QuadricFormer: Scene as Superquadrics for 3D Semantic Occupancy Prediction
Authors: Sicheng Zuo
Wenzhao Zheng
Xiaoyong Han
Longchao Yang
Yong Pan
Jiwen Lu
Venue: NeurIPS 2025 poster ()
Keywords: autonomous driving
Primary area: applications

Abstract: 3D occupancy prediction is crucial for robust autonomous driving systems as it enables comprehensive perception of environmental structures and semantics. Most existing methods employ dense voxel-based scene representations, ignoring the sparsity of driving scenes and resulting in inefficiency. Recent works explore object-centric representations based on sparse Gaussians, but their ellipsoidal shape prior limits the modeling of diverse structures. In real-world driving scenes, objects exhibit rich geometries (e.g., cuboids, cylinders, and irregular shapes), necessitating excessive ellipsoidal Gaussians densely packed for accurate modeling, which leads to inefficient representations. To address this, we propose to use geometrically expressive superquadrics as scene primitives, enabling efficient representation of complex structures with fewer primitives through their inherent shape diversity. We develop a probabilistic superquadric mixture model, which interprets each superquadric as an occupancy probability distribution with a corresponding geometry prior, and calculates semantics through probabilistic mixture. Building on this, we present QuadricFormer, a superquadric-based model for efficient 3D occupancy prediction, and introduce a pruning-and-splitting module to further enhance modeling efficiency by concentrating superquadrics in occupied regions. Extensive experiments on the nuScenes and KITTI-360 datasets demonstrate that QuadricFormer achieves state-of-the-art performance while maintaining superior efficiency. Code is available at https://github.com/zuosc19/QuadricFormer.

Quadrie Scene as Superquadrics for 3D Semantic Occupancy Prediction
Sicheng Zuo Wenzhao Zhengl.*f
Xiaoyong Han
Longchao Yang"
Yong Pan"
Jiwen Lu 1.3
Tsinghua University LLi Auto Inc Beijing National Research Center for Information Science and Technology
Project Page: attps://zuoscl:: gi thub. 1o/ hto/Quadrico SeraddiiFormer//
Scene Repre.
Occupancy Pred.
GaussianFormer
12800 Gaussians
20.02 mioU
1600 Superquadrics 20.12 mloU
QuadricFormer
bicycle Figure I: Considering the ellipsoidal shape prior of Gaussians, propose leveraging expressive
driveable surfice car
motoreyele
lerrain
vegetation
sidewalk
other flat
pedestrian
manmade
superquadrics to build an efficient and powerful object-centric representation. Our QuadricFormer achieves state-of- the-art performance with superior efficiency for 3D occupancy prediction.
Abstract
3D occupancy prediction is crucial for robust autonomous driving systems it enables comprehensive perception of environmental structures and semantics. Most existing methods employ dense voxel-based scene representations, ignoring the sparsity of driving scenes and resulting in inefficiency. Recent works explore object-centric representations based on sparse Gaussians, but their ellipsoidal shape prior limits the modeling of diverse structures. In real-world driving scenes, objects exhibit rich geometries (e.g., cuboids, cylinders, and irregular shapes), necessitating excessive ellipsoidal Gaussians densely packed for accurate modeling, which leads inefficient representations. To address this, we propose to use geometrically expressive superquadrics scene primitives, enabling efficient representation of complex structures with fewer primitives through their inherent shape diversity. We develop probabilistic superquadric mixture model, which interprets each su- perquadric as an occupancy probability distribution with corresponding geometry prior, and caleulates semantics through probabilistic mixture. Building this, we present QuadricFormer, a superquadric-bart based model for efficient 3D occupancy prediction, and introduce a pruning semning-anddsplittee and-splitting module further enhance mod- eling efficiency by concentrating superquadrics in occupied regions. Extensive experiments the nuScenes and KITTI-360 datasets demonstrate that Quadric- Former achieves state-of-the- performance while maintaining superior efficiency. Code is available at https: // thub. com/zuosc19/ /euuududriiee cFormer.
"Equal contribution. 'Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Introduction
model Vision-centric autonomous driving systems have gained much attention for their cost-effectiveness over LiDAR-based solutions [4, 17, 50, 26, 23]. However, they struggle to perceive irregularly shaped obstacles due to visual ambiguity, which compromises driving safety. Recent advances 3D semantic occupancy prediction address this by estimating voxel-level occupancy status and semantic labels in 3D scenes [43, 44, 38, 39]. This provides a full understanding of seene structures and semantics, which enables applications including self-supervised 3D scene understanding [6. 16], 4D occupancy forecasting [51, 31, 41, 46], and end-to-end autonomous driving [14, 52].
Despite promising applications, 3D semantic occupancy prediction faces efficiency challenges due to its dense 3D predictions [4, 38]. An efficient and expressive 3D representation is therefore essential. While voxel-based methods [23, 44] use dense 3D grids to capture fine details, they ignore the sparsity of driving scenes and suffer from high computational costs. Recent advances introduce object-centric representations using 3D Gaussians [18, 55] to describe scenes sparsely. Each Gaussian models the occupancy probability distribution of its local region via learnable attributes including position, covariance, opacity, and semantics. However, Gaussian representations are fundamentally limited. By their mathematical formulation, Gaussians describe the spatial occupancy probability with cllipsoidal decay pattern. This imposes a strong ellipsoidal shape prior to Gaussians and severely constrains their capacity to model diverse geometries. Real-world driving scenarios contain objects with rich structural variations, which cannot be accurately represented by few ellipsoidal Gaussian. Consequently, Gaussian-basee models must aggregate numerous densely packed Gaussians to approximate target shapes, causing significant efficiency degradation.
In this paper, we propose an efficient and expressive object-centric 3D representation using su- perquadrics [1] as scene primitives. Superquadrics are family of parameterized shapes with high geometric expressiveness and compact shape parameters, offering great flexibility in modeling diverse geometries. This allows superquadrics to model complex structures with sparse packing, enabling an efficient and powerful representation [12]. We represent scenes with a set of learnable superquadrics, each characterized by attributes including position, scale, rotation, opacity, semantics, and shape exponents. For occupancy prediction, we adopt a probabilistic superquadric mixture model that interprets each superquadric local occupancy probability distribution, and calculates seman- ties through probabilistic mixture. Building on this representation, we introduce QuadricFormer, superquadric-based framework for efficient 3D semantic occupancy prediction. Moreover, we design a gruning-and-splitiig module that concentrates superquadrics on occupied regions to fur- ther enhance modeling efficiency. Extensive experiments on the nuScenes and KITTI-360 dataset demonstrate that our QuadricFormer achieves state-of-thed tf-t---rt performance with superior efficiency.
2 Related Work
3D Semantic Occupancy Prediction. 3D semantic occupancy prediction reconstructs fine-grained 3D scenes by labeling each voxel with geometric and semantic information, which critical for autonomous driving [4, 17,38, 38, 50, 51]. LiDAR and cameras are the two most commonly used sensors. While LiDAR- based methods excel in depth accuracy [8, 7, 10, 20, 21, 28, 33, 36, 45, 47, 48, 53, 54], their limitations in adverse weather and long-range detection motivate the vision-centric approaches, which reconstruct scenes from multi-view visual input [26, 44, 49, 4, 17]. Early approaches lifted image features directly into dense voxel grids for 3D occupancy prediction [9. 23, 44, 30]. However, given the sparsity of occupied voxels in driving scenes, subsequent works prioritized efficiency through alternative representations. Planar representations like BEV [25] and TPV [17] compress 3D data into 2D feature maps for efficient processing, but sacrifice geometric fidelity. Object-centric modeling preserves geometric fidelity by focusing computation 55], alleviating both the redundancy of uniform voxel grids and the information loss from planar compression. However, these methods still struggle to balance efficiency and modeling capacity due to the complexity of real- world structures. To address this, we propose a superquadric- that achieves efficient and accurate representation of complex geometries.
salient regions [18, 15, 29, 37,
Object-centric Scene Representation. Existing 3D scene representations primarily use voxel-based frameworks for fine-grained volumetric modeling [44, 23], excelling in semantic prediction tasks. However, their uniform processing of all voxels introduces spatial redundancy, particularly in sparse environments. To address this, recent works explore object-centric representations [37,20 29, 18, 15, 55].

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Superquadric-Baser
Performance
Voxel-Based
20.5
Object
1108 Voxels
20.0
19.5
Gaussian- Laassian-BBsedd
19.0
Speed
Gaussians
6 Superquadrics
(a) Scene Representations.
(b) Performance Comparison.
Figure 2: Comparisons between different representations. (a) Quadric-basedd method represents the same object with smaller number of primitives and greater shape expressiveness. (b) Quadric-based representation outperforms existing methods in both accuracy and speed with far fewer primitives.
One line of methods partitions dense grids into localized regions, preserving only detected object areas [37, 29]. While efficient, non-empty regions may be falsely pruned, leading to irreversible loss of critical geometry. Alternatively, point-based methods
sparse points queries for iterative refinement [34, 40]. However, points inherently lack spatial extent, limiting their ability to capture contextual geometry. Recent advances adopt 3D semantic Gaussians [18, 15, 55], where probability densities radiate from Gaussian centers to enable adaptive spatial coverage. While Gaussians mitigate point rigidity through probability spread, complex geometries often require multiple densely packed primitives, particularly for fine structures, leading to inefficient representations. In this paper, propose geometrically expressive superquadrics compact scene primitives. Unlike conventional object-centric methods, superquadrics natively parameterize diverse geometries (e.g., cuboids, cylinders) without dense packing, achieving superior reconstruction fidelity using fewer primitives.
Superquarics. Superquadrics parametric geometric primitives introduced by Barr et al. [1] to model diverse shapes with compact parameterizations. canonical superquadric is defined by five parameters: three scale parameters along each of its semi-axes and two exponents that determine its shape [19]. The scale and shape parameters of superquadrics allow for smooth interpolation between different geometric shapes, such cuboids, cylinders, and spheres. When combined with six pose parameters for translation and rotation, a superquadric can represent a complete 3D object using only 1l parameters. Recent works employed superquadrics decompose complex environments into compact geometric primitives [12]. These methods demonstrate compelling reconstruction capability and editing flexibility, while maintaining model efficiency. However, existing approaches operate exclusively on point clouds and are limited to object-level reconstructions. Differently, we present the first superquadric-bart based framework for holistic scene reconstruction directly from multi-view images, delivering state-of of-the-art performance with superior efficiency.
3 Proposed Approach
In this section, we present our method based on the superquadric representation for efficient 3D semantic occupancy prediction. We first review the Gaussian- object-centric representation and analyze limitations (Sec 3.. We then introduce our superquadric representation and probabilistic modeling approach for efficient occupancy prediction (Sec 3.2). Finally, we describe the overall architecture of QuadricFormer for vision-centric 3D occupancy prediction. 3.3).
3.1 Object-Centric Representation
Vision-centric 3D semantic occupancy prediction aims estimate the occupancy status and semantic label of cach voxel in 3D space based on visual inputs. Formally, given input images I [1,

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from N views, the model aims to predict voxel-level semantic labels O E XXXXXX of the 3D scene, where C denotes the semantic classes and X x Z represents the spatial shape of occupancy.
To achieve this, voxel-based methods [44, 50] adopt dense voxel features to model 3D scenes, resulting in extremely high computational complexity of O(XYZ). This inefficiency stems from their uniform processing of all voxels in space, which ignores the inherent sparsity of real-world scenes. Considering this, recent works [18, 15] explore object-centric representations based on 3D Gaussians to focus computational resources on salient regions for efficient scene modeling. Gaussian- based method [15] typically employs set of P semantic 3D Gaussian primitives g {G; / to represent 3D scenes sparsely. Each Gaussian G; models flexible local region with its explicit mean m,, scale s,, rotation rs, opacity a, and semantic probability C, For a point x in 3D space, its geometric occupancy probability associated with the Gaussian G is:
a(x: G) exp(
2 x m) m)
T 'x m)).
(2) where x denotes the point position, and Σ. R, S represent the covariance matrix, the rotation matrix constructed from the quaternion r, and the diagonal scale matrix from the scale s. Furthermore, a probabilistic Gaussian mixture model is used to aggregate multiple Gaussians for predicting the structure and semantics of the scene. As each Gaussian represents flexible region of the scene, the Gaussian- representation enables adaptive allocation of resources and efficient modeling.
Σ = RSS Th R S = diag(s), R = q2r(r,,
Although 3D Gaussian representation is more efficient than dense voxels (e.g., 6400 Gaussians vs. 200 x 200 16 voxels per scene), it still exhibits limitations that prevent an optimal efficiency- performance balance. Our key insight is that Gaussians inherently impose an ellipsoidal shape prior, which limits their ability to model diverse structures. As shown Eq. 1, the occupancy probability distribution of the Gaussian G can be viewed as a set of iso-probability surfaces defined by:
g(x) = - ] (
1 x
(2)
2 8x
8y
82
where x (I, y, 2) denotes the point position, & denotes the hyperparameter of the surface family, and = (s2, Sy: sz)) represents the Gaussian's 's scales along three axes. The rotation and mean of the Gaussian omitted for simplicity in Eq. 3, which describes standard ellipsoid. Each Gaussian then models occupancy probability with an ellipsoidal decay in 3D space. But real-world objects often have diverse shapes, such cuboids, cylinders, and irregular shapes, which cannot be accurately represented by a few ellipsoidal Gaussians. This forces the model to use numerous densely packed Gaussians approximate complex structures, leading inefficient scene representations. In contrast, our method employs expressive superquadrics as scene primitives, enabling efficient and compact modeling of complex structures with only a few sparsely packed superquadries.
3.2
Scene as Superquadrics
We introduce an object-centric scene representation leveraging superquadric primitives for their efficiency and expressive power. Superquadrics are parametric shape family with strong geometric expressiveness, defined as follows:
(
f(x)
2
y
+
2
22
= K
8x
8y
8
where x = (x, 2) denotes the point position, and denotes the hyperparameter of the surface family. Compared to the ellipsoids in Eq. 3, superquadries introduce only two additional shape- defining exponents e1, E2 yet can represent a much wider variety of shapes. As shown in Fig. 2a, superquadrics allow for continuous and diverse shape variations as the shape parameters change. This inherent parameter efficiency and geometric expressiveness enable superquadrics to model diverse shapes without being densely packed. Consequently, only small number of superquadrics are needed to represent complex scene structures, achieving an efficient yet powerful scene representation.
We thus utilize a set of P parameterized superquadries Q (Q: Each superquadric characterized by its scale s and shape exponents 61; 62 to define its geometry. To extend the representation to the global coordinate system, each primitive is also assigned
represent the 3D scene.

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Initial
Pred.
Superquadrics
Superquadrics
Pos. Guide
Ref. Points
Residual
Update
Quadric
Quadric
Encoder
Decoder
Pruning
Voxelization
Cross Attn
Conv.
Sparse
FFN
Splitting
Refine
Blocks
Image
Prob. Modeling
Encoder
Image Input
Image Features
3D Occupancy
Refined Superquadrics
Figure 3: Overall Framework of QuadricFormer. We use several quadric-encoder blocks to update
superquadrics, and employ gruning-and-splittnng module to further enhance modeling efficiency.
position and rotation r. Beyond geometric attributes, each superquadric is further equipped with an opacity a and a semantic probability с to incorporate semantic information. In summary, our superquadric-based representation can be formulated as:
Q = = {(x,, Sj, r,, Oi, Elgs 62 C;, )
(5)
We now explore obtaining 3D occupancy prediction from the superquadric representation. Existing methods [12] typically treat superquadrics as deterministic surfaces, fitting them to object parts for point cloud reconstruction. However, these surface-based approaches face key limitations in vision- centric occupancy prediction. primary challenge supervision. While point cloud reconstruction directly optimizes the distance between points and the superquadric surfaces, occupancy prediction requires fine-grained scene understanding, which lacks clear surface-based constraints. Furthermore, surface-based methods rely the explicit structure from point cloud inputs, whereas visual inputs introduce structural uncertainty. making deterministic modeling unstable. Lastly, surface-based methods focus on object-level reconstruction with simple spatial relationships. But real-world driving scenes involve far more complex surface interactions, posing significant modeling difficulties.
To achieve robust 3D semantic occupancy prediction, design probabilistic modeling mechanism that converts superquadrics into occupancy probabilities. Inspired by GaussianFormer adopt probabilistic superquadric mixture model, where each superquadric defines the occupancy probability distribution in its local neighborhood. To compute the probability of a 3D point x being occupied by the superquadric Q, first transform into Q's local coordinate system, defined by its position m and rotation r:
[15], we
XQ = R(x m),
(6)
where xQ denotes the local coordinate of x, and denotes the rotation matrix constructed from the rotation The occupancy probability of associated with Q is then computed as:
Po( G) = exp( f(xx)) = cxp
XQ
yQ
+
7QQ
(7)
8x
Sy
82
where xQ (rq VQ. = and (8z, Mrr 2z) the position and scale parameters, respectively, and 61, are the shape exponents of the superquadric Q. Assuming conditional independence of occupancy among different superquadries, the final occupancy probability at computed
P
(x =
II
Po (x; Q:)).
(8)
5

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Semantic predictions are subsequently inferred by weighted aggregation of semantic probabilities from all contributing superquadries, where weights correspond their occupancy influence x:
Pe(x) Eis ( Q,)
(9)
Po=1
The key to this probabilistic modeling is incorporating the superquadric geometry shape priors within the probability distribution, realized as iso-probability surfaces conforming to its geometry in Eq. 4. Leveraging the geometrically expressive power of superquadrics, our model can efficiently represent complex 3D structures using a sparse set of primitives without dense packing, achieving an efficient yet powerful scene representation. Moreover, this probabilistic framework effectively models structural uncertainties arising from visual ambiguities, significantly improving the model's robustness and generalization capabilities.
3.3 QuadrieFormer
We present the overall framework of QuadricFormer in Fig. 3. Starting from the image inputs of N views I = (I. j we first employ an image backbone Er to extract multi-scale image features Fr:
Fi EI),,
(10)
Due to the lack of any structural prior of the scene, we randomly initialize a few superquadrics Qinit in 3D space, and use B muadric-encoder blocks EB predict the final superquadries from images. In each block, we first encode current superquadrics Q into features FQ via a quadric encoder Eq:
Fq = Eq
(11)
We then use 3D sparse convolution Econe for superquadric feature self-encoding and deformable attention Eatta for interaction between superquadric and image features:
Fq = Ecomo (Fq. xq), Fq = Euttn (Fq. xq. F1).
(12)
where xq denotes the explicit position of the superquadric Q, serving auxiliary information guide feature encoding. Finally, a quadric decoder DQ is used to predict the update of superquadric attributes AQ, which are combined with the original attributes Q via residual addition:
AQ (FQ). Q Q AQ
(13)
After B blocks update, we get the final superquadric prediction Q, and the 3D semantic occupancy prediction O e eXxVx2 can be inferred through the probabilistic modeling mechanism:
O (Pob(Q):
(14)
For optimization, we adopt the cross entropy loss and the lovaszsoftmax [2] loss for training.
Due to the lack of structural priors, superquadrics uniformly initialized in 3D space. As result, some superquadrics in empty regions are optimized to small scales and contribute little to scene modeling, which leads to inefficiency. To address this, introduce pruning-splitting module after initial training. Small-scale superquadrics (likely in empty regions) are pruned, while large-scale ones (likely occupied regions) are split for finer modeling. We keep the number of superquadrics unchanged and use two additional blocks to further refine their properties. Notably, this lightweight module improves superquadric utilization for more efficient scene representation without introducing significant computational overhead.
4 Experiments
4.1 Datasets and Metrics
nuScenes [3] comprises 1,000 urban driving sequences collected in Boston and Singapore. The dataset is officially split into 700 sequences for training, 150 for validation, and 150 for testing. Each sequence spans duration of 20 seconds with RGB images captured by 6 surrounding cameras, and the key frames are annotated at a 2 Hz frequency. For supervision and evaluation, we leverage the dense semantic occupancy annotations from SurroundOcc. The annotated voxel grid extends from

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Table 1: 3D semantic occupancy prediction results nuScenes. a means supervised by dense occupancy annotations as opposed to original LiDAR segmentation labels. Sq. denotes the number of Superquadrics in our model. Our method achieves state-of-the-an performance.
motoreycle
padestria
other flat
sideoelk
momnaade
bartier
bicycle
const
trailer
trock
dowee
cur
Method
mloU
MonoSoene [5]
23.96
7.31
4.01
0.35
8.00
8.04
2,90
0.28
1.16
0.67
4.01
4.35
27.72
5.20
15.13
11.29
9.03
14.86
Atlas [32]
6.47
15.46
11.21
BEVFomer [25]
30.50 16.75
14.22
6.58
23.46
28.28
8.66
10.77
6.64
4.05
11.20
17.78
37.28
18.00
22,88
22.17
13.80
22.21
TPVFumer [77
17.13
10.46
17002
4,90
TPVHomer" [17]
90.86 17:10
15.96
5:31
23,86
22.52
9.79
8.74
7.09
5:20
10.97
19.22
58.87
21 25
24.26
23
11.73
20.81
OceFormer [50]
31.39
18.65
10:41
23,92
30.29
10.31
14.19
13.59
10.13
12.49
20.77
38.78
19.79
24
22
13.48
21.35
SurroundOce [44]
31.49 20.30
20.59
11.68
28.06
30.86
10.70
15.14
14.09
12.06
14.38
22.26
37,29
23.70
24.49
22.77
14.89
21.86
GausianFomerr [1S]
29.83 19.10
19.52
11.26
26.11
29.78
10:47
13.83
12.58
8.67
12.74
21.57
39.63
23.28
24.46
22.99
9.59
19.12
GaussinFommer-2 [15]
31.74 20.82
21.39
13.44
28.49
30.82
10.92
13
13.55
10.53
14,04
22.92
40.61
24.36
26.08
24.27
13.83
21.98
QuadrieFormer (1600 Sq.)
31.22
20.12
19:58
13.11
27.27
29.64
11.25
16
12.65
12:51
21.24
24.34
25.00
24.24
12.95
21.86
QuadrieFurmer (12800 Sq.)
(32.13
21.11
21.38
13.41
28.40
31.01
11.32
17.10
13.94
11:28
14.75
22.66
40.81
24.71
26.51
25.22
13.54 21.78
Table 2: Monocular 3D semantic occupancy prediction results on SSCRench-KKTTTI-al Num of Prims. denotes the number of primitives in the model. Our method achieves comparable performance to CeuusianFFommer [15] with much fewer primitives.
Num of Prime.
Noyele
mokoneyk
bock
other veh.
p20s00
purking
Sdewalk
Of ofhee-gano
beilding
fence
vegeSation
Mrrinn
pole
thf-4gg
object
Iupar
Method
IoU
mloU
LMSCNet
20.91
13.51
43.67
0.33
26.80
3.63
SSCNer [35]
53.58
16.95
31.95
0.17
10.29
0.58
0.07
65.7
17.33
41.24
3.22
44.41
6.77
43.72
29.87
0.78
0.75
8.60
0.67
MonoSene [5]
C
262144
$7.87
12:31
19.34
0.43
0.58
8.02
2.03
0.86
48.35
11 38
28
3.22
32 89
3.53
26.15
16.75
6.92
5.67
4.20
3.09
Vexformer [24]
38.76
1.63
9.67
27
3.79
TPVRomer [17]
81920
40.22
13.64
21.56
1.09
1.37
8.06
2.57
2.38
52.99
11.99
51.07
3.78
24
4
90.08
17.51
46
5.86
5.48
2.70
OceFormer [50]
C
262144
40.27
13.81
22.58
0.66
0.26
9.89
3882
2.77
54.30
13444
51.55
3.55
36.42
80
01
19.51
7.77
8.5
6.95
4.60
GunssinnFomer [18]
6.62
GuusiunFommee-2 [15]
38400
38.37
13.90
21.08
2.55
4.21
12
5.73
1.59
54.12
11.04
32.31
3.34
32.01
4.98
28.94
17.33
3.57
5:48
5.88
3.54
QuadricFormer
C
12800
[38.89
13.63
|3.63|18.80
18.80
1,31
4.43
16.57
8.57
3.44
45.49
13.77
25
25.92
5.25
29.73
6.73
31.95
9.13
4.47
4.02
10.88 4.88
-50m to 50m along both the X and Y axes, and from -5m 3m along the Z axis, with spatial resolution of 200 x 200 x 16. Each voxel is classified into one of the 18 categories(16 semantics, 1 empty and unknown).
KITTI-360 [27] comprises over 320k images collected suburban driving scenes with comprehen- sive 360 sensory coverage, including two perspective cameras, two fisheye cameras, Velodyne LiDAR, and a laser scanner. our experiments, we use the RGB images from the left perspective camera of the ego vehicle model input. For supervision and evaluation. cupancy annotations provided by JSCBench-KITTTI-B5 for training, 1 for validation, and 1 for testing, corresponding
adopt the semantic oc- [22]. The official split contains 7 sequences
8487, 1812, and 2566 key frames, respectively. The annotated voxel grid covers a region 51.2 x 51.2 x 6.4 m3 in front of the ego vehicle, with spatial resolution of 256 256 x 32. Each voxel is categorized into one of 19 classes (18 semantic classes and empty).
The evaluation metrics adhere to common practice namely mean Intersection-over-nniio (mloU) and Intersection-ovve--niioo (loU):
TP,
mIoU
(15)
CCI SEC
TP. - +F,+FN
TP
IoU
(16)
TP4c, + F + FN
Where C², co. TP, FP, and FN represent the non-empty classes, the empty class, and the number of true positive, false positive, and false negative predictions, respectively.
4.2 Implementation Details
The input images are at resolutions of 900x 1600 for nuScenes and 376x 1408 for KITTI-360 [27]
with random flipping and photometric distortion augmentations. We employ ResNet101-DCN [13]
with FCOS3D checkpoint [42] for nuScenes [3], and ResNet50 [13] pretrained on ImageNet [11]
7

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Table Performance and efficiency comparison with Gaussian-based methods. The latency and memory are tested on an NVIDIA 4090 GPU with batch size one during inference, in accordance with caussian-based methods [18, 15]. Our method achieves better performance-efficinngg trade-off.
Method
Number of Primitives
Latency (ms)
Memory (MB)
mloU
loU
25600
227
4850
16.00
28.72
GaussianFormer [18]
144000
372
6229
19.10
29.83
1600
341
3075
18.73
28.99
-aussianFormer-22 [15]
3200
355
3076
18.75
29.64
(Depth Initialized)
6400
395
3652
19.55
30.37
12800
451
4535
19.69
30.43
1600
162
2554
20.04
30.71
QuadricFormer (Ours)
3200
164
2556
20.35
31,62
6400
165
2560
20.79
31.89
12800
2563
21.11
32.13
for KITTI-360 [27]. The numbers of Superquarics are set to 1600 in our main results for nuScenes and KITTI-360. For optimization, we train our model using AdamW with weight decay 0.01, and maximum learning rate of 4 x 10-1 which decays with cosine schedule. We train our model for 20 epochs on nuScenes and KITTI-360 with a batch of 8.
4.3 Main Results
3D Semantic Occupancy Prediction. We report the performance of our QuadricFormer nuScenes dataset [3] in Table 1. Compared to other methods, our approach achieves state-of-the-art performance. Specifically, QuadricFormer outperforms other methods categories such bicycle, motorcycle, truck and various ground-related classes (drivable surface, sidewalk, terrain, etc.), demonstrating superior capability in modeling both small and structural objects. Moreover, our method significantly surpasses Formera [15] while using substantially fewer superquadrics (1600 vs. 12800), further validating its efficiency and effectiveness. Furthermore, We report the results for monocular 3D semantic occupancy prediction on CeC-Bennh-KTTTLL [22] in Table 2. Our method achieves comparable mloU performance to GaussianFormer-22 [15], demonstrating the effectiveness of our approach for monocular 3D semantic occupancy prediction.
Performance and Efficiency Comparison with Gaussian-based Methods. We report the perfor- mance and efficiency comparison for QuadricFormer with Gaussian methods on nuScenes in Table 3. QuadricFormer consistently outperforms prior methods in both 3D semantic occupancy prediction and computational efficiency. Specifically, our method achieves the highest mloU (up 21.11) and IoU (up to 32.13), surpassing all Gaussian-based approaches. In terms of efficiency, QuadricFormer significantly reduces both latency and memory usage. For similar or even fewer primitives (e.g.. 1600 3200), our method achieves a latency low 162 and 2554 MB memory consumption, which are substantially lower than others. Notably, even when increasing the number of primitives in QuadricFormer those of Gaussian-based methods using only 1600 primitives. This further highlights the superior efficiency of our approach for the complex structures in real-world applications.
12800, both latency and memory usage remain lower than
4.4 Ablation Study
Effect of the Range. We conduct ablation study the range of the superquadric exponent parameters E in Eq. 4, as reported in Table 4. We set the number superquadrics to 12800 for these experiments. The table explores the effect of different ranges on 3D semantic occupancy prediction performance. We observe that setting the range of (0.1,2) yields the best results, achieving the highest mloU (20.51) and IoU (31.25).
Effect of the Pruning-splitting Module. conduct ablation studies on the effect of the pruning- splitting module, as shown in Table 5. The results demonstrate that increasing the crop & split number consistently improves performance. This confirms that reallocating primitives from low to high occupancy regions effectively enhances the accuracy and efficiency of our 3D scene representation.

---

FRONT LEFT
FRONT
FRONT RIGHT
3D Supercuadries
Occupancy Prediction
Oocupancy Ground Truth
BACK_RIGHT
BACK
BACK LEFT
driveable
vegetation
sdewalk
pedestrian
bicycle
monmidee
molureyele
berrier
consruction vehicle
traller
traffic
Figure 4: 3D Superquadrics and occupancy visualizations on nuScenes. Our model able to predict ligh-fidelity shapes and achieves comprehensive occupancy results.
Table 4: Effect of the range.
Table 5: Effect of the pruming splittinggiiiiignggg module.
Range of
mIoU
IoU
Crop & Split Number
mloU
IoU
(0.01, 2)
20.39
31.13
0
19.41
39.77
(0.01, 5)
20.25
30,63
200
19.65
30.35
(0.1, 2)
20.51
31.25
400
19.90
30.67
50 19.86
30.65
800
20.12
31.22
4.5 Visualizations
We present visualizations of the predicted superquadrics and occupancy results in Figure 4. Our model is able to predict high-fidelit shapes using superquadrics and achieves comprchensive occupancy results. Further, we compare our method against GaussianFormer--2 [15] in Figure 5, showing that our predicted superquadries offer more adaptive shapes than Gaussians. Moreover, high-quality performance using only 1600 superquadrics, compared to 6400 Gaussians. Figure shows sample for 3D semantic occupancy prediction on the nuScenes [3] validation set. Compared to monnssiinoormr-22 [15], our QuadricFormer exhibits enhanced modeling capability for complex objects and road surfaces.
method achieves
Conclusion
In this paper, we have proposed superquadric-based object-centric representation for efficient 3D semantic occupancy prediction. Specifically, we leverage the geometric expressiveness of su- perquadrics model complex structures with far fewer sparsely packed primitives. We formulate probabilistic superquadric mixture model, where each superquadric encodes an occupancy probability distribution with corresponding geometry prior, and semantics are inferred via probabilistic mixture. Furthermore, we introduce a pruning-and saahingg-nd-splitingg module that adaptively concentrates superquadrics in occupied regions to further enhance modeling efficiency. Our proposed QuadricFormer demon- strates state-of-thee-e performance and superior efficiency on the nuScenes benchmark, providing an effective and compact solution for scene understanding in vision-centric autonomous driving systems.
Limitations. With random initialization, QuadricFormer cannot fully learn accurate superquadric positions, leaving some superquadrics in empty regions and reducing representation efficiency.

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3D Primitives
Occupancy
Prediction
3D Gaussians
3D Superquadrics
GaussianFormer-2
Ours
Occupancy GT
driveable surface
bus
track
lerain
vegetation
sidewalk
other flat
pedestrian
bicycle
mazmade
motoreyele
banier
constuctioon volicle
trallr
saffle cone
Figure 5: Qualitative comparisons. QuadricFormer predicts more flexible and adaptive shapes.
GaussianFormer-22
QuadricFormer
Figure 6: Visualizations of the proposed QuadricFormer compared to GaussianFormer-22 [15] for 3D semantic occupancy prediction the nuScenes [3] validation set. We visualize the six surrounding camera inputs, the corresponding occupancy prediction results, and the primitive representations. The upper shows the predicted occupancy (left) and the primitive representation (right) by GaussianFormer-22 The lower row shows the prediction results QuadricFormer.
Broader impact. Our work autonomous driving has the potential improve traffic efficiency in the future, but it may also contribute to job displacement for drivers.
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China under Grant 62576188 Grant 62336004, Grant 62321005, and Grant 62125603, in part by the Beijing Natural Science Foundation under Grant 1.247009, and part by the Beijing National Research Center for Information Science and Technology.
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14

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61 = 1.0
6 = 0.1
E1 = 2.0
E2 = 0.1
E2 1.0
E2 2.0
Figure 7: Superquadrics of different shape parameters. The figure illustrates how varying 6 and Cg produces wide range of shapes, from star-like and rounded shapes square- like structures. Such diversity enables superquadrics to flexibly model complex object geometries in 3D scenes.
A Additional Superquadric Details
Superquadrics powerful family of parameterized surfaces that represent various geometric shapes. With just a few parameters, superquadrics can generate shapes ranging from basic ellipsoids, cuboids, and cylinders more complex shapes with rounded corners, star-like profiles, and smooth transitions between them. This geometric flexibility makes superquadrics ideal for efficiently model- ing diverse objects in autonomous driving scenes. The shape of superquadric mainly controlled by two groups of parameters. The first group consists of scaling factors S8, 82), 82), superquadric's dimensions "radii" along its three principal axes, determining the object's overall size and aspect ratio. The second group includes two key shape parameters (c1, eg) that determine the degree of "squareness" or "roundness" of the object. é1 primarily controls the object's 's profile in planes containing the z-axis (such as the xz- yz-plane): smaller values (close to 0.1) create sharper profiles, 6 1.0 produces elliptical outlines, and larger values (up to 2.0) result flatter contours. Similarly, 62 controls the shape of the cross-section in the xy-plane. A small c2 yields star-shaped pross-section, 120 gives circular outline, and large (2 values produce square-like shapes. As shown in Fig 7, varying e and (2 of superquadrics results in wide range of shapes. By combining these scaling and shape parameters, superquadrics can efficiently represent diverse object geometries in autonomous driving scenes. This capability allows them to capture complex structures with signifi- cantly fewer primitives than traditional representations (like ellipsoidal Gaussians), highlighting their superior modeling efficiency and expressive power for 3D scene understanding tasks.
which define the
B Additional Experiments
We visualize the position distributions of scene primitives using 1600 superquadrics versus 6400 Gaussians in Figure& 8. Gaussian-based methods require a dense arrangement of Gaussians throughout the entire 3D space to model the scene, leading to numerous redundant Gaussians and low modeling efficiency. In contrast, our superquadric-bar method learns well-structured spatial arrangements, enabling it to effectively model the scene structure with significantly fewer primitives.
15

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Gaussians
3D Superquadrics
3D Gaussiars
Superquadrics
driveable suface
GAT
track
territ
Vegetation
sideralk
other
padestraan
bicyde
mummade
motortycle
Figure 8: Visualizations of primitive position distributions learned by different methods, Our approach produces well-structured spatial arrangements while using significantly fewer primitives.
C Additional Implementation Details
We provide implementation details of the prunning-and-splitee and-splitting module. To clarify, we take the example and describe the process follows:
QuadricFormer with N superquadries
Initial Training: We first train a QuadricFormer with B=4 quadric-encoder blocks and without the prunning-and-pplittng module. The model starts from N randomly initialized superquadrics Qinit and predicts adjusted superquadrics Q.
During experiments, we observed that some superquadrics in Q contribute little to scene modeling, which are usually located in empty regions with very small scales. To address this, we introduce the prunning-and and-sitttigg module:
Prunning-ande -nd-iiiginnSSpliiinggg Module:
We divide all superquadries in Q into two groups based the product of their scales: the N Nerop superquadrics C' with the smallest scales and the remaining Noalid superquadrics V where N Nootid + Nevop-
We discard the smaller superquadries as they are most likely contribute little scene modeling.
We randomly sample Nerop superquadrics from V to form S. The features of S remain unchanged, and only their positions slightly adjusted.
Further Refinement: Finally, S and are passed through two additional quadric-encoder blocks to further refine their attributes, resulting in the final superquadrics Q ginal At this stage, load the pretrained model parameters and continue training for more epochs.
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Reviews:
[{"review_id": "QRNp3TGQyv", "reviewer": "Reviewer_N2Bk", "summary": "This work proposes QuadricFormer, a novel 3D occupancy prediction model that uses probabilistic superquadrics instead of Gaussians to efficiently represent complex scene geometries. It achieves state-of-the-art performance on the nuScenes dataset with significantly improved representation efficiency.", "questions": "see weakness. If these concerns are clarified and the results remain solid, I would be happy to increase my score.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths**:\n\n1.The introduction of superquadrics for scene geometry representation is the core innovation of this paper. Compared to previous 3D Gaussian-based representations, superquadrics offer significantly greater geometric expressiveness, allowing complex structures—such as cuboids, cylinders, and planes—to be modeled with far fewer primitives.\n\n2.The experimental results are impressive, particularly in terms of speed improvement, where the proposed method significantly reduces latency and memory consumption.\n\n3.The paper is logically well-structured and clearly written, making it easy to follow and understand.\n\n**Weaknesses**:\n\n**1. Issue with SOTA Claim in Table 1**\n\nWhile the paper claims state-of-the-art performance, the results in Table 1 do not fully support this assertion. Specifically:\n\nOccFormer reports a higher IoU (31.39 vs. 31.22) than QuadricFormer.\n\nSurroundOcc achieves both higher mIoU (20.30 vs. 20.12) and IoU (31.49 vs. 31.22).\n\nAlthough the differences are relatively minor, the current claim of SOTA is not strictly accurate based on these metrics. The authors are encouraged to revise the statement to more precisely reflect the strengths of QuadricFormer—such as efficiency-performance trade-off or performance with fewer primitives—to ensure consistency between the claims and the presented results.\n\n2.**The evaluation is limited to nuScenes.** Results on KITTI-360 or other datasets would help demonstrate the generalization and robustness of the proposed method.\n\n3.**Pruning-and-Splitting Module Is Somewhat Confusing.**\nThe pruning-and-splitting module is described as a key innovation, yet its implementation is underspecified, and Table 4 contains a puzzlingly high IoU (39.77 for number=0) that contradicts other results. The efficiency gain attributed to this module is not clearly quantified. More clarity, quantitative impact, and validation are needed to justify this component.", "was_revised": true, "final_justification": "The author's clarification in the response addressed my concerns regarding the issues of SOTA comparison, generalization evaluation, and the design of the Pruning-and-Splitting Module. While this method has the potential to serve as a new baseline, the performance improvement is not particularly significant. Therefore, I consider this paper to be at the borderline of acceptance.", "rebuttal": "We thank the reviewer for the constructive comments and positive feedback on our paper. Regarding the concerns of the reviewer N2Bk, we provide the following responses.\n\n> **W1:  Issue with SOTA Claim in Table 1**\n\n- We apologize for the lack of clarity in Table 1, where we only reported the performance of QuadricFormer with **1600** superquadrics. This presentation may have caused confusion about our SOTA claim. **Our model actually can be configured to use different numbers of superquadrics, and using more superquadrics yields better accuracy with only a slight reduction in efficiency.** As shown in Table 2, with **6400** and **12800** superquadrics, QuadricFormer achieves mIoUs of **20.79** and **21.11** and IoUs of **31.89** and **32.13**, respectively, surpassing all previous methods and achieving SOTA results. \n\n- Moreover, unlike GaussianFormer-2, we do not use the heavy depth-initialized module, so our model maintains high efficiency even with 6400 or 12800 superquadrics (see Table 2).\n\n\n- To avoid confusion, we have updated Table 1 in the revised manuscript to clarify the SOTA claim and clearly indicate the results for different numbers of superquadrics.\n\n> **W2: The evaluation is limited to nuScenes.**\n\n- In response to the reviewer’s concerns about robustness and generalizability of our method, we have conducted additional experiments on the SSCBench-KITTI-360 [1] dataset. The results are summarized in the table below.\n\n\n- **Compared to previous dense voxel-based and sparse Gaussian-based methods, our method achieves comparable performance with much fewer scene primitives**. This highlights our method’s efficiency, as it is able to represent complex scenes with fewer expressive superquadrics without sacrificing much accuracy.\n\n\n- **We would like to clarify a key difference with GaussianFormer-2, which employs a heavy depth backbone to initialize Gaussians for improved performance**. While this strategy can yield better results, it comes at the cost of significantly reduced efficiency (i.e., high inference latency and memory usage), as evidenced by Table 2 in the paper. In contrast, to preserve the efficiency advantage of our method, we did not incorporate such a heavy depth-initialized module.\n\n- These results demonstrate both the effectiveness and the efficiency of our approach. We hope this addresses your concerns and further highlights the practical advantages of our method.\n\n- **Due to the limited time during the rebuttal period, we only conducted the experiments with 12800 superquadrics on SSCBench-KITTI-360. We will provide more experiments on Occ3D and SSCBench-KITTI-360 later**.\n\n|        Method        | Input Modality |   Number of Primitives   |  IoU  | mIoU  |\n| :------------------: | :------------: | :----------------------: | :---: | :---: |\n|     LMSCNet [2]      |     LiDAR      |            -             | 47.53 | 13.65 |\n|      SSCNet [3]      |     LiDAR      |            -             | 53.58 | 16.95 |\n|    MonoScene [4]     |     Camera     |   262144  (128x128x16)   | 37.87 | 12.31 |\n|    Voxformer [5]     |     Camera     |   262144  (128x128x16)   | 38.76 | 11.91 |\n|    TPVFormer [6]     |     Camera     | 81920 (256x256+256x32x2) | 40.22 | 13.64 |\n|    OccFormer [7]     |     Camera     |   262144  (128x128x16)   | 40.27 | 13.81 |\n|  GaussianFormer [8]  |     Camera     |          38400           | 35.38 | 12.92 |\n| GaussianFormer-2 [9] |     Camera     |          38400           | 38.37 | 13.90 |\n|       **Ours**       |     Camera     |        **12800**         | 36.81 | 12.86 |\n\n> **W3: Pruning-and-Splitting Module Is Somewhat Confusing.** \n\n- We provide implementation details of the prunning-and-splitting module. To clarify, we take the QuadricFormer with $N$ superquadrics as an example and describe the process as follows:\n\n  1. **Initial Training:** We first train a QuadricFormer with $B=4$ quadric-encoder blocks and without the prunning-and-splitting module. The model starts from $N$ randomly initialized superquadrics $\\mathbf{Q}_{init}$ and predicts adjusted superquadrics $\\mathbf{Q}$.\n\n  2. **Prunning-and-Splitting Module:**\n     During experiments, we observed that some superquadrics in $\\mathbf{Q}$ contribute little to scene modeling, which are usually located in empty regions with very small scales. To address this, we introduce the prunning-and-splitting module:\n\n     - We divide all superquadrics in $\\mathbf{Q}$ into two groups based on the product of their scales: the $N_{crop}$ superquadrics $\\mathbf{C}$ with the smallest scales and the remaining $N_{valid}$ superquadrics $\\mathbf{V}$, where $N=N_{crop}+N_{valid}$.\n     - We discard the smaller superquadrics $\\mathbf{C}$ as they are most likely to contribute little to scene modeling.\n     - We randomly sample $N_{crop}$ superquadrics from $\\mathbf{V}$ to form $\\mathbf{S}$. The features of $\\mathbf{S}$ remain unchanged, and only their positions are slightly adjusted.\n\n  3. **Further Refinement:**\n     Finally, $\\mathbf{S}$ and $\\mathbf{V}$ are passed through two additional quadric-encoder blocks to further refine their attributes, resulting in the final superquadrics $\\mathbf{Q}_{final}$. At this stage, we load the pretrained model parameters and continue training for 10 more epochs.\n\n- We provide more results to quantitatively analyze the impact of the pruning-and-splitting module on both model performance and efficiency. All experiments used a fixed total number of 1600 superquadrics. **The results show that this module clearly improves performance with only a minor efficiency loss.** The best performance is achieved when $N_{crop}=800$ (i.e., the crop & split number in the table). Increasing $N_{crop}$ further actually reduces the number of valid superquadrics and leads to a drop in performance. Moreover, changes in $N_{crop}$ have only a minor effect on inference speed and memory usage, allowing the model to achieve better performance while maintaining high efficiency.\n\n  | Crop & Split Number | mIoU  |  IoU  | Latency (ms) | Memory (MB) |\n  | :-----------------: | :---: | :---: | :----------: | :---------: |\n  |          0          | 19.41 | 29.77 |     158      |    2554     |\n  |         200         | 19.65 | 30.35 |     161      |    2554     |\n  |         400         | 19.90 | 30.67 |     161      |    2554     |\n  |         800         | 20.12 | 31.22 |     162      |    2554     |\n  |        1200         | 19.91 | 30.41 |     164      |    2554     |\n\n- Regarding the puzzlingly high IoU (39.77 for number=0) in Table 4, we apologize for this typographical error. The correct value is 29.77 (not 39.77), and this typo has been fixed in the revised manuscript.\n\n**References**\n\n[1] SSCBench: A Large-Scale 3D Semantic Scene Completion Benchmark for Autonomous Driving, IROS 2024.\n\n[2] LMSCNet: Lightweight Multiscale 3D Semantic Completion, 3DV 2020.\n\n[3] Semantic Scene Completion From a Single Depth Image, CVPR 2017.\n\n[4] MonoScene: Monocular 3D Semantic Scene Completion, CVPR 2022.\n\n[5] VoxFormer: Sparse Voxel Transformer for Camera-Based 3D Semantic Scene Completion, CVPR 2023.\n\n[6] Tri-Perspective View for Vision-Based 3D Semantic Occupancy Prediction, CVPR 2023.\n\n[7] OccFormer: Dual-path Transformer for Vision-based 3D Semantic Occupancy Prediction, ICCV 2023.\n\n[8] GaussianFormer: Scene as Gaussians for Vision-Based 3D Semantic Occupancy Prediction, ECCV 2024.\n\n[9] GaussianFormer-2: Probabilistic Gaussian Superposition for Efficient 3D Occupancy Prediction, CVPR 2025."}, {"review_id": "TRwNmmloWQ", "reviewer": "Reviewer_cJXu", "summary": "This paper introduces a novel vision-based 3D semantic scene completion method that employs geometrically expressive superquadrics as scene primitives instead of traditional voxel-based representations. Extensive experiments on the nuScenes dataset demonstrate that this new representation enables a more lightweight 3D SSC framework with improved latency and memory efficiency, while maintaining competitive performance.", "questions": "- In Table 1, the authors claim to achieve state-of-the-art performance. However, both the IoU and mIoU scores are lower than those of existing methods. Please clarify this discrepancy.\n- I would like to see results on additional datasets such as SemanticKITTI. This would be necessary to better demonstrate the generalizability and practical effectiveness of the proposed method.\n- In Table 4, the best performance is achieved when the Crop & Split Number is set to 800. Would increasing this number further lead to better performance? Additionally, how does the Crop & Split Number affect inference speed and memory usage?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n- The paper is well-written and the methodology is easy to understand with clear intuition.\n- Applying superquadrics to 3D semantic scene completion is a novel, effective, and highly interesting approach.\n- The experimental results are promising, particularly in terms of efficiency, and support the proposed approach.\n\nWeaknesses\n- The proposed method shows lower IoU and mIoU performance compared to SurrondOcc. However, this gap is acceptable considering the improved efficiency in terms of latency and memory usage.\n- To further demonstrate the robustness of the proposed method, evaluations on more diverse datasets beyond a single benchmark, nuScene, would be beneficial.", "was_revised": true, "final_justification": "Thank you for your response. However, given the lower performance of the proposed method on the other dataset, I would like to maintain my initial score.", "rebuttal": "We thank the reviewer for the constructive comments and positive feedback on our paper. Regarding the concerns of the reviewer cJXu, we provide the following responses.\n\n> **Q1: In Table 1, the authors claim to achieve state-of-the-art performance. However, both the IoU and mIoU scores are lower than those of existing methods.**\n\n- We apologize for the lack of clarity in Table 1, where we only reported the performance of QuadricFormer with **1600** superquadrics. This presentation may have caused confusion about our SOTA claim. **Our model actually can be configured to use different numbers of superquadrics, and using more superquadrics yields better accuracy with only a slight reduction in efficiency.** As shown in Table 2, with **6400** and **12800** superquadrics, QuadricFormer achieves mIoUs of **20.79** and **21.11** and IoUs of **31.89** and **32.13**, respectively, surpassing all previous methods and achieving SOTA results.  \n\n- Moreover, unlike GaussianFormer-2, we do not use the heavy depth-initialized module, so our model maintains high efficiency even with 6400 or 12800 superquadrics (see Table 2).\n\n- To avoid confusion, we have updated Table 1 in the revised manuscript to clarify the SOTA claim and clearly indicate the results for different numbers of superquadrics.\n\n> **Q2: I would like to see results on additional datasets such as SemanticKITTI. This would be necessary to better demonstrate the generalizability and practical effectiveness of the proposed method.**\n\n- In response to the reviewer’s concerns about robustness and generalizability of our method, we have conducted additional experiments on the SSCBench-KITTI-360 [1] dataset. The results are summarized in the table below.\n\n\n- **Compared to previous dense voxel-based and sparse Gaussian-based methods, our method achieves comparable performance with much fewer scene primitives**. This highlights our method’s efficiency, as it is able to represent complex scenes with fewer expressive superquadrics without sacrificing much accuracy.\n\n\n- **We would like to clarify a key difference with GaussianFormer-2, which employs a heavy depth backbone to initialize Gaussians for improved performance**. While this strategy can yield better results, it comes at the cost of significantly reduced efficiency (i.e., high inference latency and memory usage), as evidenced by Table 2 in the paper. In contrast, to preserve the efficiency advantage of our method, we did not incorporate such a heavy depth-initialized module.\n\n- These results demonstrate both the effectiveness and the efficiency of our approach. We hope this addresses your concerns and further highlights the practical advantages of our method.\n\n- **Due to the limited time during the rebuttal period, we only conducted the experiments with 12800 superquadrics on SSCBench-KITTI-360. We will provide more experiments on Occ3D and SSCBench-KITTI-360 later**.\n\n\n|        Method        | Input Modality |   Number of Primitives   |  IoU  | mIoU  |\n| :------------------: | :------------: | :----------------------: | :---: | :---: |\n|     LMSCNet [2]      |     LiDAR      |            -             | 47.53 | 13.65 |\n|      SSCNet [3]      |     LiDAR      |            -             | 53.58 | 16.95 |\n|    MonoScene [4]     |     Camera     |   262144  (128x128x16)   | 37.87 | 12.31 |\n|    Voxformer [5]     |     Camera     |   262144  (128x128x16)   | 38.76 | 11.91 |\n|    TPVFormer [6]     |     Camera     | 81920 (256x256+256x32x2) | 40.22 | 13.64 |\n|    OccFormer [7]     |     Camera     |   262144  (128x128x16)   | 40.27 | 13.81 |\n|  GaussianFormer [8]  |     Camera     |          38400           | 35.38 | 12.92 |\n| GaussianFormer-2 [9] |     Camera     |          38400           | 38.37 | 13.90 |\n|       **Ours**       |     Camera     |        **12800**         | 36.81 | 12.86 |\n\n> **Q3: Would increasing this number further lead to better performance? Additionally, how does the Crop & Split Number affect inference speed and memory usage?**\n\n- We provide more results to quantitatively analyze the impact of the pruning-and-splitting module on both model performance and efficiency. All experiments used a fixed total number of 1600 superquadrics. \n\n- **The results show that this module clearly improves performance with only a minor efficiency loss.** Moreover, changes in $N_{crop}$ have only a minor effect on inference speed and memory usage, allowing the model to achieve better performance while maintaining high efficiency.\n\n- The best performance is achieved when $N_{crop}=800$ (i.e., the crop & split number in the table). Increasing $N_{crop}$ beyond 800 actually leads to a slight drop in performance. We believe this is because excessive cropping removes too many superquadrics, including some valid ones, which negatively impacts the performance.\n\n  | Crop & Split Number | mIoU  |  IoU  | Latency (ms) | Memory (MB) |\n  | :-----------------: | :---: | :---: | :----------: | :---------: |\n  |          0          | 19.41 | 29.77 |     158      |    2554     |\n  |         200         | 19.65 | 30.35 |     161      |    2554     |\n  |         400         | 19.90 | 30.67 |     161      |    2554     |\n  |         800         | 20.12 | 31.22 |     162      |    2554     |\n  |        1200         | 19.91 | 30.41 |     164      |    2554     |\n\n**References**\n\n[1] SSCBench: A Large-Scale 3D Semantic Scene Completion Benchmark for Autonomous Driving, IROS 2024.\n\n[2] LMSCNet: Lightweight Multiscale 3D Semantic Completion, 3DV 2020.\n\n[3] Semantic Scene Completion From a Single Depth Image, CVPR 2017.\n\n[4] MonoScene: Monocular 3D Semantic Scene Completion, CVPR 2022.\n\n[5] VoxFormer: Sparse Voxel Transformer for Camera-Based 3D Semantic Scene Completion, CVPR 2023.\n\n[6] Tri-Perspective View for Vision-Based 3D Semantic Occupancy Prediction, CVPR 2023.\n\n[7] OccFormer: Dual-path Transformer for Vision-based 3D Semantic Occupancy Prediction, ICCV 2023.\n\n[8] GaussianFormer: Scene as Gaussians for Vision-Based 3D Semantic Occupancy Prediction, ECCV 2024.\n\n[9] GaussianFormer-2: Probabilistic Gaussian Superposition for Efficient 3D Occupancy Prediction, CVPR 2025."}, {"review_id": "dbxRis8ROD", "reviewer": "Reviewer_GNa2", "summary": "The paper replace the Gaussian with superquadrics as scene primitives in GaussianFormer to overcome the ellipsoidal shape limitation of Gaussian-based methods By leveraging a probabilistic superquadric mixture model and a pruning-splitting module, it concentrates primitives in occupied regions for better efficiency. Experiments on nuScenes show QuadricFormer achieves good performance with fewer primitives.", "questions": "- Could the authors provide more details on the pruning-and-splitting module? According to Table 4, this component plays a significant role in the model’s performance. However, the current version of the paper lacks sufficient explanation regarding its design and implementation.\n- [minor] In Table 1, the caption mentions “Ch”, but this notation does not appear anywhere in the table itself. \n- [minor] The statements in lines 244–245 do not align with the results reported in Table 1. The authors should revise the text to accurately reflect the experimental outcomes.", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- The motivation to replace Gaussians with a more general and expressive representation is commendable.\n- The presentation of the paper is clear.\n\nWeaknesses:\n- The experimental evaluation in the current version is insufficient. Most existing occupancy prediction methods report results on benchmarks such as OpenOccupancy or Occ3D, which facilitates fair and consistent comparison across approaches. However, the authors only evaluate their model on the dataset introduced by SurroundOcc, limiting the ability of the community to properly assess the model’s effectiveness. I strongly encourage the authors to include additional evaluations to compare with other sparse occupancy prediction methods.\n- The performance claims regarding QuadricFormer are misleading. The authors state in the main results (Tab. 2) that their model achieves state-of-the-art (SOTA) performance. However:\n  - In Table 2, QuadricFormer achieves 31.22 IoU and 20.12 mIoU, which are both lower than those of SurroundOcc (31.49 IoU, 20.30 mIoU) and OccFormer (31.39 IoU). Highlighting QuadricFormer as the best-performing model is potentially misleading to readers.\n  - Additionally, the reported numbers for GaussianFormer-2 (30.56 IoU, 20.02 mIoU) are not its best-performing results. According to its original paper, the best configuration of GaussianFormer-2 achieves 31.74 IoU and 20.82 mIoU, which outperforms QuadricFormer. The authors should ensure fair and accurate comparisons by reporting the strongest results for all baselines.", "was_revised": true, "final_justification": "After reading all the responses, I still have concerns on the benchmark used. The paper evaluates their method on the dataset provided by SurroundOcc rather than widely adpoted benchmarks such as Occ3D. Although this dataset seems to be chosen by several works such as SurroundOcc, GaussianFormer, and GaussianFormer-2, it appears that these works originate from authors and institutions with close ties. In my view, this phenomenon is detrimental to the community, as it prevents researchers from fairly assessing works in the field.\n\nOverall, the quality of the paper is good; however, my opinion remains quite borderline.", "rebuttal": "We thank the reviewer for the constructive comments and positive feedback on our paper. Regarding the concerns of the reviewer GNa2, we provide the following responses.\n\n> **W1: The experimental evaluation in the current version is insufficient. I strongly encourage the authors to include additional evaluations to compare with other sparse occupancy prediction methods.** \n\n- Thanks for your valuable suggestion. Due to the limited time of the rebuttal period, we were only able to provide additional results on SSCBench-KITTI-360 [1], following the experimental protocol of GaussianFormer-2. The results are summarized in the table below.\n\n\n- Compared to previous dense voxel-based and sparse Gaussian-based methods, our method achieves comparable performance with much fewer scene primitives. This highlights our method’s efficiency, as it is able to represent complex scenes with fewer expressive superquadrics without sacrificing much accuracy.\n\n\n- **We would like to clarify a key difference with GaussianFormer-2, which employs a heavy depth backbone to initialize Gaussians for improved performance**. While this strategy can yield better results, it comes at the cost of significantly reduced efficiency (i.e., high inference latency and memory usage), as evidenced by Table 2 in the paper. In contrast, to preserve the efficiency advantage of our method, we did not incorporate such a heavy depth-initialized module.\n\n- These results demonstrate both the effectiveness and the efficiency of our approach. We hope this addresses your concerns and further highlights the practical advantages of our method.\n\n- **Due to the limited time during the rebuttal period, we only conducted the experiments with 12800 superquadrics on SSCBench-KITTI-360. We will provide more experiments on Occ3D and SSCBench-KITTI-360 later**.\n\n|        Method        | Input Modality |   Number of Primitives   |  IoU  | mIoU  |\n| :------------------: | :------------: | :----------------------: | :---: | :---: |\n|     LMSCNet [2]      |     LiDAR      |            -             | 47.53 | 13.65 |\n|      SSCNet [3]      |     LiDAR      |            -             | 53.58 | 16.95 |\n|    MonoScene [4]     |     Camera     |   262144  (128x128x16)   | 37.87 | 12.31 |\n|    Voxformer [5]     |     Camera     |   262144  (128x128x16)   | 38.76 | 11.91 |\n|    TPVFormer [6]     |     Camera     | 81920 (256x256+256x32x2) | 40.22 | 13.64 |\n|    OccFormer [7]     |     Camera     |   262144  (128x128x16)   | 40.27 | 13.81 |\n|  GaussianFormer [8]  |     Camera     |          38400           | 35.38 | 12.92 |\n| GaussianFormer-2 [9] |     Camera     |          38400           | 38.37 | 13.90 |\n|       **Ours**       |     Camera     |        **12800**         | 36.81 | 12.86 |\n\n> **W2.1: QuadricFormer achieves lower IoU and mIoU than SurroundOcc and OccFormer. Highlighting QuadricFormer as the best-performing model is potentially misleading to readers.**\n\n- We apologize for the lack of clarity in Table 1, where we only reported the performance of QuadricFormer with **1600** superquadrics. This presentation may have caused confusion about our SOTA claim. **Our model actually can be configured to use different numbers of superquadrics, and using more superquadrics yields better accuracy with only a slight reduction in efficiency.** As shown in Table 2, with **6400** and **12800** superquadrics, QuadricFormer achieves mIoUs of **20.79** and **21.11** and IoUs of **31.89** and **32.13**, respectively, surpassing all previous methods and achieving SOTA results. \n\n- Moreover, unlike GaussianFormer-2, we do not use the heavy depth-initialized module, so our model maintains high efficiency even with 6400 or 12800 superquadrics (see Table 2).\n\n- To avoid confusion, we have updated Table 1 in the revised manuscript to clarify the SOTA claim and clearly indicate the results for different numbers of superquadrics.\n\n> **W2.2: The reported numbers for GaussianFormer-2 (30.56 IoU, 20.02 mIoU) are not its best-performing results.**\n\n- Thanks for your suggestion. **In Table 1, we only reported the results of GaussianFormer-2 (Ch=128, mIoU=20.02) with a feature dimension of 128 to ensure a fair comparison, since our method is under the same setting**. However, we agree that the best results should also be included to provide a more complete picture. In the revised version, we have added the strongest results of GaussianFormer-2 (Ch=192, mIoU=20.82) and clarified this in the manuscript. \n\n\n- Notably, even when compared with the best configuration of GaussianFormer-2, our QuadricFormer (with 12,800 superquadrics) still achieves superior performance with clear efficiency advantages. We appreciate your suggestion, which has improved the completeness and transparency of our experimental comparisons.\n\n\n> **Q1: Could the authors provide more details on the pruning-and-splitting module?**\n\nWe provide implementation details of the prunning-and-splitting module. To clarify, we take the QuadricFormer with $N$ superquadrics as an example and describe the process as follows:\n\n1. **Initial Training:** We first train a QuadricFormer with $B=4$ quadric-encoder blocks and without the prunning-and-splitting module. The model starts from $N$ randomly initialized superquadrics $\\mathbf{Q}_{init}$ and predicts adjusted superquadrics $\\mathbf{Q}$.\n\n2. **Prunning-and-Splitting Module:**\n   During experiments, we observed that some superquadrics in $\\mathbf{Q}$ contribute little to scene modeling, which are usually located in empty regions with very small scales. To address this, we introduce the prunning-and-splitting module:\n   - We divide all superquadrics in $\\mathbf{Q}$ into two groups based on the product of their scales: the $N_{crop}$ superquadrics $\\mathbf{C}$ with the smallest scales and the remaining $N_{valid}$ superquadrics $\\mathbf{V}$, where $N=N_{crop}+N_{valid}$.\n   - We discard the smaller superquadrics $\\mathbf{C}$ as they are most likely to contribute little to scene modeling.\n   - We randomly sample $N_{crop}$ superquadrics from $\\mathbf{V}$ to form $\\mathbf{S}$. The features of $\\mathbf{S}$ remain unchanged, and only their positions are slightly adjusted.\n\n3. **Further Refinement:**\n   Finally, $\\mathbf{S}$ and $\\mathbf{V}$ are passed through two additional quadric-encoder blocks to further refine their attributes, resulting in the final superquadrics $\\mathbf{Q}_{final}$. At this stage, we load the pretrained model parameters and continue training for 10 more epochs.\n\n> **M1 & M2**\n\n1. Thanks for pointing out this editing error. We have now removed the incorrect \"Ch\" notation from the caption of Table 1.\n2. We acknowledge that there was a mismatch between the text and results in Table 1. This was because Table 1 did not include model performance under settings of more than 1600 superquadrics, which were included in Table 2. We have updated Table 1 and revised the corresponding statements to ensure full consistency between our description and the reported results.\n\n**References**\n\n[1] SSCBench: A Large-Scale 3D Semantic Scene Completion Benchmark for Autonomous Driving, IROS 2024.\n\n[2] LMSCNet: Lightweight Multiscale 3D Semantic Completion, 3DV 2020.\n\n[3] Semantic Scene Completion From a Single Depth Image, CVPR 2017.\n\n[4] MonoScene: Monocular 3D Semantic Scene Completion, CVPR 2022.\n\n[5] VoxFormer: Sparse Voxel Transformer for Camera-Based 3D Semantic Scene Completion, CVPR 2023.\n\n[6] Tri-Perspective View for Vision-Based 3D Semantic Occupancy Prediction, CVPR 2023.\n\n[7] OccFormer: Dual-path Transformer for Vision-based 3D Semantic Occupancy Prediction, ICCV 2023.\n\n[8] GaussianFormer: Scene as Gaussians for Vision-Based 3D Semantic Occupancy Prediction, ECCV 2024.\n\n[9] GaussianFormer-2: Probabilistic Gaussian Superposition for Efficient 3D Occupancy Prediction, CVPR 2025."}, {"review_id": "u4yq2rG2IP", "reviewer": "Reviewer_uPb2", "summary": "The paper QuadricFormer proposes a novel and efficient object-centric scene representation for 3D semantic occupancy prediction using superquadrics instead of traditional dense voxels or Gaussian primitives. By leveraging the geometric flexibility of superquadrics, the proposed QuadricFormer framework efficiently models complex scene structures with significantly fewer primitives. The paper introduces a probabilistic superquadric mixture model and design a pruning-and-splitting module to further enhance representation efficiency. Extensive experiments on the nuScenes dataset demonstrate that QuadricFormer achieves state-of-the-art performance while substantially reducing computational cost and memory usage.", "questions": "The main concerns, as outlined in the Weaknesses section, can be summarized as follows:\n\n1. The proposed idea lacks sufficient impact.\n\n2. The efficiency comparison requires further clarification.\n\n3. The experiments are insufficient in terms of benchmark diversity and baseline comparisons.\n\n4. The evaluation metrics are inadequate and need to be updated.", "limitations": "Yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. This paper proposes a novel and efficient object-centric scene representation for 3D semantic occupancy prediction based on superquadrics.\n2. The proposed model achieves superior performance while significantly reducing computational cost and memory usage compared to previous methods.\n\nWeaknesses:\n1. **The idea lacks sufficient impact**.\n\nWhile this paper provides a valuable attempt to apply superquadrics to the occupancy prediction task, the performance improvement over previous methods, such as GaussianFormer-2, appears to be limited.\n\nRegarding efficiency, memory usage is influenced by various factors, including the backbone architecture, the number of layers, and other design choices. Therefore, the reported efficiency improvements are difficult to attribute solely to the use of superquadric representations. Based on the current information, the comparison in Table 2 does not appear to be entirely fair.\n\nOverall, this paper seems to have made a modest contribution and, at best, would likely receive only a lukewarm response within the community.\n\n2. **Insufficient experiments**.\n\nThe experiments are conducted only on the nuScenes dataset and primarily compared with outdated methods such as TPVFormer and SurroundOcc. Several recent state-of-the-art approaches, including SparseOcc [1], FB-Occ [2], CVT-Occ [3], and many others, are notably missing from the comparisons. Additionally, evaluations on more widely adopted benchmarks, such as Occ3D-nuScenes and Occ3D-Waymo [4], are essential to convincingly demonstrate the advantages of the proposed method.\n\nFurthermore, SparseOcc [1] has challenged the use of IoU and mIoU as evaluation metrics, advocating for the adoption of RayIoU instead. An update of the evaluation metrics is therefore necessary to ensure fair and meaningful comparisons.\n\n**Reference**: \n\n[1] Fully Sparse 3D Occupancy Prediction, ECCV 2024.\n\n[2] FB-OCC: 3D Occupancy Prediction based on Forward-Backward View Transformation, arXiv 2023.\n\n[3] CVT-Occ: Cost Volume Temporal Fusion for 3D Occupancy Prediction, ECCV 2024.\n\n[4] Occ3D: A Large-Scale 3D Occupancy Prediction Benchmark for Autonomous Driving, arXiv 2023.", "was_revised": true, "final_justification": "The authors' rebuttal partially addresses my concerns. However, the proposed method demonstrates only moderate performance on the SSCBench-KITTI-360 benchmark. Since the introduction of the Occ3D benchmark, it has become a widely adopted standard, with over a hundred methods evaluated on it. Additionally, SparseOcc introduces RayIoU, a more principled metric that extends the conventional mIoU. Therefore, comparison experiments with both the Occ3D benchmark and RayIoU are crucial for a comprehensive evaluation. The current experimental results remain insufficient. Given that further experiments are still necessary to validate the soundness and effectiveness of the proposed approach, I maintain my negative rating.", "rebuttal": "We thank the reviewer for the constructive comments. Regarding the concerns of the reviewer uPb2, we provide the following responses.\n\n> **W1 & Q1 & Q2: The proposed idea lacks sufficient impact. The efficiency comparison requires further clarification.**\n\n- **On the fairness and validity of efficiency comparison:**\n  1. We would like to clarify that our efficiency comparison is fair and meaningful. As noted, model efficiency (inference speed and memory usage) can be affected by various factors. To ensure a fair comparison with Gaussian-based methods, we made the model architectures and evaluation settings as consistent as possible.\n  1. **The only difference is that GaussianFormer-2 requires an additional depth backbone for Gaussian initialization, while our method dose not. Instead, we employ a lightweight pruning-and-splitting module to enhance performance.**\n  1. **Since the depth backbone in GaussianFormer-2 is a heavy ResNet-101, it becomes the main bottleneck for inference speed and memory usage.** As a result, even with the same number of primitives, our method achieves better performance and efficiency. This highlights the effectiveness and efficiency of our method.\n\n\n- **On performance gains and broader impact:**\n  1. We respectfully disagree that the performance improvements over GaussianFormer-2 are limited. While GaussianFormer-2 achieves strong results by leveraging a heavy depth backbone and increasing feature dimensions, this comes at the cost of significant efficiency loss (see Table 2). \n  1. **Without relying on these additional tricks, QuadricFormer (with 12800 superquadrics) surpasses GaussianFormer-2 in mIoU (21.11 vs 20.82) with superior efficiency (179 ms latency vs 451 ms)**. This demonstrates that our method not only exceeds the performance of existing baselines but also sets a new standard for efficiency, which is valuable for real-world applications.\n\n- In summary, our results demonstrate that the proposed superquadric representations leads to meaningful advances in both performance and efficiency, supporting the impact and relevance of our work. We thank you for your suggestions, which have encouraged us to further clarify these points in the revised manuscript.\n\n> **W2 & Q3 & Q4: The experiments are insufficient in terms of benchmark diversity and baseline comparisons. The evaluation metrics are inadequate and need to be updated.**\n\n- **Experiments on additional benchmarks:** \n\n  - Thanks for your valuable suggestion. Due to the limited time of the rebuttal period, we were only able to provide additional results on SSCBench-KITTI-360 [1], following the experimental protocol of GaussianFormer-2. The results are summarized in the table below.\n\n\n  - **Compared to previous dense voxel-based and sparse Gaussian-based methods, our method achieves comparable performance with much fewer scene primitives**. This highlights our method’s efficiency, as it is able to represent complex scenes with fewer expressive superquadrics without sacrificing much accuracy.\n\n\n  - **We would like to clarify a key difference with GaussianFormer-2, which employs a heavy depth backbone to initialize Gaussians for improved performance**. While this strategy can yield better results, it comes at the cost of significantly reduced efficiency (i.e., high inference latency and memory usage), as evidenced by Table 2 in the paper. In contrast, to preserve the efficiency advantage of our method, we did not incorporate such a heavy depth-initialized module.\n\n  - These results demonstrate both the effectiveness and the efficiency of our approach. We hope this addresses your concerns and further highlights the practical advantages of our method.\n\n  - **Due to the limited time during the rebuttal period, we only conducted the experiments with 12800 superquadrics on SSCBench-KITTI-360. We will provide more experiments on Occ3D and SSCBench-KITTI-360 later**.\n\n  |        Method        | Input Modality |   Number of Primitives   |  IoU  | mIoU  |\n  | :------------------: | :------------: | :----------------------: | :---: | :---: |\n  |     LMSCNet [2]      |     LiDAR      |            -             | 47.53 | 13.65 |\n  |      SSCNet [3]      |     LiDAR      |            -             | 53.58 | 16.95 |\n  |    MonoScene [4]     |     Camera     |   262144  (128x128x16)   | 37.87 | 12.31 |\n  |    Voxformer [5]     |     Camera     |   262144  (128x128x16)   | 38.76 | 11.91 |\n  |    TPVFormer [6]     |     Camera     | 81920 (256x256+256x32x2) | 40.22 | 13.64 |\n  |    OccFormer [7]     |     Camera     |   262144  (128x128x16)   | 40.27 | 13.81 |\n  |  GaussianFormer [8]  |     Camera     |          38400           | 35.38 | 12.92 |\n  | GaussianFormer-2 [9] |     Camera     |          38400           | 38.37 | 13.90 |\n  |       **Ours**       |     Camera     |        **12800**         | 36.81 | 12.86 |\n\n- **Evaluation metrics:** \n  - While SparseOcc [10] introduced the RayIoU metric, the majority of recent and leading works on the SSCBench-KITTI-360 continue to report results primarily with mIoU and IoU as evaluation metrics. Therefore, for consistency and comparability with prior art, we continue to evaluate our model using these established metrics.\n  - Nevertheless, we acknowledge the value of more comprehensive evaluation. In future work, we will conduct additional experiments on the Occ3D dataset and adopt metrics such as RayIoU to enable a more thorough comparison with more recent occupancy prediction methods.\n\n**References**\n\n[1] SSCBench: A Large-Scale 3D Semantic Scene Completion Benchmark for Autonomous Driving, IROS 2024.\n\n[2] LMSCNet: Lightweight Multiscale 3D Semantic Completion, 3DV 2020.\n\n[3] Semantic Scene Completion From a Single Depth Image, CVPR 2017.\n\n[4] MonoScene: Monocular 3D Semantic Scene Completion, CVPR 2022.\n\n[5] VoxFormer: Sparse Voxel Transformer for Camera-Based 3D Semantic Scene Completion, CVPR 2023.\n\n[6] Tri-Perspective View for Vision-Based 3D Semantic Occupancy Prediction, CVPR 2023.\n\n[7] OccFormer: Dual-path Transformer for Vision-based 3D Semantic Occupancy Prediction, ICCV 2023.\n\n[8] GaussianFormer: Scene as Gaussians for Vision-Based 3D Semantic Occupancy Prediction, ECCV 2024.\n\n[9] GaussianFormer-2: Probabilistic Gaussian Superposition for Efficient 3D Occupancy Prediction, CVPR 2025.\n\n[10] Fully Sparse 3D Occupancy Prediction, ECCV 2024."}, {"review_id": "dRV3ux3HxH", "reviewer": "Reviewer_VvnD", "summary": "This paper introduces a novel method for 3D occupancy prediction that leverages superquadrics as a more efficient and expressive scene representation compared to traditional voxels or Gaussians. The core motivation is that the greater representative power of superquadrics allows them to model fine-grained scene geometry with fewer primitives, thereby reducing computational requirements. The authors propose a probabilistic superquadric mixture model, where each superquadric defines an occupancy probability distribution. This is integrated into a query-based network, QuadricFormer, which features a pruning-and-splitting module for efficient prediction. The method reports state-of-the-art (SOTA) results on the nuScenes dataset while demonstrating superior computational efficiency.", "questions": "I already included all questions in Strengths And Weaknesses section. \n\nOverall, while this paper introduces a compelling and novel approach by leveraging superquadrics for efficient 3D occupancy prediction, its central claim -- that the observed gains stem directly from the superior representational power of superquadrics -- is not yet fully substantiated. The primary concern is that the performance and efficiency improvements may originate from the QuadricFormer architecture and its aggressive pruning module rather than the choice of primitive itself, a suspicion reinforced by qualitative results (Figs. 1 & 4) where the advertised \"deforming\" capability of superquadrics is not apparent. They often appear as simple, large-scale cuboids rather than adaptively capturing fine-grained geometric details. To resolve this, the authors should replace superquadrics with Gaussians within the same architectural framework is essential. The authors should provide new visualizations that offer close-up, side-by-side comparisons of a geometrically complex object (e.g., a vehicle, a traffic sign, or a building corner) as reconstructed by your method versus a Gaussian-based method. This direct comparison would make any superior detail-capturing ability immediately apparent. Finally, adjust the table to have fairer SOTA comparisons and evaluate on an additional dataset like SSCBench as in GaussianFormer2.", "limitations": "yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "# Strengths\n\n- The paper is well-written and effectively illustrated. Figures 1, 2, and 3 are particularly helpful for building intuition, clarifying the differences between primitives, and explaining the method's architecture.\n\n- While superquadrics have been explored for object-centric and indoor scene modeling, this paper presents a novel and timely application to the challenging domain of 3D occupancy prediction for autonomous driving.\n\n- The central narrative -- that the superior representational capacity of superquadrics enables more efficient scene modeling by requiring fewer primitives -- is clearly articulated and consistently woven throughout the paper, making the motivation and design choices easy to follow.\n\n\n# Weaknesses and Questions\n- The paper's central argument is that superquadrics are inherently more efficient due to their expressive power. However, the evidence does not fully substantiate this claim. A key concern is that the observed reduction in primitives may stem more from the aggressive pruning-and-splitting module rather than the intrinsic properties of superquadrics. It is unclear if a similar architecture using Gaussians with the same pruning strategy would also achieve a comparable reduction in primitives.\n    \n    - Suggestion: To isolate the benefit of superquadrics, please replace the superquadrics in QuadricFormer with Gaussians, keeping the rest of the architecture (including the pruning module, query design, and training strategy) as identical as possible. This would directly test whether the representational choice itself is the primary driver of the efficiency gains.\n        \n- While the qualitative results in Figures 1 and 4 are visually appealing, they do not strongly demonstrate the claimed advantage of superquadrics in capturing fine-grained geometric details. The rendered superquadrics often appear as simple cuboids, quite similar in shape to what Gaussians would produce, just at a larger scale. The \"deforming\" capability that gives superquadrics their power (e.g., creating boxier or more cylindrical shapes) is not apparent. They do not seem to wrap around object corners or capture complex surfaces any better than their Gaussian counterparts in the visualizations provided. This weakens the core motivation of the paper.\n    - Suggestion: Please provide more detailed visualizations that highlight the advantages of superquadrics in capturing fine-grained geometric details.\n    \n- The evaluation is currently limited to the nuScenes dataset. To demonstrate the generalizability and robustness of the proposed method, it is crucial to include results on other standard benchmarks for this task.\n    \n    - Suggestion: Please add results on SemanticKITTI and/or SSCBench-KITTI-360. Given that recent works like GaussianFormer-2 also report on SSCBench.\n        \n- Table 2 presents a confusing picture regarding efficiency. A superquadric contains more parameters than a Gaussian (e.g., shape parameters in addition to pose and scale). Therefore, it is counter-intuitive that a model with N superquadrics would be faster and require less memory than a model with N Gaussians, as the table seems to imply.\n    \n    - Suggestion: Please clarify this by augmenting Table 2. It would be very helpful to include columns that distinguish between network parameters and primitive parameters, and to explicitly state the number of primitives used in each configuration being compared. This would help readers understand the true source of the efficiency gains.\n        \n- The comparison with GaussianFormer-2 appears to be against a weaker variant (Ch=128, mIoU=20.02) rather than its best-performing published model (Ch=192, mIoU=20.82), which has a higher mIoU than the proposed method.\n    \n    - Suggestion: For a fair and transparent comparison, the paper should include the strongest published version of prior works. \n\n\n- Several key hyperparameters are missing. Please specify:\n    - The initial number of quadrics before the pruning-and-splitting stage.\n    - The value of B, the number of blocks in the decoder (line 209). It is also unclear what a \"block\" refers to in this context.\n    - The definition of \"small-scale\" and \"large-scale\" quadrics used for the pruning criteria (line 207).\n        \n- Recent relevant LiDAR-based methods are missing: PaSCo (CVPR'24), SCPNet (CVPR'23), and CAL (ICML'25).", "was_revised": true, "final_justification": "The authors have convincingly addressed all my concerns, and in my view, have also adequately responded to those raised by other reviewers.\n\nThis work introduces the use of superquadrics as a novel representation for 3D occupancy prediction in urban environments, while prior work only focused only on indoor scenes. The application to complex urban settings is both non-trivial and novel. The response clearly demonstrates that the observed performance gains are attributable to the use of superquadrics rather than auxiliary architectural components such as the pruning-and-splitting module. Notably, the method does not require depth initialization, which is a significant practical advantage.\n\nThe proposed approach achieves performance on par or better than recent SOTA models such as GaussianFormer-2, while operating under fewer constraints (i.e., no depth init). The improvements on large object classes (e.g., road surfaces) are particularly compelling, as shown in Tab. 1 on nuScenes. As the authors note, and I agree, modeling large flat surfaces with Gaussians is inefficient, whereas superquadrics (e.g., cuboids) offer a much more compact and interpretable representation. \n\nRegarding benchmark selection, I find the evaluation strategy reasonable. The authors follow the standards established by recent leading works (e.g., TPVFormer, SurroundOcc, GaussianFormer). Given the concurrent release of Occ-3D and SurroundOcc, I do not find sufficient justification for requiring both benchmarks, especially when one is already widely accepted in the community.\n\nThe clarifications on the pruning-and-splitting module are now clear, and any needed refinements appear minor.\n\nFinally, I disagree with reviewer #uPb2’s claim that the idea lacks impact. Demonstrating that superquadrics can be effectively applied to urban 3D occupancy prediction, with competitive results and practical benefits, is a meaningful contribution. Research impact should not be measured only by numerical performance but also by the novelty, practicality, and potential for future extensions.\n\nIn conclusion, the paper presents a novel idea, strong empirical evidence, and sound motivation. I recommend acceptance.", "rebuttal": "We thank the reviewer for the constructive comments and positive feedback on our paper. Regarding the concerns of the reviewer GNa2, we provide the following responses.\n\n> **W&Q1: A key concern is that the observed reduction in primitives may stem more from the aggressive pruning-and-splitting module rather than the intrinsic properties of superquadrics.**\n\n- Thanks for your valuable suggestion! To directly evaluate the advantage of superquadrics, we performed an ablation experiment where we replaced the superquadrics in QuadricFormer (with 1,600 primitives) with Gaussians, while keeping all other aspects of the model exactly the same. \n\n- The results in the table below show that the Gaussian-based model achieves much lower performance. This is because, without a heavy depth backbone and with a limited number of primitives, the Gaussian-based method cannot model the scene as effectively as superquadrics. In contrast, the superquadric-based approach maintains strong performance and efficiency.\n\n- These results demonstrate that the core improvements in performance and efficiency stem from the intrinsic representational power of superquadrics, rather than from architectural choices or the pruning strategy alone. We have included these findings in the revised manuscript for greater clarity. Thank you for prompting us to further validate this important point.\n\n|       Method       | Depth-Initialization | Pruning & Splitting | Latency (ms) | Memory (MB) |  IoU  | mIoU  |\n| :----------------: | :------------------: | :-----------------: | :----------: | :---------: | :---: | :---: |\n|   Gaussian-based   |          ✔           |          ✘          |     341      |    3075     | 28.99 | 18.73 |\n|   Gaussian-based   |          ✘           |          ✔          |     162      |    2554     | 29.31 | 18.91 |\n| Superquadric-based |          ✘           |          ✔          |     162      |    2554     | 30.71 | 20.04 |\n\n> **W&Q2: The rendered superquadrics often appear as simple cuboids, quite similar in shape to what Gaussians would produce, just at a larger scale. They do not seem to wrap around object corners or capture complex surfaces any better than their Gaussian counterparts in the visualizations provided.**\n\n- Thanks for your insightful suggestion. We acknowledge that superquadrics cannot capture precise object boundaries or highly complex surfaces in the occupancy prediction task. This is because the task uses 0.5-meter voxel labels, which only represent approximate object geometry rather than detailed surfaces. \n\n- However, superquadrics do possess clear advantages over Gaussians in modeling typical scene structures. For example, modeling large flat regions (such as road surfaces) would require many overlapping Gaussian ellipsoids, whereas only a small number of cuboid superquadrics are needed. \n\n- While images cannot be included in the NIPS rebuttal, we have added more detailed visualizations in the revised manuscript to better demonstrate the structural advantages of superquadrics in capturing geometric details within the limitations of current occupancy benchmarks.\n\n\n> **W&Q3: The evaluation is currently limited to the nuScenes dataset. To demonstrate the generalizability and robustness of the proposed method, it is crucial to include results on other standard benchmarks for this task.**\n\n- In response to the reviewer’s concerns about robustness and generalizability of our method, we have conducted additional experiments on the SSCBench-KITTI-360 [1] dataset. The results are summarized in the table below.\n\n\n- **Compared to previous dense voxel-based and sparse Gaussian-based methods, our method achieves comparable performance with much fewer scene primitives**. This highlights the efficiency of our method, as it can represent complex scenes with fewer expressive superquadrics without sacrificing much accuracy.\n\n\n- **We would like to clarify a key difference with GaussianFormer-2, which employs a heavy depth backbone to initialize Gaussians for improved performance**. While this strategy can yield better results, it comes at the cost of significantly reduced efficiency (i.e., high inference latency and memory usage), as evidenced by Table 2 in the paper. In contrast, to preserve the efficiency advantage of our method, we did not incorporate such a heavy depth-initialized module.\n\n- These results demonstrate both the effectiveness and the efficiency of our approach. We hope this addresses your concerns and further highlights the practical advantages of our method.\n\n- **Due to the limited time during the rebuttal period, we only conducted the experiments with 12800 superquadrics on SSCBench-KITTI-360. We will provide more experiments on Occ3D and SSCBench-KITTI-360 later**.\n\n|        Method        | Input Modality |   Number of Primitives   |  IoU  | mIoU  |\n| :------------------: | :------------: | :----------------------: | :---: | :---: |\n|     LMSCNet [2]      |     LiDAR      |            -             | 47.53 | 13.65 |\n|      SSCNet [3]      |     LiDAR      |            -             | 53.58 | 16.95 |\n|    MonoScene [4]     |     Camera     |   262144  (128x128x16)   | 37.87 | 12.31 |\n|    Voxformer [5]     |     Camera     |   262144  (128x128x16)   | 38.76 | 11.91 |\n|    TPVFormer [6]     |     Camera     | 81920 (256x256+256x32x2) | 40.22 | 13.64 |\n|    OccFormer [7]     |     Camera     |   262144  (128x128x16)   | 40.27 | 13.81 |\n|  GaussianFormer [8]  |     Camera     |          38400           | 35.38 | 12.92 |\n| GaussianFormer-2 [9] |     Camera     |          38400           | 38.37 | 13.90 |\n|       **Ours**       |     Camera     |        **12800**         | 36.81 | 12.86 |\n\n> **W&Q4: Table 2 presents a confusing picture regarding efficiency. It is counter-intuitive that a model with N superquadrics would be faster and require less memory than a model with N Gaussians, as the table seems to imply.**\n\n- The key reason for the efficiency difference is not the number of parameters per primitive, but rather the architectural choices. Specifically, **GaussianFormer-2 relies on a heavy depth backbone (ResNet-101) to initialize the Gaussians, which becomes the main bottleneck for inference speed and memory usage**. In contrast, QuadricFormer adopts cost-free random initialization for the superquadrics, which substantially reduces the computational and memory overhead.\n\n- We appreciate your suggestion, which helped us improve Table 2 to avoid any confusion. In the revised table, we have now indicated whether depth-backbone-based initialization is used and provided model parameters, making it clear where the efficiency gains originate.\n\n\n> **W&Q5: The comparison with GaussianFormer-2 appears to be against a weaker variant (Ch=128, mIoU=20.02) rather than its best-performing published model (Ch=192, mIoU=20.82), which has a higher mIoU than the proposed method.**\n\n- Thanks for your suggestion. **In Table 1, we only reported the results of GaussianFormer-2 (Ch=128, mIoU=20.02) with a feature dimension of 128 to ensure a fair comparison, since our method is under the same setting**. However, we agree that the best results should also be included to provide a more complete picture. In the revised version, we have added the strongest results of GaussianFormer-2 (Ch=192, mIoU=20.82) and clarified this in the manuscript. \n\n- Notably, even when compared with the best configuration of GaussianFormer-2, our QuadricFormer (with 12,800 superquadrics) still achieves superior performance with clear efficiency advantages. We appreciate your suggestion, which has improved the completeness and transparency of our experimental comparisons.\n\n\n> **W&Q6: Several key hyperparameters are missing.**\n\nThanks for your detailed comments and suggestions. We address your questions as follows:\n\n1. **Number of Quadrics before Pruning-and-Splitting:** The number of superquadrics remains unchanged before and after the pruning-and-splitting stage, since each pruned superquadric is replaced by a newly added one.\n2. **Definition of a Block and Value of B in the Decoder:** A \"quadric-encoder block\" refers to a module that consists of a sparse convolutional layer, a cross-attention layer, and a residual update layer. Our model employs $B=4$ blocks to encode superquadrics.\n3. **Small-scale and Large-scale Quadrics:** The distinction between small-scale and large-scale superquadrics is determined by the product of their scale values. More details can be found in our general response (GR3).\n\nWe appreciate your valuable suggestions. We will include these clarifications in the revised version of our manuscript.\n\n> **W&Q7: Recent relevant LiDAR-based methods are missing: PaSCo (CVPR'24), SCPNet (CVPR'23), and CAL (ICML'25).**\n\n- Thanks for your suggestion. We will include these works and discuss them in the revised version of our paper.\n\n**References**\n\n[1] SSCBench: A Large-Scale 3D Semantic Scene Completion Benchmark for Autonomous Driving, IROS 2024.\n\n[2] LMSCNet: Lightweight Multiscale 3D Semantic Completion, 3DV 2020.\n\n[3] Semantic Scene Completion From a Single Depth Image, CVPR 2017.\n\n[4] MonoScene: Monocular 3D Semantic Scene Completion, CVPR 2022.\n\n[5] VoxFormer: Sparse Voxel Transformer for Camera-Based 3D Semantic Scene Completion, CVPR 2023.\n\n[6] Tri-Perspective View for Vision-Based 3D Semantic Occupancy Prediction, CVPR 2023.\n\n[7] OccFormer: Dual-path Transformer for Vision-based 3D Semantic Occupancy Prediction, ICCV 2023.\n\n[8] GaussianFormer: Scene as Gaussians for Vision-Based 3D Semantic Occupancy Prediction, ECCV 2024.\n\n[9] GaussianFormer-2: Probabilistic Gaussian Superposition for Efficient 3D Occupancy Prediction, CVPR 2025."}]

Author rebuttal:

Meta-review: The paper introduces a method for 3D occupancy prediction using superquadrics as a scene geometry representation in urban environments. It demonstrates that superquadrics can model complex scene structures with significantly fewer primitives compared to traditional dense voxels or Gaussian primitives.

The paper received one accept, three borderline accepts, and one borderline reject. All reviewers noted that (a) the method is novel, and (b) the experiments show superior performance while substantially reducing computational cost and memory usage compared to prior methods. The main weakness, raised by the negative reviewer (uPb2), was the lack of exhaustive comparisons with other methods discussed during the author–reviewer exchange. In response, reviewer VvnD argued during the AC-reviewer discussion:
"While I agree with reviewer uPb2 that SOTA results on Occ3D would be valuable, their absence doesn't diminish this paper's scientific contribution. The main contribution is demonstrating superquadrics' benefits over Gaussians and voxels. Achieving SOTA often requires dataset-specific engineering tricks that obscure core methodological contributions. Additionally, I think requiring every paper to beat SOTA is bad as it shifts focus from fundamental insights to incremental optimizations."

The AC agrees with this perspective: the novelty of the method should be valued over incremental SOTA improvements. Accordingly, the AC recommends acceptance. Still, the authors are strongly encouraged to address uPb2’s concerns and carefully consider all reviewer feedback from both the reviews and the author-reviewer discussion when preparing the final version of the paper!
Decision: Accept (poster)