SuperDec: 3D Scene Decomposition with Superquadric Primitives

Over the past decade, 3D scene understanding has evolved from simple point cloud processing to sophisticated neural implicit models like NeRF and Gaussian Splatting, which produce photorealistic reconstructions. However, these methods often require significant memory and lack explicit geometric interpretability. Geometric primitives such as cuboids and superquadrics have been explored for their interpretability and compactness, but existing approaches are either category-specific or computationally expensive. Recent works like EMS and DBW attempted hierarchical fitting or scene-level optimization, but faced limitations in scalability and real-world applicability. The need for a universal, efficient, and interpretable scene representation remains pressing, especially for robotics and virtual content creation.

The core challenge is to develop a scene representation that balances geometric fidelity, interpretability, and computational efficiency. Existing methods either lack generalization across object categories, are too memory-intensive, or rely on complex optimization that hampers scalability. Achieving a category-agnostic, compact, and accurate geometric decomposition at scene scale is crucial for advancing applications in robotics, AR/VR, and content editing. The difficulty lies in designing a model that can learn shape priors, handle diverse geometries, and operate efficiently in real-world noisy scenarios.

SuperDec introduces several key innovations:

1) Transformer-based prediction of superquadric parameters, enabling flexible and accurate shape modeling.

2) Integration of a self-supervised training scheme with combined loss functions, promoting sparsity and robustness.

3) Use of class-agnostic shape priors trained on synthetic data, allowing generalization to real scenes.

4) Extension to scene-level decomposition via Mask3D, capturing multiple objects simultaneously.

These innovations collectively enable a scalable, interpretable, and highly accurate scene decomposition framework, surpassing prior object-centric or optimization-heavy methods.

• �� Input: raw point cloud of an object or scene.
• �� Feature extraction: use PVCNN encoder to obtain rich point features.
• �� Primitive prediction: Transformer decoder outputs parameters for P superquadrics (shape, pose, existence).
• �� Point assignment: soft segmentation matrix assigns points to primitives.
• �� Loss computation: combines reconstruction (Chamfer distance), sparsity (parsimony), and existence (binary cross-entropy).
• �� Optimization: Levenberg–Marquardt algorithm refines primitive parameters iteratively.
• �� Scene extension: apply object-level predictions to all instances detected by Mask3D, rescale, and assemble scene representation.

This pipeline enables end-to-end training and scalable scene understanding.

The model was trained on ShapeNet with 13 classes, using 4096 sampled points per object, P=16 primitives, and hyperparameters tuned for convergence. Evaluation involved quantitative metrics like L1 and L2 Chamfer distances, primitives count, and qualitative visualizations. Comparisons with EMS, CSA, and SQ demonstrated significant improvements. Cross-dataset tests on ScanNet++ and Replica validated generalization. Ablation studies confirmed the importance of each component, especially the shape prior and optimization step. The experiments also included robotic path planning and grasping tasks, where the compact primitives facilitated efficient computation and high success rates.

SuperDec achieved a sixfold reduction in L2 error over previous methods on ShapeNet, with primitives count halved. On real-world datasets, it maintained superior accuracy despite noisy and partial data. In robotic applications, it reduced memory usage by up to 50% and improved path success rates over 90%. The scene-level decomposition effectively captured complex geometries, enabling downstream tasks like scene editing and content generation with high fidelity. These results demonstrate both the technical robustness and practical utility of the approach.

The compact scene representation benefits robotics (path planning, grasping), virtual scene editing, and content creation. Its efficiency allows deployment on resource-constrained devices, supporting real-time applications. The interpretability of primitives facilitates human-in-the-loop editing and semantic understanding. Long-term, integrating semantic labels and dynamic scene modeling could revolutionize autonomous navigation and immersive environments.

Current superquadric primitives have limited capacity to model highly detailed or irregular geometries, especially under occlusion or noise. Dependence on accurate instance segmentation affects overall performance; failures propagate to scene decomposition. Computational costs, though reduced, still pose challenges for real-time large-scale scene processing. Future work should focus on enhancing primitive expressiveness, reducing reliance on segmentation accuracy, and optimizing runtime.