Point clouds are one of the fundamental representations of 3D data, and widely used for both academia and industry because of the development of 3D sensing technology and relevant applications. Generally, 3D point clouds can be collected by 3D scanners  utilizing physical touch or non-contact measurements e.g. light, sound, LiDAR etc. Particularly, LiDAR scanners  are in service in many areas including agriculture, biology, and robotics, etc. Due to its tremendous contributions, point cloud analysis attracts much interest for further investigation.
that operate on 3D data incorporated estimated geometric information and reconstructed models. With the help of deep learning, recent works on 3D data focus on data-driven approaches via Convolutional Neural Networks (CNNs). Classical works can be generally categorized as: multi-view images with 2D CNNs (e.g. MVCNN ), volumetric/mesh data with 3D CNNs (e.g. VoxNet 
), 3D point cloud with multi-layer perceptrons (MLP) (e.g. ), etc.
Currently, many works are exploring different methods to improve the processing of 3D point clouds, but there remains some unsolved issues: (1) How can we force the network to automatically learn a better representation from the abstract high-level embedding space? (2) How do we refine the output features in order to focus on the crucial information? (3) Besides the regular features, can we learn from more geometric clues for a comprehensive analysis?
To investigate the possible answers to the above concerns, here we present a novel attentional feedback structure for point cloud learning via the incorporation of geometric context. As supported by substantial biological evidence, feedback mechanisms are very helpful for visual tasks, because feedback paths in our brain especially in the visual cortex consist of more neurons than the forward paths. Besides, feedback mechanisms also have been successfully utilized for stable and responsive systems in industry. Some early works managed to involve this mechanism in CNNs to deal with computer vision problems like 2D visual segmentation
or 3D hand pose estimation etc. However, for point clouds, PU-GAN  to some extent used a feedback-like unit but for feature expansion inside its generator module. Our primary motivation to investigate feedback is to automatically refine the output feature map by comparing the difference between the input and the corresponding feedback signal. Using this approach, we enable the network to generate a better learning output.
Regarding high-level feature presentation for 3D point clouds, another widely applied mechanism: Attention, can assist the network to put more emphasis on useful information . Attention modules are used in many 2D visual problems (e.g. image segmentation [42, 8, 7], image denoising ), etc. For 3D point cloud analysis, we design a Channel-wise Affinity Attention module for feature map enhancement based on affinity between channels.
To deal with the unorderedness of regular point cloud data, PointNet 
proposed to use symmetric functions to aggregate features, while most of the subsequent works apply max-pooling to extract prominent features. Despite the fact that prominent features are representative, they lack some details especially in local areas, hence, are insufficient for precise classification task. To address this problem, we propose a simple but effective way to learn fine-grained features via a shared fully connected (FC) layer on each local neighborhood. Although recent work[27, 18, 41, 47, 12] shows that CNN approaches can benefit from more geometric information, it could also negatively affect the performance since redundant or useless features can be incorporated. To maximize its advantage, we shall carefully form a low-level descriptor with explicit physical meaning to enrich the geometric information.
The contributions of our work can be summarized as:
We design a feedback CNN mechanism for local prominent feature learning on point clouds.
We introduce a Channel-wise Affinity Attention module to better refine high-level features of point clouds.
We propose an intuitive but effective structure to extract local fine-grained features as complement. And we also show that our estimated mesh descriptor can significantly improve the performance of the network.
We present experimental results showing that our proposed network on both synthetic and real-world 3D point cloud classification benchmarks outperform state-of-the-art methods.
2 Related Work
Estimating geometric relations. Although 3D scattered point cloud data has many advantages, the main drawback is the lack of geometric information. In order to acquire more underlying knowledge of point clouds, conventional methods [23, 21, 38] tried to estimate the geometry of point cloud e.g. face, normals, curvature, etc. and also proposed many hand-crafted features for recognition and matching, (e.g. shape context, point histograms, etc.), Besides, recent works [27, 18, 43, 46] with CNNs have better performance thanks to the permutation invariance of low-level geometry. To give advantages for the needs of modern methods, here we expand low-level geometric information from the given 3D coordinates, then integrate this as an explicit geometric descriptor for network processing.
Learning local features. PointNet  passes point cloud data through MLPs for a high-level feature representation of every single point, and successfully solved the unordered problem of point cloud data with a symmetric function. Due to the effectiveness, later works [27, 15, 43, 18] also adopt MLP based operation for point cloud processing. Meanwhile, researchers realize that local features are promising because they contribute additional characteristics to global features. Although the points are unordered in point cloud data, we may group points based on various metrics. Generally, one approach selects seed points as centroids, and then applies a query algorithm (e.g. Ball Query in ) based on 3D Euclidean distance to group points for local clusters. After extracting local features, the network may further process the centroids.
Another track is to find each point’s neighbors in embedding space based on N-dimensional Euclidean distance  and then group each point’s neighbors in the form of high dimensional vectors. In contrast to the previous type, this method can avoid sparsity and update dynamically in different feature dimensions. In terms of feature aggregation, max-pooling  is widely employed since it can solve the issue of unorderedness and gather information sufficiently. In spite of the benefits, there are some weak points of the current max pooling approach: it may lose local details or involve bias. To overcome these problems, we add complementary local fine-grained features and feedback structures to reduce possible bias.
Attention mechanism for CNN.
The idea of attention has been successfully used in many areas of Artificial Intelligence (AI). Like human beings, the computational resource of machine is also limited. Thus we need to focus on important aspects. Previously, Vaswaniet al. 
proposed different types of attention mechanisms for neural machine translation. Subsequently, attention mechanisms were incorporated in visual tasks, for example, Wanget al.  extended the idea of Self-attention in spatial domain for computer vision problems. Also, SENet 
credits winning the ImageNet challenge to its channel-wise attention module. Other works [44, 7, 14] derive benefits from both spatial and channel domains of 2D images.
In terms of 3D point clouds, attention modules contribute to point clouds detection , generation , segmentation [48, 16, 49], etc. However, limited work is done in well-designed attention mechanisms targeting 3D point clouds classification. On this front, Xie et al.  utilized a spatial self-attention module for the shape context  of point clouds. Subsequent works [40, 6] also applied Graph Attention  module for the constructed graph features on point clouds. Differently from existing methods, we try to enhance the high-level representation of point cloud by capturing the long-range dependencies along its channels.
As stated in Section 1, there are some unsolved problems of the existing methods. To tackle the challenges, we start from classical mapping  and edge convolution . We apply the basic operation  i.e. a 1
where is the , is the activation function, is batch normalization, is convolution and its subscript presents the filter size. Moreover, edge features defined in  is given by:
where is the centroid of a local area in -dimensional feature space, and the entire feature map can be formed as . The ’s are the neighbors found by k-nearest neighbors () algorithm.
The aim of , , is to construct radial local graphs (i.e. edge features ) consisting of edges pointing from the neighbors to the centroids, and then mapped by a shared in feature space:
Differently from these approaches, we attempt to incorporate more geometric features in different levels. As illustrated in Figure 2, our network has a series of modules with each consisting of two main parts: one extracting prominent features and the other learning fine-grained features. Our mesh descriptor explicitly expands geometric information in low-level space to meet the demand of comprehensive learning. In this section, we introduce the critical modules in detail and mathematically formulate the operations.
3.1 Attentional Feedback Module for EdgeConv
The typical feedback mechanism aims to accurately control a process by monitoring its actual output and feeding the error signal back to force the system to generate the desired output. To be more specific, the output is passed through a feedback path as a feedback signal, and then the forward path can use such feedback signals to both adjust and control the system. By forming such a closed loop, the system can reduce the error, improve stability, and enhance robustness. Inspired by this, we propose the Attentional Feedback Module for EdgeConv () illustrated in Figure 3 for edge-based prominent features.
Forward path. Here we employ as the forward path denoted as of our since this operation can explicitly capture both global shape structure and local neighborhood information. With Equation 2 and 3, the forward path as can be formulated as:
And the output of forward path is:
Feedback and error signals. Following our forward path , an ideal output feature map should fully encode global and local details. On the other hand, if the output is indeed informative, we may restore the original input from it. Suppose our feedback path () aims to restore the input, then ’s output, , can be termed as a :
Further, we take the difference between the original and restored inputs, , to formulate corresponding :
Feedback path. Since we attempt to restore the input from , the feedback path needs to simulate a reverse process of the forward path (i.e. ). In our proposal, we apply a shared Local Fully Connected () layer as the feedback path of our module:
where is the . Mathematically, is a special case of a shared with kernel size , by which the neighbors in feature space can be fully connected. In contrast to expanding a center point to local neighbors in the new embedding space, the shared layer can pull the neighbors back to the previous space and aggregate at a center point via learnable weights. In general, the feedback path follows:
Correction path. Finally, the module passes the through a correction path (), which has the same structure with forward path:
Therefore, the output features of the correction path can be formed as:
In order to form the feedback loop, here we take the output of the correction path as the correction term for our original output of forward path. After that, we apply max-pooling over the local area to obtain a compact feature map. Moreover, the Channel-wise Affinity Attention (, see Section 3.2 for details) module can further refine the final feature representation.
Finally, the operation of Attentional Feedback Module for EdgeConv () can be summarized as:
3.2 Channel-wise Affinity Attention Module
As mentioned in Section 2, most attention designs regarding point clouds operate in point-space, but the effects are not apparent. Instead, we prefer distributing attention weights along channels. Inspired by the spacetime non-local block , we can calculate the long-range dependencies without being concerned by point cloud data’s unoderedness. However, the corresponding calculations also have a high computational cost. Therefore we ought to find an appropriate method to avoid redundancy and refine the information in an abstract embedding space effectively and efficiently.
We propose our Channel-wise Affinity Attention () module targeting the channels of high-level point cloud feature maps. As Figure 4 shows, the main structure of the module includes a Compact Channel-wise Comparator () block, a Channel Affinity Estimator (
) block, and a residual connection.
Compact Channel-wise Comparator block. Since the module mainly focuses on channels, it is necessary to reduce the computing cost caused by the complexity in point-space. As we claimed above, it is hard to select the key points in such abstract high dimensional space. In the case of a given -dimensional feature map , the Compact Channel-wise Comparator () block can simplify context in each channel by an shared operating on channel vector ) to implicitly replace original points with a smaller number . In contrast to explicitly selecting some points in abstract embedding space, aims to efficiently reduce the size but sufficiently retain the information of each channel:
Specifically, and are two s operating for and :
and we apply the product of transposed and to estimate corresponding channel-wise :
where approximates the similarity between the channel and the channel of the given feature map .
Channel Affinity Estimator block. Typical self-attention structures used to calculate the long-range dependencies in spatial data based on inner-products, since the values can somehow represent the similarities between the items. In contrast, we define the non-similarities between channels and term it Channel Affinity. In our approach, the Channel Affinity Matrix of the feature map , can be modeled:
Particularly, we select the maximum similarities along the columns of , and then expand them into the same size of . By subtracting the original from the expanded matrix, the channels with higher similarities have lower affinities (illustrated in Figure 5(b)). Besides, is added to normalize the values, since is used as the weight matrix for refinement. In this way, channels can put higher weights on other distinct channels, thereby avoid aggregating similar/redundant information.
According to the weight matrix, we can refine each point’s features by taking the weighted sum of all channels. We apply another , , to get the as shown below:
This process can be easily achieved by the multiplication between and the Channel Affinity Matrix. Additionally, we use a residual connection and learn a weight to ease block training. The refined feature map by is given below:
3.3 Geometric Features
For regular scattered point clouds, the given information about 3D coordinates is minimal. In our work, we attempt to enrich the geometric features of the point cloud from two aspects: (1) we describe the low-level relations explicitly, and (2) extract the high-level information implicitly.
Explicit geometric features. Here we define the explicit geometric features in low-level space to estimate features with explicit purposes. In geometry, a mesh is a type of well-constructed 3D data format, including faces, edges, as well as vertices. Similarly, we incorporate the estimated faces and edges to expand the low-level features representation of the 3D point clouds. Hence, we propose a Naive Mesh Descriptor () to enrich the original input data (i.e. 3D coordinates) with estimated face features.
Since most of the mesh data is constructed in triangle faces, we also adapt the point cloud for triangle mesh format. To be specific, firstly we search the two nearest neighbors, i.e. with , in 3D space for point , and then we form the triangle face corresponding to with the two neighbors: . To explicitly describe the estimated triangle face, totally six items with exact geometric purposes are involved in:
Implicit geometric features. In contrast to explicit geometry in low-level space, we also expect to capture more implicit information in high-level space. As explained in Section 3.1, the Attentional Feedback Module for EdgeConv () can extract local prominent features via a max-pooling function in a high-level space. Although the prominent features can encode much geometric information for simple point clouds, more details are needed. Especially for some challenging cases e.g. real objects, complex scenes, or similar shapes etc., more fine-grained features are required for comprehensive feature representation.
Specificly, the edge features from a are employed as the input of corresponding Fine-grained Edge Feature Extractor (, Figure 6). Instead of max-pooling for prominent features, the layer can aggregate more details from all neighbors. Besides, helps to refine the features for compact outputs. Therefore, the extracted fine-grained features are formulated:
|method||input type||#points||avg class acc.||overall acc.|
In this section, we first provide the implementation and training details followed by the datasets we utilize for evaluation. We then analyze our network to establish the effects of different modules. Furthermore, we visualize the outputs, discuss the complexity of our model, and conclude this with the performance against state-of-the-art methods on synthetic and real-world point clouds.
Implementation details. Our proposed network starts with a Naive Mesh Descriptor, which expands the input 3D coordinates into a 14-degree geometric vector. Next, the geometric features are passed through four modules to learn high-level features in different embedding spaces i.e. 64, 64, 128, and 256. Moreover, each module has an Attentional Feedback Module for EdgeConv (, the number of neighbors is 20) for extracting prominent features and a Fine-grained Edge Feature Extractor () for local details.
To incorporate the information from different scales, we concatenate the output feature maps of the mentioned modules together, and a shared with module can further integrate them into a 1024 dimensional feature map. Then we apply max-pooling and average-pooling in parallel over all channels for a global vector, by which an additional three fully connected layers (having 512, 256,
output) can regress the confidence scores for all possible categories. In the end, we employ cross-entropy between predictions and ground-truth labels as our loss function.
|model||Naive Mesh Descriptor||length||overall acc.|
We apply Stochastic Gradient Descent (SGD) with the momentum of 0.9 as the optimizer for training, and its initial learning rate of 0.1 decreases to 0.001 by cosine annealing
. The batch size is set to 32, and the number of training epochs is 300. Besides, we augment the training data with random scaling and translation as in, while there is no pre or post-processing performed during testing.
Datasets. We show the performance of the proposed network on two classification datasets: a classical ModelNet40 , which contains synthetic object point clouds, and the recently introduced ScanObjectNN  composed of real-world object point clouds.
ModelNet40. As the most widely used benchmark for point cloud analysis, ModelNet40 is popular because of its various categories, clean shapes, well-constructed dataset, etc. To be specific, the original ModelNet40 consists of 12,311 CAD-generated meshes in 40 categories, of which 9,843 are used for training while the rest 2,468 are reserved for testing. Moreover, the corresponding point cloud data points are uniformly sampled from the mesh surfaces, and then further preprocessed by moving to the origin and scaling into a unit sphere. For our experiments, we only input the coordinates having 1024 points for each 3D point cloud.
ScanObjectNN. To further prove the effectiveness and robustness of our classification network, we conduct experiments on ScanObjectNN, a newly published real-world object dataset that has about 15,000 objects in 15 categories. Although it has fewer categories than ModelNet40, it is more practically challenging than its synthetic counterpart due to the background, missing parts, and various deformations.
4.1 Ablation studies
To verify the functions and effectiveness of different parts in our network, here we conduct two ablation studies about the proposed modules and the contents of Naive Mesh Descriptor, respectively. We investigate the same proposed network on the ModelNet40 dataset.
: Channel-wise Affinity Attention model,+: in Section 3.1, : Fine-grained Edge Feature Extractor, : Naive Mesh Descriptor.)
|overall acc.||avg class acc.||bag||bin||box||cabinet||chair||desk||display||door||shelf||table||bed||pillow||sink||sofa||toilet|
Effects of different modules. Table 3 shows the results of ablation study concerning different modules of our network. It can be observed that the feedback module achieves well with , and the performance of model 5 shows a further enhancement with the module applied (i.e. ). Besides, the results of model 3/4/5 prove that the network benefits from implicit and explicit geometric features. However, it is worth noting that increasing low-level geometric information () alone may not improve performance due to the redundant features that may cause overfitting (model 5&6). Further, the model benefits once we augment the geometrics in both low and high-levels.
Naive Mesh Descriptor. Although the idea of adding explicit geometric features is simple and intuitive, by comparing models 7 and 8 in Table 3, we can find a 0.4% improvement. To illustrate further, we present another ablation study to investigate the best representation of the Naive Mesh Descriptor. Table 2 shows the results of various possible forms of the . According to the experiments, we conclude that the formation of the for model 5 works better since these terms can comprehensively represent the low-level geometric details of the estimated triangle face, including the vertex, face normal, and edges etc.
Visualization and complexity. From Figure 7 we can visualize corresponding learned features by and modules in different layers of our network on ModelNet40. Particularly, all examples show the property of CNN: the shallow layers have higher impact on simpler features e.g. edges, corners, etc., while deep layers connect those simpler features for more semantically specific parts. As we stated before, mainly extracts prominent features while asists to capture missing details. From the figure we can observe that complements as expected.
Although we have similar operations to the competing methods e.g. layers, algorithm, etc., we manage to simplify the complexity by sharing weights, reducing dimensions, etc. The inference time of our model running on GeForce GTX 2080Ti is about 17.5ms. By comparing with other state-of-the-art methods under the same test conditions111please refer to our supplementary material for more experimental results., our approach has a relatively good compromise between accuracy and model complexity. And we expect to further optimize the network for real-time applications.
4.2 Classification Performance
Results on synthetic point clouds. Table 1 shows the quantitative results on the synthetic ModelNet40 classification benchmark. The result of our network (overall acc: 93.8% and average class acc: 91.0%) exceeds state-of-the-art methods comparing under the same given input i.e. 1k coordinates only. It is worth mentioning that our approach is even better than some methods using extra input points e.g. DGCNN  with 2k inputs got overall acc: 93.5% and average class acc: 90.7%. Similarly, our algorithm outperforms SO-Net , which uses more information such as 5k inputs with normals, got an overall accuracy of 93.4%, and average class accuracy of 90.8%. We also got a higher score than RS-CNN , which uses post-processing that is a ten votes evaluation arrangement during testing. In terms of the network architecture itself, our approach is indicated to be promising and effective for classification.
Results on real-world point clouds. For real-world classification, we use the same network architecture, training strategy, as well as 1k of 3D coordinates as input. To have fair comparisons with state-of-the-art methods, we conduct the classification experiment with its most challenging variant222PB_T50_RS, the hardest case of ScanobjectNN dataset as in . We present Table 4 with the accuracies of competing methods on the real-world ScanObjectNN dataset. The results of our network with an overall accuracy of 80.5% and an average class accuracy of 77.8% have significantly improved the classification accuracy on the benchmark. We perform better than other methods in 7 out of 15 categories, and for hard cases like bag or display, we increase the accuracy by more than 10%. Furthermore, our approach performs even better than DGCNN  and PointNet++  with background-aware network (BGA)  , which is designed explicitly for real-object point clouds.
Despite the fact that the ScanObjectNN dataset contains hard cases for point cloud classification, our method successfully showed its effectiveness and robustness1. As stated before, the point cloud analysis aims to solve practical problems. The excellent performance on real object dataset is a strong affirmation of our work.
In this paper, we propose a new CNN based module called the Attentional Feedback Module targeting some remaining problems of point cloud analysis: the feedback-like modules for edge features can automatically assist learning a better point cloud representation together with the Channel-wise Affinity Attention module that focuses on distinct channels. Besides, we involve more explicit geometrics using Naive Mesh Descriptor and implicit geometrics by Fine-grained Edge Feature Extractor. To compare our method with other state-of-the-art networks, we conduct experiments on both synthetic and real-world datasets. The results show the effectiveness and robustness of our approach.
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