## 7 Conclusions  
In this paper, we dealt with matching 3D scans of mechanical components to an STL triangulation from a database. This problem is of interest in all domains where the identification of an a priori unknown object is required, e.g., when searching for a drawing of a damaged component. We presented an application of principal component analysis, which turned out to be very fast but lacked robustness in the case of objects differing by small details. Therefore, we developed yet another method that is based on decomposition of the point cloud into planar and cylindrical primitives. The method compares point clouds in terms of mutual properties between the primitives such as distance and angle. The second method turned out to be very robust but computationally demanding. Hence, successive application of the methods is the right choice, minimizing the computational effort while preserving the robustness. Our work on hierarchical PCA was inspired by [4; 5], where the authors used the method for clustering of 3D surface meshes into binary trees. The method is invariant with respect to rigid body modes, which may make it superior when compared, for instance, to oct-tree algorithms. The method of decomposition into geometric primitives was inspired by the group at University of Bonn [6; 10; 11; 12]. Their work applies mostly in the area of architecture. Many similar approaches were published in geosciences when scanning terrain or in urban sciences [10; 11; 13]. In [14], the weathers are concerned with correlations  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Scan ID**} & \multicolumn{5}{c}{**Top-5 Models**} \\  & \multicolumn{5}{c}{**Model ID: Matching-Score**} \\ \hline
1 & 1: 38\% & 68: 25\% & 87: 25\% & 271: 25\% & 292: 25\% \\
2 & 2: 50\% & 164: 36\% & 1  
among clusters of points, which is in a sense similar to our PCA. The paper in [16] combined PCA and RANSAC to identify planar walls of buildings. In the context of the abovementioned references, the main contribution of our work is that we applied the methodology in robotics, where most researchers have been so far concerned with artificial intelligence techniques such as deep neural networks or support vector machines. However, such approaches are computationally demanding. In our opinion, it is worth tailoring methods to the problem structure, namely, to make use of the geometrical features of point clouds and STL models. We follow exactly this purely geometrical approach. Obviously, depending on the taste of the researchers, it can be given us a priori knowledge, e.g., to the deep neural network. In future research, we plan to accelerate the process of primitive pairing. Towards this aim, we will replace the complete graph approach, which leads to pairwise features among all the primitives, with a dense graph approach, where we will compute the pairwise features only among the primitives that are geometricaly connected. Another improvement is with regards to robustness. We will enhance the decomposition into planar and cylindrical geometric primitives using decomposition into straight and elliptical edges that arise via intersections of the primitives. Then, we will again apply the graph approach to assemble mutual pairwise features among the edges, which will make the matching more robust. In order to accelerate the most computationally expensive algorithm in our methodology, which is matching using the method of decomposition into geometric primitives, we shall employ parallelism so that evaluations of matching scores of point-cloud couples within the collection will be performed concurrently. Finally, inspired by [18; 19; 20], it will be worth implementing yet another method, the nonlinear least-square minimization approach. In this method, we will select representative points from the scanned point cloud and we will minimize their distances from the STL models. We plan to employ Newton-based methods with global minimization strategies. conceptualization, D.L., Z.B. and P.N. ; methodology, D.L., E.S. and Z.B.