## 2 Related Works
The direction and radius of elbows are estimated by fitting circles to LIDAR data at various angles, but this scheme depends heavily on accurate calibration and is sensitive to misalignment, limiting its reliability at longer distances. In [15], a 3D time-of-flight (ToF) camera is employed to model the straight pipe and identify outlier points. These points are grouped into blobs, with gradients analyzed to distinguish \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Approach** & **Sensor** & **Feature** & **Detection Approach** & \
\begin{tabular}{c} **Estimation** \\ **Parameter** \\ \end{tabular} &
\begin{tabular}{c} **Estimation Approach** \\ **Estimation Approach** \\ \end{tabular} \\ \hline
[6] & Contact & Elbow & Deviation of contact sensors & Direction &
\begin{tabular}{c} Deviation of center point \\ Angle of two most deviated \\ sensors \\ \end{tabular} \\ \hline
[8] & 2D Camera & Elbow and T-junction & Edge detection and pattern matching & No estimation & No estimation \\
[9] & 2D Camera & Elbow and T-junction & Image classification based on deep learning & No estimation & No estimation \\
[10] & 2D Camera & Elbow and T-junction & Edge detection and pattern matching & Direction & Direction of pattern \\
[11] & 2D Camera & Elbow & Edge detection and pattern matching & Direction & Distortion of pattern \\ \hline
[12] & Stereo Camera & Elbow and T-junction & Edge detection and pattern matching & Distance & Stereo matching \\
[13] & Stereo Camera & Elbow and T-junction & Edge detection and pattern matching & Distance & Stereo matching and laser \\ \hline
[14] & Pseudo 3D & Elbow and T-junction & Outlier detection of straight pipe and circle fitting & Elbow direction and radius & Circle fitting \\
[15] & 3D ToF Camera & Elbow and T-junction & Outlier detection of straight pipe by blob grouping & Distance & Position of blob \\ \hline
**RT-ETDE** & 3D ToF Camera & Elbow and T-junction & Outlier detection of straight pipe by point cloud partition and simple feature extraction, and simple geometric solutions. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of elbow and T-junction detection and estimation approaches. between elbows and T-junctions. However, both approaches require processing the entire point cloud, resulting in excessive computational complexity. The fourth approach utilizes 3D ranging sensors to detect and estimate the elbow and T-junction. In [14], a pseudo-3D ranging sensor created by rotating a 2D LIDAR is equipped in front of the robot. The elbow and T-junction are detected by recognizing the existence of points inside or outside of the straight pipe, respectively. Additionally, to estimate the direction and radius of the elbow, 2D LIDAR data at each rotating angle are fitted with the circle, and the rotating angle with the smallest fitting error indicates the direction of the elbow. However, the rotation mechanism requires multiple frame processing and careful calibration. Additionally, the elbow direction and radius estimation are sensitive to misalignment of the robot inside the pipe and only effective at close distances. The 3D ToF camera is a solution for these multiple frame issues in [15]. The measured points are first used for fitting to find the circular cylinder model of the straight pipe. Then, the measurement points that are outlier points from the straight pipe model are considered candidate regions. They are first grouped into blobs of connected pixels. Gradients of points inside a blob and between blobs are used to evaluate the shape change inside a blob and between blobs, respectively. Blobs with small shape change internally and big changes to the other shapes are considered to be elbows or T-junctions. Only the distance to these features is estimated in this work. In general, both approaches in [14; 15] rely on the processing of entire measurement points, which is high in computational complexity.