OPUS: Occupancy Prediction Using a Sparse Set

Authors: jiabao  wang
zhaojiang  liu
qiang  meng
liujiang  yan
ke  wang
jie  yang
wei  liu
qibin  hou
ming-ming  cheng
Venue: NeurIPS_cc_2024_Conference
Published: 2024-05-08 13:41:55

Abstract: Occupancy prediction, aiming at predicting the occupancy status within voxelized 3D environment, is quickly gaining momentum within the autonomous driving community. Mainstream occupancy prediction works first discretize the 3D environment into voxels, then perform classification on such dense grids. However, inspection on sample data reveals that the vast majority of voxels is unoccupied. Performing classification on these empty voxels demands suboptimal computation resource allocation, and reducing such empty voxels necessitates complex algorithm designs. To this end, we present a novel perspective on the occupancy prediction task: formulating it as a streamlined set prediction paradigm without the need for explicit space modeling or complex sparsification procedures. Our proposed framework, called OPUS, utilizes a transformer encoder-decoder architecture to simultaneously predict occupied locations and classes using a set of learnable queries. Firstly, we employ the Chamfer distance loss to scale the set-to-set comparison problem to unprecedented magnitudes, making training such model end-to-end a reality. Subsequently, semantic classes are adaptively assigned using nearest neighbor search based on the learned locations. In addition, OPUS incorporates a suite of non-trivial strategies to enhance model performance, including coarse-to-fine learning, consistent point sampling, and adaptive re-weighting, etc. Finally, compared with current state-of-the-art methods, our lightest model achieves superior RayIoU on the Occ3D-nuScenes dataset at near 2x FPS, while our heaviest model surpasses previous best results by 6.1 RayIoU.

Main paper: 
 introduction: 
 Compared with well-established box representations [8, 23, 20, 39, 29, 48, 32] , voxel based occupancy [16, 37, 10, 38, 33] can provide finer geometry and semantic information for the surrounding scene. For example, it is not straightforward to use bounding boxes to describe vehicles with doors open or cranes with outriggers deployed. While occupancy can naturally describe such uncommon shapes. Thus occupancy prediction is quickly gaining traction in the autonomous driving community.Recent approaches [3, 46, 9, 27, 16, 34] to the task predominantly rely on dense data representation, with a direct one-to-one correspondence between feature points and physical voxels. It has come to our attention that the vast majority of physical voxels is empty. For instance, in SemanticKITTI [1] , approximately 67% of all voxels are empty, while in Occ3D-nuScenes [38] , this proportion exceeds 90%. Such sparse nature of occupancy data renders the direct dense representation undeniably inefficient, as majority of the computation is allocated towards empty voxels. Alternative sparse latent representations have been explored to alleviate such inefficiency, such as the Tri-Perspective View representation [37, 9] or reduced solution spaces [21, 10] , leading to notably reduced computational costs. However, these approaches still treat occupancy prediction as a classification problem at specific locations, necessitating complex intermediate designs and explicit modeling of 3D spaces. In this work, we instead formulate the task as a direct set prediction problem, where we regress occupied locations and classify corresponding semantic labels in parallel. Our proposed framework termed OPUS leverages a transformer encoder-decoder architecture featuring: (1) an image encoder to extract 2D features from multi-view images; (2) a set of learnable queries to predict occupied locations and semantic classes; (3) a sparse decoder to update query features with correlated image features. Our OPUS eliminates the need for explicit space modeling or complex sparsification procedures, offering a streamlined and elegant end-to-end solution. However, a key challenge lies in matching predictions with ground-truths, especially given the unordered nature of predicted results. We argue that the Hungarian algorithm [12] , although widely adopted in the DETR families [5, 47, 28, 22, 13, 42] , is not suitable for this task. Having a O(n 3 ) time complexity and a O(n 2 ) space complexity, the Hungarian algorithm is unable to handle a substantial number of voxels. In our experiments, associating two sets with 10K points each, the Hungarian algorithm consumes approximately 24 seconds and 2,304Mb of GPU memory on a 80G A100 GPU. In reality, the voxel number can go up to ∼70K in the Occ3D-nuScenes [38] dataset. Thus directly applying the Hungrian algorithm for set-to-set matching is infeasible in the occupancy prediction context.But is accurate one-to-one association truly necessary for occupancy prediction? We recognize that the goal of one-to-one correspondence between prediction results and ground-truth annotation is to obtain supervision signals, essentially complete, precise point locations, and accurate point classes. The heavylifting of one-to-one association can be entirely avoided if we can obtain such supervision signals elsewhere. Therefore, we propose to decouple the occupancy prediction task into two parallel subtasks, as illustrated in Fig. 1 . The first task obtains supervision on point locations by aligning predicted point distributions with ground-truths, a task achievable through the Chamfer distance loss, a well-established technique for point clouds [6, 30] . The second task obtains supervision on point classes by assigning semantic labels to predicted points. This is accomplished by assigning each point the class of its nearest neighbor in the ground-truths. It's noteworthy that all operations involved can be executed in parallel and are highly efficient on GPU devices. As a result, a single matching in Occ3D-nuScenes can be processed within milliseconds, with negligible memory consumption. With a time complexity of O(n 2 ) and space complexity of O(n), our formulation breaks the ground for large-scale training for the occupancy prediction models.In addition, we propose several strategies to further boost the performance of occupancy prediction in our end-to-end sparse formulation, including coarse-to-fine learning, consistent point sampling, and adaptive loss re-weighting. On Occ3D-nuScenes, all our model variants easily surpass all prior work, verifying the efficacy and effectiveness of the proposed method. Especially, our most lightweight model achieves a 3.3 absolute RayIoU improvement compared with SparseOcc [21] while operating more than 2× faster. The heaviest configuration ultimately achieves a RayIoU of 41.2, establishing a new upper bound with a 14% advantage. Our contributions are summarized as follows:• To the best of our knowledge, for the first time, we view the occupancy prediction as a direct set prediction problem, facilitating end-to-end training of the sparse framework.• Several non-trivial strategies, including coarse-to-fine learning, consistent point sampling, and adaptive re-weighting, are further introduced for boosting the performance of OPUS.• Extensive experiments on Occ3D-nuScenes reveal that OPUS can outperform state-of-the-art methods in terms of RayIoU results, while maintain a real-time inference speed.2 Related workQuestion: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?Answer: [Yes] Justification: We have described our contributions and scope explicitly in both the abstract and introduction.Guidelines:• The answer NA means that the abstract and introduction do not include the claims made in the paper.• The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.• The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.• It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper. 
occupancy prediction: 
 Occupancy prediction entails determining the occupancy status and class of each voxel within a 3D space. This task has recently become a foundational perception task in autonomous driving and raises great interests from both academic and industrial communities. Conventional methods [3, 46, 9, 27, 16, 41, 38, 4] typically employ the continuous and dense feature representation, which, however, suffer from computational redundancy due to the inherent sparsity of occupancy data. In addressing this issue, Tang et al. [37] compresses the dense feature using the Tri-Perspective View representation for model efficiency. Recently, several transformer-based approaches [21, 10, 14] with sparse queries have emerged. For example, OccupancyDETR [10] conducts object detection followed by assigning each object with one query for occupancy completion. VoxFormer [14] generates 3D voxels from a set of sparse queries, corresponding to occupied locations identified through a pre-task of depth estimation. Meanwhile, SparseOcc [21] employs a series of sparse voxel decoders to filter out empty grids and predict occupied statuses of retained voxels in each stage. While these approaches have succeeded in reducing computational costs, they often necessitate multi-stage processes and intricate space modeling. In contrast, our method directly applies sparse queries to regress the occupied locations without pre-defined locations, facilitating an elegant and end-to-end occupancy prediction.The concept of directly predicting sets with Transformers was initially introduced by DETR [5] , where a set of sparse queries generates unordered detection results with feature and object interactions. By viewing the object detection as a direct set prediction problem, DETR eliminates the need for complex post-processing, enabling end-to-end performance. Following DETR, numerous variants [47, 28, 22, 13, 42, 45, 36] have been proposed for performance improvements and efficient training. The effectiveness of the sparse-query-based paradigm has also been validated in 3D object detection [43, 23, [18] [19] [20] 40] , where 3D information is encoded into the queries. For example, DETR3D [43] employs a sparse set of 3D object queries to index 2D features, linking 3D positions to multi-view images using camera transformation matrices. PETR [23] generates 3D position-aware features by encoding 3D position embedding into 2D image features, enabling queries to directly aggregate features without the 3D-to-2D projection. Sparse4D [18] further advances sparse 3D object detection by refining detection results with spatial-temporal feature fusion. Despite of the great success, set prediction with Transformers remains restricted primarily to object detection, where the query number are typically small due to the limited object number in a scene. Extending this approach to occupancy prediction poses a big challenge due to the substantially larger number of queries required.Question: Does the paper discuss the limitations of the work performed by the authors?Answer: [Yes]Justification: We describe our limitations in the section "Conclusions and Limitations" in our main text.Guidelines:• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.• The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.• The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.• The authors should reflect on the factors that influence the performance of the approach. For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.• The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.• If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.• While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. 
methodology: 
 In this part, we first recap current query-based sparsification approaches for occupancy prediction in Sec. 3.1. Then, Sec. 3.2 describes our formulation that views the task as a direct set prediction problem. Finally, we detail the proposed OPUS framework in Sec. 3.3.Transformers with sparse queries offer a promising avenue for tackling the inherent sparsity in occupancy representation. A notable approach to reduce the number of queries is allocating each query to a patch of voxels rather than a single voxel, as presented in PETRv2 [24] . However, this method still generates a dense prediction of the 3D space, thus failing to efficiently address the redundancy issue. Alternatively, VoxFormer [14] and SparseOcc [21] allocate sparse queries exclusively to occupied voxels. VoxFormer employs a depth estimation module to identify potentially occupied voxels, while SparseOcc utilizes multiple stages to progressively filter out empty regions. Nonetheless, their sparsification processes rely on accurately recognizing the occupancy status of voxels and therefore suffer from the cumulative errors. Moreover, their pipelines necessitate intricate intermediate descriptions of the 3D space, hindering seamless end-to-end operation.The dilemmas of current approaches significantly stem from treating the task as a classification problem, where each query is confined to a specific physical region for classifying the semantic labels. This constraint severely limits query flexibility, preventing adaptive focus on suitable areas. To address this, we propose to remove this restriction by allowing each query to autonomously determine its relevant area. In the end, we view occupancy prediction as a direct set prediction problem, where each query predicts point positions and semantic classes, simultaneously.At the core of our work lies the conceptualization of occupancy prediction as a set prediction task. We denote the V g occupied voxels in the ground-truth as {P g , C g }, where |P g | = |C g | = V g . For each entry in {p g , c g } ∈ {P g , C g }, p g represents the 3D coordinates of a voxel center, while c g stores the semantic class of the corresponding voxel. Given the predictions {P, C} of V points, our primary challenge is to devise an effective strategy for set-to-set matching. In other words, we must determine how to supervise the training of unordered predictions with the ground-truth data. One alternative is to adopt the Hungarian algorithm. However, our previous discussions and experiments in the appendix reveal its scalability limitations. Rather than pursuing one-to-one associations between the predictions and ground-truths, we recognize the matching essentially aims at accurate locations and classes in predictions. This motivates us to decouple the task into two parallel objectives: (1) Encouraging the predicted locations to be precise and comprehensive. (2) Ensuring the predicted points are assigned with proper semantic classes from the ground-truth labels.The first objective focuses on aligning distributions between predicted and ground-truth points, a task achievable through the Chamfer distance loss which is well-proved in the field of point clouds [6, 30, 11, 44] :EQUATIONMinimizing Chamfer distance leads to similar distributions of predictions and ground-truths, enabling direct learning of occupied voxels without necessitating knowledge of their orders.Concerning the second objective, although direct comparison between C and C g is invalid due to their correspondence to different locations, we can leverage the spatial locality properties of voxels to find a proxy. Nearby points belonging to the same object usually carry the same semantic labels, thus we propose assigning each predicted point the class of its nearest neighbor voxel in the ground-truth:{ Ĉ, P} = arg min {cg ,pg }∈{Cg ,Pg } ∥pg -p∥2, p ∈ P .Here, Ĉ is the updated classes that are prepared to supervise the learning of the predicted C.It's noteworthy that computations of both Eq. (1) and Eq. ( 2) can be executed efficiently and in parallel on GPU devices. As a result, a single matching can be swiftly processed within milliseconds, enabling feasibility of the large-scale training by viewing the occupancy prediction task as a direct set prediction problem. Next, we delve into the specifics of the proposed OPUS framework.This part describes OPUS framework, as illustrated in Fig. 2 . Initially, image features are extracted from multi-view images. And a set of learnable queries Q, point positions P, and scores C are initialized. Subsequently, these query features and prediction outcomes are fed into a sequence of decoders, undergoing iterative refinement through correlation with image features. At each stage, predicted positions and scores are supervised by the ground-truths, facilitating end-to-end training for the entire framework. It can be observed that our most important structure is the sequence of multiple decoders. Therefore, we next provide a detailed description to the inputs/outputs of the decoders and how features are aggregated and updated within the decoders.Notations. Denote the set of learnable queries, point positions, and point scores as {Q 0 , P 0 , C 0 } before feeding into decoders, and as {Q i , P i , C i } for the outcomes of the i-th decoder. The length of these sets is all Q, which corresponds to the number of queries. Each query feature q i ∈ Q i , i ∈ {0, 1, • • • , 6} has a channel size C, set to 256 in our implementation. To reduce the number of queries, which is a bottleneck for model efficiency, each query q i predicts R i points rather than a single one. Consequently, p i ∈ P i andc i ∈ C i have shapes of Q × R i × 3 and Q × R i × N , respectively.Here, N represents the number of semantic classes. (2) A series of decoders to refine the queries with image features, which are correlated via the consistent point sampling module. (3) A set of learnable queries to predict locations and classes of occupancy points. Each query obeys a coarseto-fine rule, progressively increasing the number of predicted points. In the end, the entire model is trained end-to-end using our adaptively re-weighted set-to-set losses.Coarse-to-fine prediction. High-level semantic information can be difficult to predict accurately from just low-level features. Therefore, instead of attempting to predict occupancy for the entire 3D environment, we allow the model to predict "sparse" occupancy results in early stages, as shown in Fig. 2 . To achieve this, we follow a coarse-to-fine strategy, gradually increasing the number of points generated from one query. In other words, we always haveR i-1 ≤ R i for i ∈ {1, 2, • • • , 6}.It's noteworthy that the Chamfer distance has another advantage over the Hungarian algorithm here: even when the number of predictions is smaller than that of the ground-truths, the assignment won't collapse into a local shape of the ground-truths. This is because the Hungarian algorithm could assign the predictions to any subset of the ground-truths due to its lack of distribution constraints. In contrast, the Chamfer distance maintains a global perspective, considering the overall distribution of points rather than enforcing a strict one-to-one correspondence. This ensures that the predicted points are more evenly distributed and representative of the actual 3D environment, even when fewer in number.Details of the decoder. Our decoder is analogous to that in SparseBEV [20] , a performant and sparse object detector. For a given query q i-1 ∈ Q i-1 and its corresponding point locations p i-1 ∈ P i-1 , the i-th decoder first aggregates image features through a consistent point sampling, a new scheme elaborated in our subsequent discussion. Subsequently, the query feature is updated into q i with the adaptive mixing of image and query features, along with the self-attention among all queries, mirroring operations in SparseBEV. In the end, a prediction module, comprising only Linear, LayerNorm, and ReLU layers, generates the semantic classes c i (size R i × N ) and the position offsets ∆p i (size R i × 3). As the ∆p i cannot be directly added to p i-1 due to dimension misalignment, we first compute the mean of p i-1 along the first dimension and then duplicate the results by R i times into pi-1 . The final position p i is computed asp i = pi-1 + ∆p i .Consistent point sampling. The feature sampling method utilized in SparseBEV is not applicable for our method as it is specifically designed for detection inputs. Therefore, we propose a novel process of Consistent Point Sampling (CPS), aiming at sampling 3D points and aggregating features from M image features. Given input {q, p} ∈ {Q, P}, we sample S points and find their respective coordinates in the m-th image feature by the following equation:EQUATIONwhere T m represents the projection matrix from current 3D space into the m-th image's coordinates. ϕ(q) generates S 3D points from the query feature q using a linear layer. m p and σ p denote the mean and standard deviation, respectively, of the R points in p. It's worthy to note that we re-weight the predicted offsets ϕ(q) with the standard deviation σ p to inherent the dispersion degree from previous predictions. In essence, we tend to sample more aggressively if the input p contains diverse points, and sample points in a narrower range otherwise. This operation can evidently enhance the prediction performance, as demonstrated in our experiments.Not all coordinates in c m are feasible since the sampled points might not be visible within the corresponding camera. Therefore, we generate a mask set V m where the s-th value is 1 if c s,m is valid and 0 otherwise, for s ∈ {1, 2,• • • , S} and m ∈ {1, 2, • • • , M }.Next, we aggregate information from image features {F m } M 1 for the later adaptively mixing stage. Specifically, we haveEQUATIONwhere v s,m denotes the s-th element in V m and c s,m is the coordinates of the s-th point r s mapped into the m-th image feature. The operation B refers to the bilinear interpolation. w s,m is the weight for the r s on the m-th image feature, generated from the query feature q by linear transformation.The training loss with adaptively re-weighting. The training object of our framework is to supervise the learning of {P i , C i } 6 i=1 with the ground-truth {P g , C g }. Point positions can be trained with Eq. ( 1). However, the original Chamfer distance loss focuses on the overall similarity of point distributions, neglecting whether each individual is good enough. This leads to unsatisfactory performance, as observed in our experiments. To cope with this issue, we employ a simple but effective re-weighting strategy to emphasize erroneous points, and modify the Chamfer distance loss as follows:EQUATIONHere, W (d) is the re-weighting function penalizing points with large distance to the closest groundtruths. In our implementation, we use a step function of W (d) being 5 if d ≥ 0.2 and 1 otherwise.For the classification, we first generate the target classes Ĉi for C i using Eq. (2). Subsequently, the semantic classes can be trained with the conventional classification losses. In our implementation, we adopt the focal loss [17] with mannually searched weights on different categories and denote the modified loss as FocalLoss R . In the end, the training objective of the proposed OPUS becomesEQUATIONwhere CD R (P 0 , P g ) explicitly encourages initial points P 0 to capture a general pattern of the dataset.Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?Answer: [NA] Justification: This paper does not include theoretical results.Guidelines:• The answer NA means that the paper does not include theoretical results.• All the theorems, formulas, and proofs in the paper should be numbered and crossreferenced.• All assumptions should be clearly stated or referenced in the statement of any theorems.• The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition.• Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.• Theorems and Lemmas that the proof relies upon should be properly referenced. 
experiments: 
 4.1 Experimental setup Dataset and metrics. All models are evaluated on the Occ3D-nuScenes [38] dataset, which provides occupancy labels for 18 classes (1 free class and 17 semantic classes) on the large-scale nuScenes [2] benchmark. Out of the 1,000 labeled driving scenes, 750/150/150 are used for training/validation/testing, respectively. The commonly used mIoU metric is utilized for evaluation. Recently, SparseOcc [21] points that that overestimation can easily hack the mIoU metric and proposes RayIoU as a remedy. Therefore, following their work, we also report the RayIoU results under different distance thresholds at 1, 2, and 4 meters, denoted as RayIoU 1m , RayIoU 2m , and RayIoU 4m , respectively. The final RayIoU score is the average of these three values.Implementation details. Following previous works [21, 16, 8] , we resize images to 704 × 256 and extract features using a ResNet50 [7] backbone. We denote a series of models as OPUS-T, OPUS-S, OPUS-M and OPUS-L, with 0.6K, 1.2K, 2.4K and 4.8K queries, respectively. In each model, all queries predict an equal number of points, totalling 76.8K points in the final stage. The sampling number in our CPS is 4 for OPUS-T and 2 for other models. Please refer to Appendix D.2 for more details of different models. All models are trained on 8 nvidia 4090 GPUs with a batch size of 8 using the AdamW [26] optimizer. The learning rate warms up to 2e -4 in the first 500 iterations and then decays with a Cosine Annealing [25] scheme. Unless otherwise stated, models in main results are trained for 100 epochs and those in the ablation study are trained for 12 epochs.Table 1 : Occupancy prediction performance on Occ3D-nuScenes [38] . "8f" and "16f" denote models fusing temporal information from 8 or 16 frames, respectively. Baseline results are directly copied from their corresponding papers or the SparseOcc [21] . FPS results are measured on an A100 GPU. With the same total number of points predicted, we vary the query number and correspondingly change the number of points from each query, leading to different versions of OPUS. It can be observed that increasing the query number decreases the FPS values from 22.4 to 7.2, while simultaneously boosts model performance in terms of mIoU and RayIoU. The OPUS-M (8f), with 2.4K queries, strikes a balance by achieving a comparable RayIoU while maintaining competitive FPS.Despite the vulnerability of mIoU metric to overestimation manipulations [21] , our OPUS attains a comparable mIoU of 36.2, significantly bridging the gap between dense and sparse models in this metric. These results under different metrics collectively demonstrate the superiority of our OPUS.Visualization. We visualize the predicted occupancy in Fig. 3 . It can be observed that FB-Occ tends to produce denser results compared to sparse methods. Though seems complete in the 3D environment, its predicted occupancy results are severely over-estimated, especially for the far areas. The overestimation may hack the mIoU metric [21] , while heavily penalized by RayIoU that primarily considers the first occupied voxels along rays. Consequently, FB-Occ achieves the best mIoU of 39.1 but the worst RayIoU value. On the other hand, SparseOcc occasionally exhibits discontinuous predictions with false negatives, especially in long distances. This is attributed to SparseOcc's gradual removal of empty voxels, making erroneous filtering in early stages accumulates and contributes to the final false predictions. In contrast, our OPUS maintains a more continuous prediction thanks to its end-to-end approach, resulting in a more reasonable visualization.This part details our ablation study and visualizations using the OPUS-M (8f) model. Visualizations of predicted points. In Fig. 6 , we select a few queries and visualize their predicted points. Notably, most queries exhibit a tendency to predict points with consistent classes, or even from the same instance, as depicted in Fig. 6 (a)-(g). An interesting observation is that the predicted points tend to exhibit diverse distributions in classes with large volumes, such as drivable surfaces and sidewalks. Conversely, for objects with limited sizes, such as traffic cones, motorcycles, and cars, the points are distributed more closely with respect to the instance size. The patterns can be further verified by Fig. 5 , where we present the standard deviations of points from queries with three chosen classes. These results highlight the efficacy of our model in adapting its predictions to the distinct spatial characteristics of various object classes.As we do not explicitly constrain points from one query to have the same class, it's conceivable that one query could yield points of different classes. We found this phenomenon commonly occurs at the boundaries between objects. However, even when classes vary, these points are still closely distributed, as depicted in Fig. 6 (h)-(j).Table 3 : Comparison of various treatments on initial locations P 0 . "Grid" and "Random" indicate that points are sampled uniformly in BEV space and randomly in the 3D space, respectively "Optimized" means that points are randomly initialized but supervised with ground-truths via the CD R loss. Influence of treatments on the initial points. Tab. 3 compares three different treatments on the initial points P 0 . Grid initialization divides the BEV space into evenly-distributed pillars and orderly assigns pillar centers as the initial locations, a method utilized in BEVFormer [15] . Random initialization assigns each location with a uniform distribution in the 3D space. After initialization, P 0 remains learnable during training. On top of the random initialization, our OPUS further add supervisions of the ground-truth distributions to P 0 (i.e., CD R (P 0 , P g ) in Eq. ( 6)). The results in Tab. 4 show that random initialization outperforms grid initialization, achieving an mIoU of 23.1 compared to 22.8, and a RayIoU of 29.9 compared to 28.3. This improvement is likely due to the fact the random initialization provides a more diverse 3D distribution. Furthermore, the introduced supervision results in additional improvements of 0.6 on mIoU and 0.2 on RayIoU. These results reveal the efficiency of the random initialization and the additional supervision on the initial locations.Visualization of the self-attention. For better understanding what query points attend to, we visualize top 10 query points with highest self attention weights for each query. We project them on 2D image for better visualization. Here are some interesting finding from Fig. 7 . Generally speaking, the query tends to attend to neighbouring query points. For example, the sidewalk query in the first image and the car query in the second image, allow local information from neighbouring query points flow into, enabling the query to capture detailed local information. Additionally, the query maintains the ability to attend to semantic related locations even if they are not very close to the query point. For instance, the vegetation query in the first image of Fig. 7 not only attends to the stem of the tree, but also the grass, indicating that the query can capture semantically related information for more accurate predictions. Another notable observation is that query can sense terrain-related information. For instance, in the third image, the sidewalk query points attend to other points along a straight line following the road's edge, highlighting the model's ability to understand scene related structure of the environment. Comparisons between different sparsification strategies In Tab. 4, we compare OPUS to two other models with different sparsification strategies. The first baseline is SparseOcc, which achieves sparsification by filtering out empty voxels at various cascade stages. Following PETRv2 [24] , the second baseline is a pillar-patch based method that partitions the 3D space into a small number of pillar-patches. We use 50 × 50 queries with each corresponding to the classification of neighbouring 4 × 4 × 16 voxels. For a fair comparison, all these models are trained for 100 epochs. In contrast, our model achieve best results after sufficient training with a RayIoU score of 38.0,far outperforming SparseOcc with a RayIoU score of 34.3. On the other hand, our model can also runs in a real-time speed. These results demonstrates the superiority of our sparification procedure.Comparisons on the Waymo-Occ3D dataset. We further simply implement OPUS on the Waymo-Occ3D [35] dataset to explore the generalization and robustness of OPUS. As Waymo-Occ3D is not commonly used as a standard benchmark for vision-centric approaches, the only vision-based method we found with reported results on this dataset is the Occ3D paper, which evaluates BEVDet, TPVFormer, BEVFormer, and the newly proposed CTF-Occ [38] . We trained the OPUS-L (1f) on 20% of the dataset for a fair comparison with these baselines. As reported in Tab. 5, despite not fine-tuning the training configurations, OPUS-L already achieves 19.0 mIoU, outperforming all previous methods. Moreover, OPUS-L also reaches 8.5 FPS on the Waymo-Occ3D dataset, which is around 3 times the speed of CTF-Occ and 2 times the speed of BEVFormer.Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?Answer: [Yes] Justification: We have provided implementation details in our "Experiments" section. 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conclusions and limitations: 
 This paper introduces a novel perspective on occupancy prediction by framing it as a direct set prediction problem. Using a transformer encoder-decoder architecture, the proposed OPUS directly predicts occupied locations and classes in parallel from a set of learnable queries. The matching between predictions and ground truths is accomplished through two efficient tasks in parallel, facilitating end-to-end training with a large number of points in this application. In addition, the query features are enhanced via a list of non-trivial designs (i.e., coarse-to-fine learning, consistent point sampling, and loss re-weighting), and therefore leads to boosted prediction performances. Our experiments on the Occ3D-nuScenes benchmark demonstrate that OPUS surpasses all prior arts in terms of both accuracy and efficiency, thanks to the sparse designs in our framework.However, the proposed OPUS also comes with new challenges, particularly regarding the convergence speed. The slow convergence may potentially be alleviated by drawing lessons from follow-up works of DETR, which have largely addressed the convergence issue of the original DETR. Another challenge is that while sparse approaches typically achieve higher RayIoU compared to dense counterparts, they often struggle with the mIoU metric. Improving the mIoU performance while maintaining superior RayIoU results is a promising direction for future works. Moreover, despite conducting experiments on vision-only datasets, our core formulation is directly applicable to multimodal tasks as well. We leave the multi-modal occupancy prediction as future work. GPU memory for a single matching. Scaling up to 100K points renders the matching infeasible due to CUDA memory constraints, even on an 80G A100 GPU.In contrast, our label assignment method achieves remarkable efficiency, requiring only about 1.25ms and 28.85ms for 10K and 100K points, respectively. Furthermore, the GPU memory consumption during training is negligible. These findings reveal the practicality and efficacy of our label assignment approach, particularly for the occupancy prediction where point counts can easily exceed 10K. D.2 Detailed configuration for different versions.In this section, we detail the settings of various versions of our model, as shown in Tab. 7, each tailored to prioritize different aspects of performance and speed. Our fastest model OPUS-T utilizes only 0.6K queries, with each query sampling 4 points in images. The number of predicted points are 1, 4, 16, 32, 64 and 128 for 6 stages, respectively. This configuration ensures a rapid processing time while maintaining competitive performance. Other versions of our model, such as OPUS-S, OPUS-M, OPUS-L, sample 2 points in CPS module, progressively double the number of queries and adjust the number of predicted points accordingly to balance speed and accuracy. All these models predict the same amount of points in the end. Tab. 8 assesses the impact of varying the number of predicted points in the last layer. We use OPUS-M as our model for this experiment. As shown in the table, mIoU steadily rises as the number of points increase from 8 to 64, going from 16.4 to 28.4. This trend is expected since increasing the number of points generally leads to higher mIoU by covering more voxels, as mIoU penalizes false negative (FN) heavily. However, the RayIoU results peak when model predicting 16 points and decline with further increasing points. This decline occurs partly because adding more points beyond a certain extent introduces noise, which negatively impacts RayIoU, which emphasizes first occupied voxels along the ray. 
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 Appendix: We report the RayIoU of FB-Occ and OPUS at different ranges in Tab. 9. It is evident that OPUS demonstrates a more pronounced advantage in nearby areas than at far distances. This could be attributed to the phenomenon pointed out by SparseOcc: dense approaches tend to overestimate the surfaces, especially in nearby areas. E Additional qualitative analysis E.1 Differences between SparseOcc and OPUS View perspective of occupancy prediction. The fundamental difference lies in the perspective of occupancy prediction. As depicted in the main draft, all previous methods, including SparseOcc [21] , treat occupancy prediction as a standard classification task. OPUS, however, pioneers a set prediction viewpoint, offering a novel, elegant, and end-to-end sparsification approach.Multi-stage vs. end-to-end sparsification procedure. SparseOcc generates sparse occupancy by gradually discarding voxels through multiple stages. The discarding of empty voxels at early stages is irreversible, leading to obvious cumulative errors, illustrated in Fig. 3 . Conversely, OPUS circumvents complex filtering mechanisms by directly predicting a sparse set, resulting in more coherent outcomes.In terms of a more detailed perspective of the structure, there are also many differences such as:• Query number. In NuScene-Occ3D, SparseOcc necessitates 32K queries in its final stage. OPUS, by comparison, operates with a mere 0.6K-4.8K queries for occupancy prediction, capitalizing on its flexible nature and contributing to its fast inference pace.• Coarse-to-fine procedure. SparseOcc's coarse-to-fine strategy involves progressively filtering empty voxels and subdividing occupied voxels into finer ones. In contrast, OPUS interprets coarse-to-fine as the escalation in number of predicted points across stages.• Learning objective. Our learning target encompasses predicting both semantic classes and occupied locations, simultaneously. The latter is a new objective introduced by OPUS, achieved through a modified Chamfer distance loss.E.2 Analysis of relationships between mIoU, RayIoU and driving safety.Our OPUS-L (8f) has achieved a state-of-the-art RayIoU of 41.17, outperforming the previous sparse model SparseOcc by 6.07 and the dense model FB-Occ by 7.7. The mIoU gap between sparse and dense methods is also reduced from 8.5 in SparseOcc to 3.0 in OPUS. However, the implications of this gap on safety remain ambiguous. This concern is particularly pertinent in the context of autonomous driving, and we would like to clarify this as follows:Risks of dense predictions. The biggest issue of dense predictions is the discrepancies between evaluation metrics and real-world scenarios. As shown in Fig. 8 , evaluation metrics only consider voxels within the camera mask, which is derived from camera parameters and ground truth. However, in real-world applications, we can only produce view mask based on camera intrinsics and extrinsics, failing to filtering out over-estimated voxels. From Fig. 8 and and Fig. 3 , dense methods can misidentify occupied voxels, even close to the ego vehicle. These errors are overlooked during evaluation but pose significant safety hazards in real-world scenarios. In contrast, OPUS suffer much less from this issue as it does not over-estimate occupancy.The depth errors of OPUS is much smaller than FB-Occ. In Fig. 9 , we compare the depth errors of FB-Occ and OPUS along camera rays. OPUS demonstrates lower depth errors across all scenes, despite its relatively low mIoU performance. Given the significance of the first occupied voxel for safety, OPUS's precision in this regard enhances safety rather than detracting from it.In conclusion, while it is necessary to minimize the mIoU gap between sparse and dense methods, our analysis indicates that mIoU might not fully represent potentially hazardous situations. Therefore, it would be more rational to take both mIoU and RayIoU into consideration for the occupancy task.In Fig. 10 , We further provide more visualizations of occupancy predicted by FB-Occ, SparseOcc, and proposed OPUS. As shown in Fig. 3 and Fig. 10 , a common OPUS failure mode is the prediction of scattered and discontinuous surfaces at long distances. Another is the presence of holes in predicted driving surface, a phenomenon also observed in SparseOcc due to the sparsity properties. NeurIPS Paper Checklisthttps://github.com/MCG-NJU/SparseBEV 


Decision: This paper addresses occupancy prediction from a new persepctive via a sparse set. Without explicitly modelling the full 3D space set, since there are many empty voxels, this work simultaneously predict the occupied locations as a streamlined set prediction paradigm.

All reviewers reach concensus that the manuscript has been greatly improved after rebuttal. Most concerns raised by reviewers have been resolved. AC read the paper, rebuttal, revised experiments in pdf. Please incorporate all comments in the camera-ready version.

Reviews: review: paper_summary: paper_summary: This paper introduces OPS, a novel framework that treats occupancy prediction as a set prediction problem. The approach leverages a transformer encoder-decoder architecture and Chamfer distance loss to align predicted and ground-truth points. The model improves performance with strategies like coarse-to-fine learning, consistent point sampling, and adaptive re-weighting. OPS achieves superior RayIoU and faster FPS compared to state-of-the-art methods on the Occ3D-nuScenes dataset. In summarize, this paper is technically sound and shows strong and convincing performance on a commonly used dataset.
strength_weakness: strength_weakness: 1. In a high level, the proposed method is similar to SparseOcc, although implementation details can be different. 

2. Although this method has strong performance on Occ3D-nuScenes dataset and several ablation studies are provided, I am still concerned that this method can overfit to this relatively small dataset. Can authors provide further evidences on the Occ3D-Waymo split?
questions: questions: 1. Can authors provide results on the Waymo split? Or at least can authors provide a convincing explanation why such experiments cannot be conducted on Waymo? As far as I know, Occ3D-Waymo is on a par with Occ3D-nuScenes in terms of data scale, thus computation should not be a significant concern. 

2. Can authors comment on the difference between SparseOcc and OPS? I'd like to understand both the detail differences and the high-level differences.
limitations: limitations: No potential negative societal impact is detected by reviewer.
paper_summary: paper_summary: This paper considers the problem of occupancy prediction from multi-view images for autoonomous driving. One of the main challenges in the occupancy prediction task is the high computational demand incured by discretizing the 3d space. Traditional methods typically predict the occupancy of each voxel individually and assign it a semantic class. The key idea of this work if to reduce computational burden by formulating occupancy prediction as a set prediction task. The authors employ the Chamfer distance in the loss term and propose a novel point sampling process, termed Consistent Point Sampling, to make the SparseBEV decoder applicable. In experiments on the Occ3d-nuScenes dataset, their method demonstrates superior performance with regard to the RayIoU metric while being computationally more efficient than the state-of-the-art methods.
strength_weakness: strength_weakness: This topic seems to be traditionally mainly covered in Computer Vision venues. And while the contribution of this work may also be of interest to the ML community, the writing needs to provide more background and context to be more accessible to the NeurIPS community. E.g. the readers at NeurIPS may not be familiar with the broader tasks and some more specialized architectures such as SparseBEV.

The work contains numerous writing and grammar issues. Some examples are mentioned in the minor comments section below. However, the work should undergo a careful proofread in its entirety.

Some of the mathematical notation seems off. E.g. {$\mathbb{P}^g,\mathbb{C}^g$} is denoted as a set containing two sets while it is treated as a set cotaining tuples of point locations and semantic classes. Some more minor math notation issues are given in the comments below.

The first bullet point in the contribution list is somewhat broad and focuses more on the properties of the method. It does not mention some of the new key technical ideas underlying the method such as CPS. I would recommend fully rephrasing the contribution list and focusing on what is technically new (or at least for the first time applied in the context of occupancy prediction). Simply mentioning that there are several strategies that are introduced to boost performance makes the reader wonder what these strategies are.

Minor Comments:
* l.3 "discretize 3D environment" -> "discretize the 3D environment"
* l.33/34 "Alternative sparse latent representations has been explored" -> "Alternative sparse latent representations have been explored"
* l. 37 What is meant by "necessitating complex intermediate designs and explicit"? Complex architecture?
* l.42/43 "Our OPS eliminates" should be "Our method eliminates" or "OPS eliminates"
* l.48 "unable to tacke tremendous voxels" maybe something like "unable to handle  a very high number of voxels"
* l.69/70 "all our model configurations easily surpass all prior arts" -> "all our model variants easily surpass all prior work".
* l.83 "This task recently becomes a foundational perception task in autonomous driving" -> "This task has recently become a foundational perception task for autonomous driving"
* Consider using $N_g$ instead of $N^g$ for the number of occupied voxels in ground truth. The latter looks like $N$ to the power of $g$. Same for all other occurrences of $g$ in a superscript.
* If $\mathbf{c}^g$ denotes a semantic class, it should not be defined as element of $\mathbb{R}$. This is not necessarily wrong but may be confusing as it is likely represented as an integer if not a one-hot vector?
* Using $N$ to represent the number of semantic classes may be confusing given that $N^g$ is used to represent the number of occupied ground truth voxels.
questions: questions: * From the writing, it is not really clear to me, whether some of the competing methods are also set based? I would not see why the Hungarian algorithm would be needed otherwise. If those methods are set-based, the writing might clarify this. From the abstract it seems like competing approaches perform classification of each voxel individually.
* In the right most panel of fig 2, why is "Consistent Point Sampling" written in a green box while everything else is in grey?
* What is meant by a set of learnable queries? Are these simply the queries that would be used in the traditional transformer except that they are now learned?
limitations: limitations: To the extent that I can understand it, the authors have properly addressed the limitations of this work.
paper_summary: paper_summary: This paper focuses on the sparsity property in occupancy prediction, given that most voxels are occupied. In order to reduce computation costs on empty voxels, this paper introduces a set prediction paradigm to explicitly model sparsity. OPS, the proposed framework, utilizes the encoder-decoder architecture to jointly reconstruct and classify point clouds. Chamfer distance is used as the supervision. For experiments, OPS outperforms state-of-the-art occupancy methods by 4.9 RayIoU.
strength_weakness: strength_weakness: 1. Error citation. I think the "sparseocc" mentioned frequently in this paper should be [1], instead of [2].

    [1.] Fully sparse 3D panoptic occupancy prediction

    [2.] SparseOcc: Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction

2. Is there a typo in Line 245? The query count for OPS-tiny is only 0.6k, while for OPS-S, OPS-M, and OPS-L, the query counts are as high as 12K, 24K, and 48K respectively.

3. If the query count is as high as 48K, self-attention would not be able to handle such a large query size. How did the authors manage to do this? The design details are not elaborated on.

4. Since the authors have replaced the basic representation of occupancy with point cloud, they should discuss the differences with point cloud forecasting tasks, such as 4D-Occ [3] and ViDAR [4], especially ViDAR paper which also constructs point clouds from visual images. Discussions on [3] and [4] are suggested to be included in the main paper.

    [3.] Point Cloud Forecasting as a Proxy for 4D Occupancy Forecasting

    [4.] Visual Point Cloud Forecasting enables Scalable Autonomous Driving.
questions: questions: See Weakness.
limitations: limitations: N/A
paper_summary: paper_summary: The paper presents OPS, a novel framework for occupancy prediction in autonomous driving. It formulates the task as a direct set prediction problem, using a transformer encoder-decoder architecture to predict occupied locations and classes simultaneously. This approach eliminates the need for explicit space modeling or complex sparsification. The main results of the paper demonstrate that the OPS framework outperforms previous state-of-the-art methods in occupancy prediction on the Occ3D-nuScenes dataset. It achieves superior RayIoU scores, a metric designed to address the overestimation issues of the traditional mIoU metric. The paper also includes an ablation study highlighting the effectiveness of the various strategies incorporated in OPS, such as adaptive re-weighting, consistent point sampling, and coarse-to-fine prediction. These strategies contribute to improved performance, particularly in terms of mIoU and RayIoU.
strength_weakness: strength_weakness: - **[W1] Technical soundness:** The paper proposes to use Chamfer distance as the main objective function, which is known to be sub-optimal. Although several strategies including FocalLoss, coarse-to-fine refinement have been proposed, it makes the system overly complicated and potentially unfair for comparison. For example, it is unclear whether the baseline methods can benefit from the proposed strategies as well. Please comment this in the rebuttal.

- **[W2] Limited Evaluation:** The experimental evaluation is solely conducted on the Occ3D-nuScenes dataset. While this is a standard benchmark, evaluating the method on additional datasets, such as SemanticKITTI or Waymo Open Dataset, would provide a more comprehensive assessment of its generalizability and robustness.
  - Reference: [NewRef1] Occ3D: A Large-Scale 3D Occupancy Prediction Benchmark for Autonomous Driving

- **[W3] mIoU Performance:**
  - [W3.1] Although OPS excels in RayIoU, its performance on the mIoU metric lags behind some dense models. Given that mIoU is a widely used metric in occupancy prediction, addressing this weakness would make the method more appealing to a broader audience. In comparison, RayIoU is only introduced in a recent paper that has not been peer reviewed. 

  - [W3.2] As the paper is focusing on autonomous driving applications, it is unclear whether mIoU performance can cause safety-critical problems for downstream tasks such as behavior prediction and planning. It would be good to discuss this aspect in the rebuttal and next version of the paper.

  - [W3.3] In Table 3, the reference number for FB-OCC is wrong. 

- **[W4] Lack of Qualitative Analysis:** While the paper provides some visualizations, a more thorough qualitative analysis of the predictions would be insightful. Analyzing failure cases, comparing predictions across different classes and distances, and examining the impact of the proposed strategies on the quality of predictions would provide a deeper understanding of the method's strengths and weaknesses.
questions: questions: Please check the weakness section, especially W1 and W3.
limitations: limitations: Yes, the limitations have been discussed in the paper.

Comments: title: Response
comment: We sincerely thank the reviewer for maintaining the positive assessment of this paper. We will include the details mentioned in the rebuttal in the revised version.
Thanks for the authors' rebuttal. I will maintain my rate.
We sincerely appreciate the reviewer's time and effort in offering insightful feedback and keeping a positive assessment of this paper. Due to the NeurIPS policy, we are unable to provide the reviewer with our revised version of this paper. We feel regretful for the inconvenience, but have indeed incorporated the reviewer's valuable suggestions into our new draft.
We sincerely thank the reviewer for the positive evaluation of this paper. We will further improve our revised version based on the reviewer's comments.
I appreciate the authors responses and continue to see the work on the accept side although I am not yet sure I will be able to raise my scores as some of the suggested changes are hard to judge without a full new review.
Thank you for providing these responses! They address my questions and I'll keep my positive evaluation of this paper.