SuperQuadricOcc: Multi-Layer Gaussian Approximation of Superquadrics for Real-Time Self-Supervised Occupancy Estimation

TL;DR

The paper addresses real-time semantic occupancy estimation for automated driving by replacing dense Gaussian primitives with a compact, expressive superquadric representation. It introduces SuperQuadricOcc, which uses a multi-layer Gaussian approximation to supervise superquadrics during training and a dedicated voxelization path for real-time inference. On Occ3D-nuScenes and OpenOcc benchmarks, it achieves a 5.9% improvement in mIoU while reducing primitive count by 84% and memory by 75%, and runs at 21.5 FPS. This work demonstrates the practical viability of superquadrics for scalable, real-time 3D scene understanding and opens avenues for temporal extensions and NeRF-based rendering comparisons.

Abstract

Semantic occupancy estimation enables comprehensive scene understanding for automated driving, providing dense spatial and semantic information essential for perception and planning. While Gaussian representations have been widely adopted in self-supervised occupancy estimation, the deployment of a large number of Gaussian primitives drastically increases memory requirements and is not suitable for real-time inference. In contrast, superquadrics permit reduced primitive count and lower memory requirements due to their diverse shape set. However, implementation into a self-supervised occupancy model is nontrivial due to the absence of a superquadric rasterizer to enable model supervision. Our proposed method, SuperQuadricOcc, employs a superquadric-based scene representation. By leveraging a multi-layer icosphere-tessellated Gaussian approximation of superquadrics, we enable Gaussian rasterization for supervision during training. On the Occ3D dataset, SuperQuadricOcc achieves a 75% reduction in memory footprint, 124% faster inference, and a 5.9% improvement in mIoU compared to previous Gaussian-based methods, without the use of temporal labels. To our knowledge, this is the first occupancy model to enable real-time inference while maintaining competitive performance. The use of superquadrics reduces the number of primitives required for scene modeling by 84% relative to Gaussian-based approaches. Finally, evaluation against prior methods is facilitated by our fast superquadric voxelization module. The code will be made available at https://github.com/seamie6/SuperQuadricOcc.

Figures (7)

• Figure 1: Comparison of GaussianFlowOcc boeder2025gaussianflowocc and our model, SuperQuadricOcc: Replacing Gaussians with superquadrics enables more efficient scene modeling through a sparser and more expressive representation. Our method achieves higher mIoU, faster inference, and lower memory consumption with significantly fewer primitives. Ground truth is provided in Figure \ref{['fig:vis_voxel']}.
• Figure 2: Architecture of SuperQuadricOcc: The model extracts image features and refines learnable superquadric features and means in the Transformer Network, similar to GaussianFlowOcc boeder2025gaussianflowocc. The MLP prediction heads estimate the remaining superquadric properties: $\{\boldsymbol{s}, \sigma, \boldsymbol{c}, \varepsilon_1, \varepsilon_2\}$. During training, the SuperQuadric to Gaussian Module generates a multi-layer Gaussian approximation per superquadric for rendered supervision, while during inference, the SuperQuadric Voxelizer efficiently produces voxel labels for evaluation.
• Figure 3: SuperQuadric and Gaussian Distribution: 2D slice showing a superquadric density and its Gaussian approximation from the superquadric-to-Gaussian module. Parameters: $\boldsymbol{s}=(1.0, 0.7, 0.5)$, $\varepsilon_1=0.6$, $\varepsilon_2=0.7$, $K \subset [0.5, 2.5]$.
• Figure 4: Visualization of Primitives and Voxel Estimation: Comparison between SuperQuadricOcc and the 10,000- and 1600-GaussianFlowOcc models on the Occ3D-nuScenes dataset tian2023occ3d for sample tokens edde57e6dfeb416e936d9056824b8253 and 135bf33890ba4ca2984a931444923eda.
• Figure 5: Additional Visualizations: Images, predicted semantic occupancy, superquadric primitives, and ground truth voxels visualized. For sample tokens 43cfc03be6f842ae8942c995f8e3f2fb. 997e5e6c149d4bbcb3c210335f901c3d. d21bdffbca9f4edaa4bf4f54fffa6f4b. 6b10154e2b3146ab85b43f3cfe053d6d.