SuperDec: 3D Scene Decomposition with Superquadric Primitives (2504.00992v1)

Abstract: We present SuperDec, an approach for creating compact 3D scene representations via decomposition into superquadric primitives. While most recent works leverage geometric primitives to obtain photorealistic 3D scene representations, we propose to leverage them to obtain a compact yet expressive representation. We propose to solve the problem locally on individual objects and leverage the capabilities of instance segmentation methods to scale our solution to full 3D scenes. In doing that, we design a new architecture which efficiently decompose point clouds of arbitrary objects in a compact set of superquadrics. We train our architecture on ShapeNet and we prove its generalization capabilities on object instances extracted from the ScanNet++ dataset as well as on full Replica scenes. Finally, we show how a compact representation based on superquadrics can be useful for a diverse range of downstream applications, including robotic tasks and controllable visual content generation and editing.

SuperDec: A Compact 3D Scene Representation with Superquadric Primitives

The research paper titled "SuperDec: 3D Scene Decomposition with Superquadric Primitives" presents a novel approach for creating efficient and compact 3D scene representations through decomposition into superquadric primitives. This method addresses a key limitation of existing 3D scene reconstruction techniques, which often offer high photorealism but at the cost of high memory requirements and limited geometric interpretability. SuperDec proposes a lighter and more geometrically precise representation by breaking down the input point cloud into a set of explicit superquadric primitives.

Methodology

SuperDec operates by solving the decomposition problem locally at the object level before scaling to entire scenes. The framework integrates a new neural architecture designed to decompose point clouds of arbitrary objects into superquadrics. This architecture is trained using ShapeNet and demonstrates generalizability on instances extracted from datasets such as ScanNet++ and Replica, thereby illustrating its flexibility across different domains.

The core of SuperDec's methodology involves a Transformer-based neural network. The network predicts parameters for superquadric shapes and assigns points from the input cloud to these predicted superquadrics through a segmentation matrix. Subsequently, a refinement step employing the Levenberg-Marquardt optimization further optimizes the superquadric parameters concerning the input data. This process allows SuperDec to efficiently model complex shapes with a minimal set of geometric primitives.

Experimental Results

Quantitative evaluation demonstrates SuperDec's superiority over previous state-of-the-art methods, significantly reducing L2 errors while needing fewer primitives for similar objects. On the ShapeNet dataset, it achieves a six-fold reduction in errors compared to prior approaches with almost half the number of primitives. Comparative studies on real-world data from ScanNet++ further support its robust generalization capabilities despite real-world complexities such as noise and incomplete observations.

In deploying SuperDec to full 3D scenes, instance segmentation techniques are utilized to extract object instances, enabling scene-level representations. Evaluations on Replica reveal the framework's competency in real-world scene reconstruction tasks, maintaining accuracy under variable segmentation boundaries and characteristics.

Applications and Implications

Beyond 3D scene representation, SuperDec's compact representations find utility in various downstream applications. These include robotics tasks like path planning and grasping, where spatial efficiency and accuracy are crucial. SuperDec allows for effective path planning through accurate collision detection and potential memory savings, compared to dense point clouds and voxel grids.

Moreover, SuperDec can contribute to controllable image generation powered by text-to-image diffusion models. By influencing the spatial arrangement of superquadrics, it enables both spatial and semantic control over generated visuals, thus offering a means to integrate geometric priors into AI-driven generative models.

Theoretical and Practical Implications

Theoretically, SuperDec contributes to 3D reconstruction's evolving landscape by shifting the focus towards compact and interpretable representations. Its successful implementation paves the way for future research on leveraging primitive-based decompositions in higher-level scene understanding and reasoning tasks. Practically, its application in robotics and visual content generation underscores its versatility and potential for impacting real-world scenarios, especially those necessitating efficient and robust 3D data handling.

Conclusion

In summary, SuperDec demonstrates a cohesive framework for creating efficient, expressive 3D scene representations through superquadric decompositions. By achieving a balance between compactness, interpretability, and reconstruction accuracy, it sets a new benchmark for future work in 3D scene modeling. Further exploration could enhance its application scope, including integration with open-vocabulary tasks in AI, thereby expanding its utility in AI-driven environments.