## 3 Proposed Work
### State Space Model
Table 3 displays the quantity of samples for training and testing data in the Oakland dataset. This dataset was gathered using a mobile platform that was equipped with side-looking \"SICK LMS laser scanners operating in push-broom mode\", and it portrays an urban region. \"To every 3D point is allocated one of the five semantic labels, namely wire, pole/trunk, facade, ground, and vegetation\". The dataset is separated into the training set X, validation set V, and test set Y. Table 3 provides the number of samples for each class to give readers an idea of the dataset's distribution. Following class rebalancing, the training set is reduced to 1000 training instances for each class. #### 5.1.2 Paris-rue-Madame Database

We consider the Paris-rue-Madame database [46] as our second dataset. This database was collected in the French city of Paris, with a street stretch measuring approximately 160 m in length representing the 20 million 3D points in this collection. The Velodyne HDL32-equipped Mobile Laser Scanning system L3D2 was used for data collection, and annotation was carried out with the help of a manual process. Point labels as well as segmented objects are included in the annotated dataset, with 642 objects in the database divided into 26 classes. Our tests are limited to 3D points that fall into one of the six core semantic classifications--facade, ground, autos, motorbikes, traffic signs, and pedestrians--because the remaining classes only make up less than 0.05% of the whole dataset. Table 4 shows the Paris-rue-Madame database, with the number of samples per class. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**S.No.** & **Class** & **Training Set** & **Test Set** \\ \hline
1 & Facade & 1000 & 9,977,435 \\
2 & Ground & 1000 & 8,023,295 \\
3 & Cars & 1000 & 1,834,383 \\
4 & Motorcycles & 1000 & 97,867 \\
5 & Traffic signs & 1000 & 14,480 \\
6 & Pedestrians & 1000 & 9048 \\  & Total & 6000 & 19,956,508 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: For the Paris-rue-Madame database, the number of samples per class. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**S.No.** & **Class** & **Training Set** & **Test Set** \\ \hline
1 & Wire & 2572 & 3795 \\
2 & Pole/trunk & 1087 & 7934 \\
3 & Facade & 4714 & 222,113 \\
4 & Ground & 14,122 & 934,147 \\
5 & Vegetation & 14,442 & 267,326 \\  & Total & 36,933 & 1,324,311 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: For the Oakland 3D PC Dataset, the number of samples per class. Once more, we perform a class rebalancing and choose at random a training sample X including 1000 training instances for each class. The remaining data are then used as the test set Y. ### Classifying Vegetation

We acquired a minor portion of our institute's facilities, including the building, road, ground, open stage, trees, stone benches, lane, pillar, flag, rainwater channel, and other features in the evening, for the purpose of processing as a Packet Capture Data (PCAP) file. Our LiDAR data contain approximately 28 unknown classes and 25 known classes. The Velo viewer tool was used to open the raw data and convert it to the CSV format for further processing. After loading the data in CSV format, a PC object was created. Each PC in our dataset contains approximately 100 frames. The distribution of LiDAR PC occupancy is depicted in Figure 6, where the x-axis denotes the current position of the sensor, and the \(y\)-axis denotes the number of points from the sensor. We are conducting experiments in MATLAB R2019b. The sequence of images used to generate labels is loaded following the selection of the truth. Labels are made for regions of interest, which are then imported and exported from the workspace for future use. This object serves as the foundation for subsequent processing. The k-nearest neighbor algorithm is utilized to determine if two points are connected. Using this method, 53 distinct segmented objects are categorized, and 9 of these 53 objects have pre-assigned labels, with one class named \"unknown\".