Point Transformer V2: Grouped Vector Attention and Improved Sampling
Abstract
As a pioneering work exploring transformer architecture for 3D point cloud understanding, Point Transformer achieves impressive results on multiple highlycompetitive benchmarks.
In this work, we analyze the limitations of the Point
Transformer and propose our powerful and efficient Point Transformer V2 modelwith novel designs that overcome the limitations of previous work.
In particular,we first propose group vector attention, which is more parameter-efficient andeffective than the previous version of vector attention.
Inheriting the advantagesof both learnable weight vector and multi-head attention, we present a highlyeffective implementation of grouped vector attention with a novel grouped weightencoding layer.
We also strengthen the position information for attention by an additional position encoding multiplier.
Furthermore, we design novel and lightweightgrid-based sampling methods which enable better spatial alignment for downsampling and upsampling and more efficient sampling.
Extensive experimentsshow that our model achieves better performance than its predecessor and achievesstate-of-the-art on several challenging 3D point cloud understanding benchmarks,including 3D point cloud segmentation on ScanNet v2 and S3DIS and 3D pointcloud classification on ModelNet40.
Our code will be made publicly available.
Introduction
Point Transformer (PTv1) [1] introduces the self-attention networks to 3D point cloud understanding.
Combining the vector attention [2] with a U-Net style encoder-decoder framework, PTv1 achievesremarkable performance in several 3D point cloud recognition tasks, including shape classification,object part segmentation and semantic scene segmentation.
In this work we analyze the limitations of Point Transformer (PTv1) [1] and propose a new elegantand powerful backbone named Point Transformer V2 (PTv2).
Our PTv2 improves upon PTv1 withseveral novel designs, including the grouped vector self-attention, the improved position embedding,and the new grid-based sampling schemes.
The vector attention layers in PTv1 utilize MLPs as the weight encoding to map the subtractionrelation of query and key into an attention weight vector that can modulate the individual channelsof the value vector.
However, as the model goes deeper and the number of channels increases, thenumber of weight encoding parameters also increases drastically, leading to severe overfitting andlimiting the model depth.
To address this problem, we present grouped vector attention with a moreparameter-efficient formulation, where the vector attention is divided into groups with shared vectorattention weights.
Meanwhile, we show that the well-known multi-head attention [3] and the vectorattention [2, 1] are degenerate cases of our proposed grouped vector attention.
Our proposed groupedvector attention inherits the merits of both vector attention and multi-head attention while being moreefficient and powerful.
Furthermore, point positions provide important geometric information for 3D semantic understanding.
Hence, the positional relationship among 3D points is more critical than 2D pixels.
However, previous3D position encoding schemes mostly follow the 2D ones and do not fully exploit the geometricknowledge in 3D coordinates.
To this end, we strengthen the position encoding mechanism by applying an additional position encoding multiplier to the relation vector.
Such a design strengthens thepositional relationship information in the model, and we validate its effectiveness in our experiments.
Moreover, it is worth noting that the irregular, non-uniform spatial distributions of points are significant challenges to the upsampling and downsampling modules for point cloud processing.
Previous
FPS and kNN-based point cloud downsampling and upsampling approaches [4] are time-consumingand not spatially well-aligned.
To overcome this problem, we propose a grid-based sampling approach, where the 3D space of the point cloud is divided into non-overlapping 3D grids.
We fuse thepoint within the same grid cell during downsampling and map features back to these points withinthe same grid during upsampling.
In conclusion, we propose Point Transformer V2, which improves Point Transformer [1] from severalperspectives:
• We propose an effective grouped vector attention (GVA) with a novel weight encoding layerthat enables efficient information exchange within and among attention groups.
• We introduce an improved position encoding scheme to utilize point cloud coordinates better
and further enhance the spatial reasoning ability of the model.
• We design the grid-based downsampling and upsampling strategies to enable more efficient
and spatially better-aligned sampling than previous methods.
We conducted extensive analysis and controlled experiments to validate our designs.
Our results
indicate
that PTv2 outperforms predecessor works and sets the new state-of-the-art on various 3Dunderstanding tasks.
Related Works
Image transformers.
With the great success of ViT [5], the absolute dominance of convolution invision tasks is shaken by Vision Transformer, which becomes a trend in 2D image understanding [6, 7,8, 9].
ViT introduces the far-reaching scaled dot-product self-attention and multi-head self-attentiontheory [3] in NLP into vision by considering image patches as tokens.
However, operating globalattention on the entire image consumes excessive memory.
To solve the memory consumptionproblem, Swin Transformer [6] introduces the grid-based local attention mechanism to operate thetransformer block in a sequence of shifted windows.
Point cloud understanding.
Learning-based methods for processing 3D point clouds can be classifiedinto the following types: projection-based, voxel-based, and point-based networks.
An intuitive wayto process irregular inputs like point clouds is to transform irregular representations into regular ones.
Projection-based methods project 3D point clouds into various image planes and utilize 2D CNNbased backbones to extract feature representations [10, 11, 12, 13].
An alternative approach operatesconvolutions in 3D by transforming irregular point clouds into regular voxel representations [14, 15].
Those voxel-based methods suffer from inefficiency because of the sparsity of point clouds until theintroduction and implementation of sparse convolution [16, 17].
Point-based methods extract featuresdirectly from the point cloud rather than projecting or quantizing irregular point clouds onto regulargrids in 2D or 3D [18, 4, 19, 20].
The recently proposed transformer-based point cloud understandingapproaches, introduced in the next paragraph, are also categorized into point-based methods.
Point cloud transformers.
Transformer-based networks belong to the category of point-basednetworks for point cloud understanding.
During the research upsurge of vision transformers, at almostthe same period, Zhao et al.
[1] and Guo et al.
[21] published their explorations of applying attentionto point cloud understanding, becoming pioneers in this direction.
The PCT [21] proposed by Guoet al.
performs global attention directly on the point cloud.
Their work, similar to ViT, is limitedby memory consumption and computational complexity.
Meanwhile, based on the vector attentiontheory proposed in SAN [2], Point Transformer [1] proposed by Zhao et al.
directly performs localattention between each point and its adjacent points, which alleviated the memory problem mentionedabove.
Point Transformer achieves remarkable results in multiple point cloud understanding tasks and U ! U " U " U ! γ U "
U #
MLP Δ𝑃 +
Softmax 𝑘 𝑟 𝑤 𝑉 𝑞 ℝ $ → ℝ % AGG 𝑓 & 𝑓 ’ ∈ 𝑀(𝑝 & ) 𝑝 & 𝑝 ’ 𝑓 &) 𝜔 U ! U " U " U ! γ
U "
U #
MLP MLP Δ𝑃
+
Gouped AGG Softmax 𝑘 𝑟 𝑤 𝑉 𝑞 ⊙ 𝜔ℝ $ → ℝ * 𝑓 & 𝑓 &) 𝑓 ’ ∈ 𝑀(𝑝 & ) 𝑝 & 𝑝 ’
PTv
PTv Downsampling Upsampling follows the and applies voxel hashing-based architecture to vector attention, achieving a better speed-accuracytrade-off. In this work, we analyze the limitations of the Point Transformer, and propose severalnovel architecture designs for the attention, position encoding, and sampling module, to improve theefficiency and effectiveness of the Point Transformer.
Our proposed model, Point Transformer V2,performs better than the Point Transformer across a variety of 3D scene understating tasks.
Point Transformer V2
We analyze the limitations of Point Transformer V1 (PTv1) [1] and propose our Point Transformer V2(PTv2), including several improved modules upon PTv1.
We begin by introducing the mathematicalformulations and revisiting the vector self-attention used in PTv1 in Sec. 3.1.
Based on the observationthat the parameters of PTv1 increases drastically with the increased model depth and channel size,we propose our efficient and powerful grouped vector attention in Sec. 3.2.
Further, we introduce ourimproved weight encoding in Sec.
3.1 and the new sampling method in Sec. 3.4.
We finally describeour network architecture in Sec. 3.5.
3.1 Problem Formulation and Background
Problem formulation.
Let M =
( P , F ) be a 3D point cloud scene containing a set of pointsx i =
( p i , f i ) ∈
M , where p i ∈ R 3 represents the point position, and f i ∈ R c represents the pointfeatures.
Point cloud semantic segmentation aims to predict a class label for each point x i , and thegoal of scene classification is to predict a class label for each scene M .
M ( p ) denotes a mappingfunction that maps the point at position p to a subset of M denoted as “reference set”.
Next, werevisit the self-attention mechanism used in PTv1 [1].
Local attention.
Conducting the global attention [5, 21] over all points in a scene is computationallyheavy and infeasible for large-scale 3D scenes.
Therefore, we apply local attention where the attentionfor each point x i works within a subset of points, i.e ., reference point set, M ( p i ) .
A common practice [23, 24, 25, 26] for image transformer is shifted-grid attention [6], where attentionis alternatively applied over two sets of non-overlapping image grids.
Similarly, the 3D space can be split into uniform non-overlapping grid cells, and the reference set is defined as the points within thesame grid, i.e ., M ( p i ) =
{ ( p j , f j ) | p j in the same grid cell as p i } .
However, such attention relieson a cumbersome shift grid operation to achieve a global receptive field, and it does not work well onpoint clouds where the point densities within different grids are not consistent.
PTv1 adopted neighborhood attention , where the reference point set is a local neighborhood of thegiven point, i.e ., M ( p i ) =
{ ( p j , f j ) | p j ∈ Neighborhood ( p i ) } .
Specifically, the neighborhoodpoint set M ( p i ) is defined as the k nearest neighboring (kNN) points of p i in PTv1.
Our experiments(Sec. 4.3) show that neighborhood attention is more effective than shifted-grid attention, so ourapproach adopts the neighborhood attention.
Scalar attention and vector attention.
Given a point x i =
( p i , f i ) ∈
M , we apply linearprojections or MLPs to project the point features
f i to the feature vectors of query q i , key k i , andvalue v i , each with c h channels.
The standard scalar attention (SA) operated on the point x i and itsreference point set M ( p i ) can be represented as follows,
[Equation]
The attention weights in the above formulation are scalars computed from the scaled dot-product [3]between the query and key vectors.
Multi-head scalar attention (MSA) [3] is an extension of SAwhich runs several scalar attentions in parallel.
MSA is widely applied in transformers, and we willshow in Sec.
3.2 that MSA is a degenerate case of our proposed grouped vector attention.
Instead of the scalar attention weights, PTv1 applies vector attention , where the attention weights arevectors that can modulate the individual feature channels.
In SA, the scalar attention is computed bythe scaled dot-product between the query and key vectors.
In vector attention, a weight encodingfunction encodes the relation between query and key to a vector.
The vector attention[2] is formulatedas follows,
[Equation]
where ⊙ is the Hadamard product.
γ is a relation function ( e.g ., subtraction).
ω :
R c
→ R c is alearnable weight encoding ( e.g ., MLP) that computes the attention vectors to re-weight v j by channelsbefore aggregation.
Fig.
2 (a) shows a method using vector attention with linear weight encoding.
3.2 Grouped Vector Attention
In vector attention, as the network goes deeper and there are more feature encoding channels, thenumber of parameters for the weight encoding layer increases drastically.
The large parameter sizerestricts the efficiency and generalization ability of the model.
In order to overcome the limitations ofvector attention, we introduce the grouped vector attention, as illustrated in Fig. 1(left).
Attention groups.
We divide channels of the value vector v ∈ R c evenly into g groups ( 1 ≤ g ≤ c ).
The weight encoding layer outputs a grouped attention vector with g channels instead of c channels.
Channels of v within the same attention group share the same scalar attention weight from thegrouped attention vector.
Mathematically,
[Equation]
where γ is the relation function and ω :
R c
→ R g is the learnable grouped weight encoding definedin the next paragraph.
The second equation in Eq.
3 is the grouped vector aggregation .
Fig.
2(a) presents a vanilla GVA implemented by a fully connected weight encoding, the number of thegrouped weight encoding function parameters reduced compared with the vector attention (Fig. 2(b)), leading to a more efficient and powerful model.
GVA is a generalized formulation of VA and MSA.
GVA is also a generalized form of multi-headscalar attention.
In Eq.
3, if we define: Our GVA degenerates to vector attention (VA) when g = c ,
[Figure]
𝛾(𝒒,𝒌) 𝒘 𝒗 𝛾(𝒒,𝒌) 𝒘 𝒗 𝛾(𝒒,𝒌) 𝒘 𝒗 𝛾(𝒒,𝒌) 𝒘 𝒗
and it degenerates to multi-head self-attention (MSA) if ω in Eq.
3 is defined as follows,
[Equation]
where c g = c/g and r ∈ R 1 × c .
Grouped linear.
Inspired by the weight encoding function of MSA, we design the grouped linearlayer ζ ( r ) :
R c
→ R g where different groups of the input vector are projected with differentparameters independently.
Grouped linear further reduce the number of parameters in the weightencoding function.
Our final adopted grouped weight encoding function is composed of the groupedlinear layer, normalization layer, activation layer, and a fully connected layer to allow inter-groupinformation exchange.
Mathematically,
[Equation]
where c g = c/g , p 1 , . .
. , p g ∈ R cg are learnable parameters, and ◦ represents function composition.
3.3 Position Encoding Multipler
Different from the discrete, regular-grid pixels in 2D images, points in the 3D point cloud areunevenly distributed in a continuous Euclidean Metric space, making the spatial relationship in 3Dpoint cloud much more complicated than 2D images.
In transformers and attention modules, thespatial information is obtained with the position encoding δ bias ( p i − p j )) added to the relation vectorγ ( q i , k j ) as a bias.
We strengthen the position encoding with an additional multiplier ω ( δ mul ( p i − p j ) to the relationvector.
As shown in Fig.
1 (left), our improved position encoding is as follows,
[Equation]
where ⊙ is the Hadamard product.
δ mul , δ bias : R d (cid:55)→ R d are two MLP position encoding functions,which take relative positions as input.
3.4 Grid-based Sampling Methods
The farthest-point-sampling-based downsampling method and the interpolation-based upsamplingmethod presented in PointNet++ [4] and used in PTv1 [1] are time-consuming, and the downsamplingand upsampling are not spatially well-aligned.
Therefore, we propose the more efficient and effectivegrid-based upsampling and downsampling approach, shown in Fig.
Grid fusion downsampling.
Given a point set M =
( P , F ) , we partition M into subsets[ M 1 , M 2 , ..., M n ′ ] by partitioning the space into non-overlapping grid cells.
The size of thegrid cells is denoted as s .
We downsample each subset of points M i =
( P i , F i ) from a single gridcell as follows,
[Equation]
where ( p ′ i , f ′ i ) is the downsampled point position and features form subset M i , and
U ∈ R c × c ′ isthe linear projection.
Collecting the sampled points from n ′ subsets gives us the downsampled pointset M ′ =
{ p ′ i , f ′ i } n ′ i =1 .
Grid mapping upsampling.
To upsample the downsampled point set M ′ back to M , the pointlocations in M are known from the downsampling process, and we only need to obtain the upsampledfeatures for each point in M .
With the help of the grid-based partitioning [ M 1 , M 2 , ..., M n ′ ] duringthe downsampling stage, we can map a point feature to all points from the same subset,
[Equation]
3.5 Network Architecture
Backbone structure.
Following previous works [17, 1], we adopt the U-net architecture with skipconnections.
There are four stages of encoders and decoders with block depths [2, 2, 6, 2] and[1, 1, 1, 1], respectively.
The grid size multipliers for the four stages are [x3.0, x2.5, x2.5, x2.5],representing the expansion ratio over the previous sampling stage.
The attention is conducted in alocal neighborhood, described in “neighborhood attention” in Sec. 3.1.
In Sec.
4.3 we compare theneighborhood attention with shift-grid attention.
The initial feature dimension is 48, and we first embed the input channels to this number with a basicblock with attention groups of 6.
Then, we double this feature dimension and attention groups eachtime entering the next encoding stage.
The initial feature dimension is 48.
For the four encodingstages, the feature dimensions are [96, 192, 384, 384], and the corresponding attention groups are[12, 24, 48, 48].
Output head.
For point cloud semantic segmentation, we apply an MLP to map point featuresproduced by the backbone to the final logic for each point in the input point set.
For point cloudclassification, we apply global average pooling over the point features produced by the encodingstages to obtain a global feature vector, followed by an MLP classifier for prediction.
Experiments
To validate the effectiveness of the proposed method, we conduct experimental evaluations on ScanNetv2 [45] and S3DIS [46] for semantic segmentation, and ModelNet40 [47] for shape classification.
Implementation details are available in the supplementary materials.
4.1 Semantic Segmentation
Data and metric.
For semantic segmentation, we experiment on ScanNet v2 [45] and S3DIS [46].
The ScanNet v2 dataset contains 1,513 room scans reconstructed from RGB-D frames.
The dataset isdivided into 1,201 scenes for training and 312 for validation.
Point clouds for the model input aresampled from vertices of reconstructed meshes, and each sampled point is assigned a semantic labelfrom 20 categories (wall, floor, table, etc.).
The S3DIS dataset for semantic scene parsing consistsof 271 rooms in six areas from three different buildings.
Following a common protocol [37, 4, 1],area 5 is withheld during training and used for testing.
Different from ScanNet v2, points of S3DISare densely sampled on the mesh surfaces and annotated into 13 categories.
Following a standardprotocol [4], we use mean classwise intersection over union (mIoU) as the evaluation metric for
[Table] [Table]
validation and test set of ScanNet v2.
And we use mean classwise intersection over union (mIoU),mean of classwise accuracy (mAcc), and overall point-wise accuracy (OA) for evaluating performanceon S3DIS area5.
Performance comparison.
Table 1 and Table 2 show the results of our PTv2 model comparedwith previous methods on ScanNet v2 and S3DIS, respectively.
Our PTv2 model outperforms priormethods in all evaluation metrics.
Notably, PTv2 significantly outperforms PTv1 [1] by 4.9% mIoUon the ScanNet v2 validation set.
Visualization.
The qualitative results of point cloud semantic segmentation are shown in Fig.
3 and
Fig.
Our PTv2 model is able to predict semantic segmentation results that are quite close theground-truth.
It is worth noting that our model can capture the detailed structure information andpredict the correct semantics for challenging scenarios.
For example, in the S3DIS scenes with chairs,
PTv2 is able to cleanly predict the chairs’ legs and armrests.
4.2 Shape Classification
Data and metric.
We test our proposed PTv2 model for 3D point cloud classification on ModelNet40dataset.
The ModelNet40 [47] dataset consists of 12,311 CAD models belonging to 40 objectcategories.
9,843 models are split out for training, and the rest 2,468 models are reserved for testing.
Following the common practice in the community, we report the class-average accuracy (mAcc) andoverall accuracy (OA) on the test set.
Performance comparison.
We test our PTv2 model and compare it with previous models on the
ModelNet40 dataset for shape classification.
Results are shown in Table 3, demonstrating that ourproposed PTv2 model achieves state-of-the-art performance on ModelNet40 shape classification.
Thevisualization results of shape classification are provided in the supplementary materials.
4.3 Ablation Study
We conduct ablation studies to examine the effectiveness of each module in our design.
The ablationstudy results are reported on ScanNet v2 validation set.
Attention type.
We first investigate the effects of different attention designs.
We experiment withtwo types of local attention introduced in Sec. 3.1, namely shifted-grid attention and neighborhoodattention [1].
Then, to validate the effectiveness of our proposed grouped vector attention (denoted as“GVA”), we compare it with the commonly-used multi-head self-attention (denoted as “MSA”).
Weuse the vanilla position encoding in PTv1 [1] and our proposed grid-based sampling scheme in all ofthe experiments in Table 4.
It shows neighborhood attention performs significantly better than shiftedgrid attention, indicating that the neighborhood attention is better suited for point clouds which arenon-uniformly distributed.
Moreover, our proposed grouped vector attention consistently outperforms
[Table] [Table]
[Table] [Table]
[Table]
the commonly-used multi-head self-attention with both shifted-grid attention and neighborhoodattention.
So our grouped vector attention is not only more efficient, but also more effective, thanmulti-head self-attention.
The comparison between GVA and MSA indicates the effectiveness of thelearnable parameters in the grouped linear layer of the grouped weight encoding in Sec. 3.2.
Weight encoding.
We study the effects of different weight encoding functions ω in Table 6.
Theweight encoding functions are introduced in Sec.
3.1 and Sec. 3.2, and different attention mechanismsadopt different weight encoding functions.
We use the vanilla position encoding in PTv1 [1] and ourproposed grid-based sampling scheme in all of the experiments in Table 4.
We experimented withthe following weight encoding functions: (1) The weight encoding for MSA in Eq.
4, denoted as“MSA”.
(2) Weight encoding as a linear layer denoted as “L”.
The grouped linear layer, whichis ζ in Eq.
5, denoted as “GL”.
The linear layer followed by batch normalization, activation,and another linear layer, denoted as “L+N+A+L”.
The grouped linear layer, followed by batchnormalization, activation, and a linear layer, denoted as “GL+N+A+L”.
(5) is also the groupedweight encoding function used for our grouped vector attention, introduced as ω in Eq.
Resultsin Table 6 demonstrate that our grouped weight encoding function outperforms other compareddesigns.
Specifically, comparing (1), (3) and (5), GL slightly outperforms MSA but adding additionalinter-group information exchange combined with proper normalization and activation can boostthe performance to be better than MSA.
Moreover, the comparison between (5) and (4) and thecomparison between (3) and (2) both indicate that our grouped linear layer outperforms the naivelinear layer, even though the grouped linear layer has g times fewer parameters and requires lesscomputing than the linear layer.
Sampling method.
In Sec.
3.4 we discuss potential limitations of the FPS-based sampling in
PTv1 and propose a new grid-based upsampling and downsampling scheme.
We experiment withdifferent downsampling-upsampling schemes in Table 5.
For our grid-based sampling, the basegrid size is 0.02 meters, which is identical to the voxelization grid size during data pre-processing.
The grid size multipliers are the grid size expansion ratio over the previous sampling stage.
Forexample, [ × 4 . 0 , × 2 . 0 , × 2 . 0 , × 2 . 0 ] means that the sampling grid sizes are: [ 0 .
32 , 0 . 64 ]meters, respectively.
We choose a relatively large value for initial grid sizes ( × 3 . 0 and × 4 . 0 ) toprovide sufficiently large receptive fields, which is analogous to the common practice in image
Input
Ground truth
PTv
Input
Ground truth
PTv
[Figure] [Figure]
transformers [5].
For subsequent subsampling stages, we observe that × 2 . 0 grid size increase resultsin an approximate downsample ratio of 4 for the point cloud, while × 2 .
5 grid size increase resultsin an approximate downsample ratio of 6.
We choose the same sampling ratio of 4 and 6 in FPSbased sampling experiments to ensure a fair comparison.
The results in Table 5 illustrate that ourgrid-based sampling achieves higher mIoU than the FPS-based method.
For FPS-based sampling,the performance decreases significantly when the sampling ratio increases from 4 to 6.
However, forour grid-based sampling, we observe that initial grid size and subsequent grid size multipliers do notsignificantly affect the overall performance, so we can use larger grid sizes to reduce the number ofpoints in each stage to save memory.
Module design.
We ablate different modules: grouped vector attention (VGA), position encodingmultiplier (PE mul), grid fusion downsampling (Grid down), grid mapping upsampling (Grid up).
The results are shown in Table 7.
Experiment I is PTv1 [1] with structural parameter adjustments andbetter data processing, which are also shared with the rest of experiments.
Experiment II to V addeach of our proposed components in turns.
The increasing mIOU indicates the effectiveness of eachcomponent.
Conclusion
We propose Point Transformer V2 (PTv2), a powerful and efficient transformer-based backbonefor 3D point cloud understanding.
Our work makes several non-trivial improvements upon Point
Transformer V1 [1], including the grouped vector attention, improved position encoding, and gridbased sampling.
Our PTv2 model achieves state-of-the-art performance on point cloud classificationand semantic segmentation benchmarks.
Limitations.
Our limitation is that we have not yet explored the effect of parameter initialization forour point transformer, which plays an essential role in the convergence of image transformers.
Moreinformation is in the supplementary materials.
Potential negative social impact.
When training the Point Transformer V2 model on large datasets,researchers should be aware of the potential negative social impact introduced by the dataset bias andimproper usage of the model.
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