## 1 Introduction  
Nowadays, remote sensing techniques, such as 3D scanning (e.g., [1, 2]), structure from motion (SFM) photogrammetry [3, 4], or UAV lidar [5]) constitute common approaches for georeferencing and capture of historical objects. These methods produce huge amounts of data that can, among other uses, assist the documentation and preservation of cultural heritage objects for future generations [6, 7] and/or the sharing of digital data on these objects among researchers or even with the public. Prior to processing, the dense point clouds collected by these techniques are typically diluted to a density that must correspond to the required detail. This leads to the need for compromise between the preservation of the most detailed parts of the object (such as reliefs or statues decorating a building) and the overall data size. If high detail is needed for the decorations, flat areas of such buildings (walls) would likely be oversampled, unnecessarily inflating the total data size. For this reason, a progressive dilution preserving a high point density on the parts needing high detail while reducing it for flat areas could be a promising approach for the storage of point clouds of such buildings. Algorithms used for point cloud dilution can be generally classified into those working directly with point clouds, those using a triangular mesh for creating a surface, and other algorithms using, e.g., deep learning (neural networks). Approaches directly diluting the point cloud are the simplest and most widely used. Algorithms performing uniform dilution are typical representatives of such approach, working, e.g., through random sampling (random selection of a user-defined number of points), octree sampling (the cloud point space is divided into voxels with user-defined size and one point--usually the closest one to the center of the voxel--is left in the cloud), or, the most widely used, space sampling method (points are excluded from the cloud on the basis of a user-defined minimal distance). These methods are very simple, fast, and implemented in the available software, e.g., in the CloudCompare software; thus, they are typically used as one of the first steps of point cloud processing ([1,8]). The mesh-based approaches (e.g., [9; 10; 11; 12; 13; 14]) build on the fact that real-world objects consist of surfaces and the point cloud only \"samples\" these surfaces. Combining the individual neighboring points into a network of triangles formed by neighboring points from the cloud then approximates the surface. Obviously, where the surface is more curved, more points are needed for its accurate description than where the surface is flat. The generation of such surfaces is, however, too computationally demanding and typically requires further manual editing. For these reasons, the use of these algorithms for historical buildings or objects is quite complicated, making their suitability for point cloud dilution in these applications rather questionable. Other approaches use, for example, deep learning- or artificial intelligence-based algorithms [15; 16]. Similarly to algorithms using mesh, however, their practical use is complicated by high computational demands; moreover, to the best of our knowledge, it has never been used for historical buildings. Simplification approaches, known especially from the field of computer graphics, are based on the preservation of only feature (key) points, such as edges, from the cloud, ensuring that the reduction causes a minimal change in the shape of the captured object (e.g., [17; 18; 19; 20; 21]). Specialized methods for the point cloud density reduction that have been originally designed for point clouds describing terrain- [22; 23; 24] could be also used for the description of cultural heritage objects. A vast majority of the above-mentioned approaches for point cloud dilution has been developed for other purposes, such as small objects or terrain.