# Spatiotemporal Contextual 3D Semantic Segmentation for Intelligent Outdoor Mining
## 2 Methodology
### Spatiotemporal Feature Select State-Space Module  
Effectively modeling the long-term dependencies of the aggregated long-term spatiotemporal features and fully utilizing these features during the encoding and decoding processes is crucial for achieving accurate segmentation. Although Transformer models excel at capturing contextual information, their computational cost grows quadratically with the input size. This becomes particularly challenging when dealing with high-dimensional, unstructured data such as point clouds, resulting in significant computational overhead and limiting their efficiency and scalability in practical applications. In contrast, Mamba achieves linear complexity, which significantly reduce computational costs while maintaining the ability to process long sequences and model global contexts. Mamba achieves linear time complexity, primarily due to its state-space model formulation, which enables sequence processing through a recurrent structure that is highly parallelizable and hardware-friendly. Unlike Transformers that rely on quadratic-time self-attention mechanisms, Mamba models temporal dependencies using selective kernel-based state updates, decoupling computation from sequence length. We chose Mamba for two main reasons: (1) its computational efficiency makes it particularly well-suited for long spatiotemporal point cloud sequences in real-time applications, and (2) its strong inductive bias toward sequential structures allows it to capture long-range dependencies more naturally, which is advantageous for structured 3D time-series modeling. Recent studies have applied Mamba to sparse, unstructured data like point clouds, but these works have focused on either optimizing the internal structure of Mamba [28] or leveraging the advantages of multimodal data [32], without fully exploring the potential of the vanilla Mamba in point cloud processing. Therefore, we propose a spatiotemporal feature select state-space module, which leverages the advantages of 3D sparse convolutions in point cloud data. This allows the vanilla Mamba network to fully utilize its ability for global context modeling. Specifically, as shown in Figure 3, the spatiotemporal feature select state-space module consists of a spatiotemporal encoder and a spatiotemporal decoder. The spatiotemporal encoder is composed of convolutional layers and Mamba blocks. The convolutional layers progressively expand the receptive field, facilitating the interaction of local features with long-term dependencies. After each convolutional layer, the features undergo global context modeling via Mamba blocks. Compared to efficient attention-based Transformer variants such as Performer [33] and Linformer [34], Mamba adopts a fundamentally different modeling paradigm. While Performer approximates softmax attention using random feature mappings and Linformer reduces attention complexity via low-rank projections, Mamba replaces attention entirely with a structured state-space model, enabling direct modeling of temporal dependencies through selective convolutional recurrence. This formulation achieves linear time and space complexity without relying on pairwise token similarity computations. The process is described by the following equation:  
\[X_{E-Latent}=\sigma(\text{BatchNormNorm}(\text{SpC}(X_{STAF}))) \tag{7}\]  
\[X_{EO}=\text{ MambaBlock}(X_{E-Latent}) \tag{8}\]  
where SpC represents 3D sparse convolution and \(\sigma\) is the ReLU activation function. The Mamba block is composed of the basic Mamba model, with its core being the parameterized SelectiveSSM state-space model, which introduces a selection mechanism. SelectiveSSM transforms the time-invariant system into a linear time-varying system, which can be represented as follows:  
\[\text{SelectiveSSM}(x_{t})=y_{t} \tag{9}\]  
\[y_{t}=Ch_{t} \tag{10}\]  
\[h_{t}=\bar{A}h_{t-1}+\bar{B}x_{t}^{\prime} \tag{11}\]  
Here, \(x_{t}\) is the input representation, which is obtained by applying a linear mapping to \(X_{EO}\).