# Advanced Methods for Point Cloud Processing and Simplification
## 1 Introduction
### Our Point Cloud Processing Contribution  
The first work of object detection, which we proposed, was the algorithm for point cloud unfolding into a single plane with height preservation, as in reference [27]. The presented method works correctly for rectangular rooms with four walls, a known scanner position, and walls not occupied by many objects. The aim of this work was to unfold all walls with objects into a single plane. The single plane representation allows the removal of walls close to zero and analyzing of the remaining objects. Finally, this method proved to be a dead-end for follow-up utilization. The unfolding of the objects placed on the corner splitting line caused their division into two parts. The global position of the object is also lost.  
Many researchers are using depth images in their work (as shown in references [9; 10; 11; 12; 13]). The depth images contain the real physical sizes and distances which are possible to utilize further. We had a point cloud without depth information, so we decided to develop the algorithm for the depth map construction, which we described in reference [28]. The main advantage of this algorithm lies in the possibility to create a depth map from any point cloud with the arbitrary camera position and arbitrary camera orientation. The concept of space quantization has shown to be useful for further space data processing. Moreover, we can process these images by image processing methods and for example, transform depth pixels back into the point cloud by using the reverse process. The depth image includes space information about the structure and the quality of an analyzed surface. The depth image offers to detect surfaces or other objects (see references [9; 10; 11; 12; 13]). A depth camera covers only the area, which is seen by the camera itself. This is the main disadvantage for global object detection and segmentation. Some objects cover the other objects and areas present in a scene. For this reason, a depth image is not suitable for global space segmentation and description, but the space quantization into the image with a connection of image processing methods offers wide possibilities for basic object detection and detailed space description.  
In the papers [29; 30], we introduced a novel algorithm called the Level Connected Component Labeling (LCCL) for global 3D data analysis in terms of detecting global levels with high data concentration in selected space dimensions. A planar surface presence is indicated mainly by the high concentration of points in the particular dimension at the specific level. To find the high point concentration at the specific level is not sufficient for planar surface detection. Several planar surfaces can be present in one of the detected levels. Thus, we are using space quantization into an image for this purpose. This allows the use of classically connected labeling to separate individual planar surfaces. A planar surface is presented by the tool called Level Image (\(L_{I}\)), which is described in references [29; 30; 31; 32]. For each \(L_{I}\), its origin and rotation angle are known. The surface selected dimension is calculated as the average of the points on this surface. From the LCCL output, the statistical parameters, such as the mean value, variance, standard deviation, and data mode, are also known. These parameters describe the quality of the detected planar surface.  
The connection of a \(L_{I}\) with image processing methods allows expression of a planar surface area and perimeter [30] or interactive visualization [31], including color presentation when available. One of our last research works [32] deals with fine plane range estimation. In this paper, we will present the next methods for point cloud preprocessing and processing, which we did not publish yet, helping to decrease a point amount for the planar surface description, fill the gaps in the point clouds, and obtain other important space features.