such as edges and objects. However, the use of methods such as feature-based reduction [24] or curvature methods [25] is very time-consuming and not suitable for real-time reduction. One of the methods that can be used during reduction is the OptD method [26; 27]. The method has been tested in various studies [28; 29; 30]. The assumption of the OptD method is to reduce the number of observations in datasets using the optimization criterion of the size of the dataset, e.g., percentage p% or the number m of points preserved in the dataset after reduction. During each iteration, the algorithm assesses whether the current tolerance level and the width of the measuring strip allow for meeting the specified percentage of retained points. If the criteria are not met, the tolerance range may be adjusted or width of the measuring strip can be changed. This adjustment helps find the optimal balance between point reduction and the preservation of critical terrain features.