# Painting Path Planning for a Painting Robot with a RealSense Depth Sensor
## 2 Related Work  
Plane detection and extraction is a common problem in robotic vision. This operation can be crucial in certain applications where it is necessary to separate certain objects from the background. There are various ways to make this distinction, but one of the most common methods is to use the RANSAC algorithm [28; 29]. [PERSON] et al. [1] compared devices through four types of experiments: with the error measured using a calibrated sphere at a very close distance; with the errors measured with the Association of German Engineers (VDI)/Association for Electrical, Electronic, and Information Technologies (VDE) 2634 part 2 standard; with the systematic depth errors produced through the acquisition of a planar surface at increasing ranges; and with the 3D reconstruction of an object. Experiments have shown that the RealSense D415 model is fully comparable to its predecessor model in terms of errors assessed through the VDI/VDE standard. The D415 camera is also in line with results obtained from other cameras in the scientific literature and surpasses their performance when considering filtered data. [PERSON] et al. [32] proposed a new method for plane detection from 3D point clouds. The method is contingent on two concepts to achieve a balance between high-accuracy and fast performance. The first concept is to utilize a fast new octree-based, balanced density down-sampling technique to reduce the number of points. The next concept is the fact that the number of planes in any dataset is much lower than the number of the points. Random points are inspected to find the 3D planes. It has been demonstrated experimentally that the suggested algorithm yields precise results and has expeditious performance, is robust to noise, and has a high potential to detect planes with small angle variations. [PERSON] et al. [33] introduced a new algorithm, the connected components RANSAC (CC-RANSAC), which uses only the largest connected components of inliers to estimate the suitability of a candidate plane. They stated that this allegedly minor modification could yield appreciably better fits than RANSAC. [PERSON] et al. [34] considered the task of ground plane estimation in range image data acquired from a time-of-flight camera. They extended the 3D spatial RANSAC for ground plane estimation to a 4D spatiotemporal RANSAC by including a time axis. The ground plane models were obtained from spatiotemporal random data points, thereby making the proposed method robust against short-term transitory effects such as passing cars and pedestrians. They noted that the computationally fast and robust assessment of ground planes led to the reliable identification of obstacles and pedestrians using statistically obtained spatial thresholds. [PERSON] et al. [35] introduced two robust statistical methods for outlier detection and robust saliency properties, such as surface normal and curvature assessments in laser scanning 3D point cloud data. The first was formed using a robust z-score, while the second technique uses a Mahalanobis-type robust distance. They stated that the algorithms are fast, accurate, and robust. [PERSON] et al. [36] presented an ameliorative RANSAC method, relying on normal distribution transformation (NDT) cells in their research to avoid false planes for 3D point cloud plane segmentation. They selected a planar NDT cell as a minimal sample in each iteration to ensure the correctness of sampling on the same plane surface. Basically, the 3D NDT presents the point cloud with a set of NDT cells and models the observed data with a normal distribution within each cell. The geometric representations of NDT cells were used to separate them into planar and non-planar cells. The experiments showed that the correctness exceeded 88.5% and the completeness exceeded 85.0%. These results indicate that the introduced method is more dependable and accurate than the standard RANSAC. [PERSON] et al. [37] proposed an accurate plane-fitting procedure for a structured light-based red-green-blue-depth (RGB-D) sensor.