As shown in Figure 3 , to obtain the point-wise and channel-wise features of the point cloud, this paper refers to the hybrid attention network of CBAM [16] and designs a Multi-attention Point Encoding (MPE) module in the Point Feature Encoding branch as the basic unit for point feature extraction. In the Point Feature Encoding branch, to enhance the network’s generalization ability, the MPE module is stacked twice sequentially. First, the original pillar features $P_k$ are fed into the first MPE module for processing, resulting in the primary feature ${P^{\prime }}_k$. Then, ${P^{\prime }}_k$ is concatenated with the original feature $P_k$ and passed through a fully connected layer to map it into a higher-dimensional space, which is then forwarded to the next MPE module. The final output is further processed by a fully connected layer and a max-pooling layer to aggregate the features of all points within the pillars, thus obtaining the final output feature ${P^{″}}_k$.

The structure of the MPE module is shown in Figure 4 . First, channel attention [17] and point attention are applied to calculate the attention weights for each point within the pillars. Then, these two attention weights are fused, and the fused weights are applied to the point cloud’s pillar feature matrix $P_k$, allowing the encoding network to adaptively extract pillar features based on the importance of both points and channels.

In the Point-wise attention part of the MPE, the input pillar feature matrix $P_k$ is processed to fully capture the feature relationships between each channel. Max pooling and average pooling operations are applied to the input feature map for point-wise feature aggregation. Then, the two resulting weight matrices are fed into a shared network that includes fully connected layers and a nonlinear activation function. Finally, the point attention weight $F_{\text{p},k}$ is obtained by element-wise addition of the weight matrices $M_{\text{p},k}^{\text{m}}$ and $M_{\text{p},k}^{\text{a}}$ from the max pooling and average pooling operations, respectively. This step primarily describes the spatial correlation between points within the pillars. The corresponding computational formulas for this process are provided in Equation (1), Equation (2) and Equation (3) below:

$M_{\text{p},k}^{\text{m}}=W_2\left(\sigma W_1\left(\text{max\_c}\left(P_k\right)\right)\right)$(1)

$M_{\text{p},k}^{\text{a}}=W_2\left(\sigma W_1\left(\text{avg\_c}\left(P_k\right)\right)\right)$ (2)

$F_{\text{p},k}=M_{\text{p},k}^{\text{m}}+M_{\text{p},k}^{\text{a}}$ (3)

Here, $\text{max\_c}(·)$ represents the max pooling operation along the channel dimension of the feature map, $\text{avg\_c}(·)$ represents the average pooling operation along the channel dimension of the feature map, $\text{σ}(·)$ represents the ReLU activation function, and $W_1$ and $W_2$ represent the weight matrices of the two fully connected layers in the point attention module shown above.

In the Channel-wise attention part, it is similar to the Point-wise attention part. To more comprehensively aggregate the channel features across the point dimension, max pooling and average pooling operations are applied to aggregate the point features of the input feature matrix $P_k$, as shown in the lower part of the channel-wise attention section in Figure 4 . Then, the two weight matrices are fed into a shared network that includes fully connected layers and a nonlinear activation function. Finally, the channel attention weight $F_{\text{c},k}$ is obtained by element-wise addition of the weight matrices $M_{\text{c},k}^{\text{m}}$ and $M_{\text{c},k}^{\text{a}}$ from the max pooling and average pooling operations, respectively. This step is primarily used to describe the spatial correlation between points within the pillars. The corresponding computational formulas for this process are provided in Equation (4), Equation (5) and Equation (6) below:

$M_{\text{c},k}^{\text{m}}={W^{\prime }}_2\left(\sigma {W^{\prime }}_1\left(\text{max\_p}\left(P_k\right)\right)\right)$(4)

$M_{\text{c},k}^{\text{a}}={W^{\prime }}_2\left(\sigma {W^{\prime }}_1\left(\text{avg\_p}\left(P_k\right)\right)\right)$(5)

$F_{\text{c},k}=M_{\text{c},k}^{\text{m}}+M_{\text{c},k}^{\text{a}}$(6)

Here, $\text{max\_p}(·)$ represents the max pooling operation along the point dimension of the feature map, $\text{avg\_c}(·)$ represents the average pooling operation along the point dimension of the feature map, and ${W^{\prime }}_1$ and ${W^{\prime }}_2$ represent the weight matrices of the two fully connected layers in the channel attention module shown above.

Finally, the point attention weight $F_{\text{p},k}$ and the channel attention weight $F_{\text{c},k}$ are element-wise multiplied, and the result is passed through the ReLU activation function to obtain the mixed attention weight $F_{\text{m},k}$. The mixed attention weight is then applied to the original pillar features $P_k$ by performing an element-wise multiplication, resulting in the final output feature ${P^{\prime }}_k$. The corresponding computational formulas for this process are provided in Equation (7) and Equation (8) below:

$F_{\text{m},k}=\sigma \left(F_{\text{c},k}\times F_{\text{p},k}\right)$(7)

${P^{\prime }}_k=F_{\text{m},k}\odot P_k$ (8)

As shown in the Global Pillar Feature Encoding branch in Figure 2 , to encode the relationship features between each pillar and the entire point cloud, this paper designs an extension for the pillar features (Pillar Feature Augmentation) in the Global Pillar Feature Encoding branch, constructing pillar features $V_k=\left[x_k^{\text{c}},y_k^{\text{c}},z_k^{\text{c}},x_k^{\text{p}},y_k^{\text{p}},z_k^{\text{p}},\Delta x_k^{\text{c}},\Delta y_k^{\text{c}},\Delta z_k^{\text{c}},\Delta x_k^{\text{p}},\Delta y_k^{\text{p}},\Delta z_k^{\text{p}}\right]$, $V_k\in {\text{R}}^{\text{1}\times \text{12}}$ that include global association information. Here, $\left[x_k^{\text{c}},y_k^{\text{c}},z_k^{\text{c}}\right]$ represents the centroid coordinates of all points in the k-th pillar (the arithmetic average of all point coordinates), $\left[x_k^{\text{p}},y_k^{\text{p}},z_k^{\text{p}}\right]$ represents the center coordinates of the k-th pillar, $\left[\Delta x_k^{\text{c}},\Delta y_k^{\text{c}},\Delta z_k^{\text{c}}\right]$ represents the coordinate offset of the centroid of all points in the k-th pillar relative to the centroid of the entire point cloud, and $\left[\Delta x_k^{\text{p}},\Delta y_k^{\text{p}},\Delta z_k^{\text{p}}\right]$ represents the coordinate offset of the center of the k-th pillar relative to the center of the entire point cloud.

In the encoding of the k-th pillar’s features, the input pillar feature vector is first processed by a Multi-Layer Perceptron (MLP) for feature extraction and mapping. Since the MLP layer includes operations such as Batch Normalization and ReLU activation functions, these steps effectively enhance the expressive ability of the features, resulting in an expanded pillar feature vector ${V^{\prime }}_k$, as expressed in Equation (9):

${V^{\prime }}_k=f\left(V_k;W_3\right)$(9)

The $f(·)$ represents the result of applying the MLP operation to $V_k$, where $V_k$ represents the weight parameters of the MLP.

This paper utilizes the open-source KITTI dataset for algorithm validation, which includes diverse traffic scenarios, such as urban, suburban, and highway environments, and provides rich image and LiDAR data. The dataset consists of 7481 training samples and 7518 testing samples. Following the methodology outlined in the PointPillars paper, the training samples of KITTI are further split into 3712 samples for the training set and 3769 samples for the validation set, which are used during the network training process. The KITTI dataset includes three types of objects: cars, pedestrians, and cyclists. Based on the height, occlusion, and truncation levels of the object bounding boxes in the dataset, the object detection task is classified into three difficulty levels: Easy, Moderate, and Hard. The performance of the proposed algorithm is evaluated at these three difficulty levels.

The experiments are conducted using the PyTorch deep learning framework, with the operating system being Ubuntu 18.04. The computer processor is an Intel Core i5-11600 CPU, with 64GB of memory. An NVIDIA GeForce RTX 3090 GPU is used to accelerate the training process. The batch size during training is set to 1, the learning rate is set to 0.00075, and the Adam optimizer is used for training. The maximum number of iterations is set to 180.

This paper employs average precision (AP) to evaluate the experimental results of the NPFE-improved PointPillars algorithm (Ours), which outperforms both the original baseline network and other methods in terms of 3D detection AP for the Car, Pedestrian, and Cyclist categories on the KITTI dataset. The results are compared with those of the original PointPillars algorithm, as well as several other prominent point cloud 3D object detection algorithms, including VoxelNet, SECOND, and PointRCNN. The comparison results are presented in Table 1 .

In the same experimental setup, qualitative evaluations of the aforementioned models were conducted, with the results summarized in Table 1 . The NPFE-improved PointPillars outperforms the baseline and other methods in 3D detection AP for cars, pedestrians, and cyclists due to its ability to better preserve global contextual information and focus on critical point features. Specifically, under the Moderate difficulty level, the proposed algorithm achieves a 3.07% increase in car detection AP, a 3.35% increase in cyclist detection AP, and a notable 7.79% improvement in the detection of smaller targets such as pedestrians. Furthermore, as indicated in Table 1 , the NPFE-enhanced PointPillars also outperforms several other classic algorithms.

This section presents a qualitative evaluation of the NPFE-improved PointPillars algorithm (Ours) through visual analysis. For this experiment, two complex scenes from the KITTI dataset validation set were selected to conduct a comparative 3D object detection experiment, as shown in Figure 5 . Specifically, Figure 5(a) depicts a scene with occlusion, while Figure 5(b) illustrates a scene containing numerous small targets and occlusions. In Figure 5 , the RGB images corresponding to each scene are shown at the top, while the point cloud data processed for visualization is displayed at the bottom. The detection results of both algorithms are marked in the figure, with the NPFE-improved PointPillars algorithm on the left and the original PointPillars algorithm on the right. The purple boxes indicate cars, the red boxes represent cyclists, and the blue boxes highlight pedestrians. Additionally, the yellow ellipses emphasize misidentified targets found in the improved algorithm’s results.

As shown in Figure 5 , the NPFE-improved PointPillars algorithm has superior detection performance in both occluded and small target scenarios. In scene 1, which features a diverse and densely distributed set of object types, the original PointPillars algorithm fails to detect a vehicle occluded by a crowd (highlighted by the yellow elliptical frame), whereas the improved algorithm successfully identifies the target, showcasing its advantage in handling occlusion. Similarly, in scene 2, which contains sparse and small distant targets, the improved algorithm outperforms the original in detecting densely packed vehicles and avoids the issue of misidentifying small roadside trees as pedestrians, thereby significantly enhancing detection accuracy and reliability, particularly under occlusion conditions and for small target 3D detection.