3D Shape Tokenization via Latent Flow Matching (2412.15618v3)

Abstract: We introduce a latent 3D representation that models 3D surfaces as probability density functions in 3D, i.e., p(x,y,z), with flow-matching. Our representation is specifically designed for consumption by machine learning models, offering continuity and compactness by construction while requiring only point clouds and minimal data preprocessing. Despite being a data-driven method, our use of flow matching in the 3D space enables interesting geometry properties, including the capabilities to perform zero-shot estimation of surface normal and deformation field. We evaluate with several machine learning tasks, including 3D-CLIP, unconditional generative models, single-image conditioned generative model, and intersection-point estimation. Across all experiments, our models achieve competitive performance to existing baselines, while requiring less preprocessing and auxiliary information from training data.

• The paper introduces Shape Tokens as a novel method for compactly encoding 3D shapes using probability density functions with minimal assumptions.
• The approach leverages flow-matching generative models trained on surface-sampled points to achieve high fidelity reconstructions with reduced latent dimensions.
• Empirical results on datasets like ShapeNet and Objaverse show competitive chamfer distance performance and versatility in tasks such as 3D generation and text-3D alignment.

Analysis of "3D Shape Tokenization" Paper

The paper presents a novel approach called Shape Tokens (ST) for 3D shape representation in learning systems. This method introduces a continuous, compact representation, leveraging flow matching models to encode shape information effectively for machine learning tasks. It addresses a key challenge in determining suitable representations for 3D shapes in computational and memory-constrained environments without relying heavily on assumptions like watertightness or volumetric rendering.

Core Methodology

Shape Tokens model 3D shapes as probability density functions, which are concentrated on the surfaces of the shapes. The method utilizes a flow-matching generative model to learn these representations by training on points sampled from the shapes' surfaces. The key idea is to treat these shapes as 3D delta functions and encode them into a set of real-valued vectors, termed Shape Tokens. The paper demonstrates that these tokens can serve as effective latents or features for various downstream tasks, such as shape generation, text-3D alignment, and neural rendering.

Key Features and Advantages

1. Compact Representation: Shape Tokens represent diverse 3D shapes using a continuous and compact format of 1,024 vectors, each with 16 dimensions, which significantly reduces the data footprint required for 3D tasks while maintaining high fidelity.
2. Minimal Assumptions: The approach assumes only the ability to sample points from 3D shapes, unlike many existing methods that require complex preprocessing to convert 3D shapes into specific formats.
3. Data Efficiency: Shape Tokens are trained using point clouds alone, bypassing the need for complex data formats like meshes or signed distance functions. This facilitates scalability and broader applicability across datasets where meshes are not pre-processed for such representations.
4. Geometric Analysis Capabilities: The framework includes robust tools for analyzing geometric properties, such as surface normals and deformation fields, providing deeper insight into the shape's structure beyond mere visual reconstruction.

Empirical Evaluation

The paper empirically validates Shape Tokens on several datasets, including ShapeNet and Objaverse. Across all evaluated tasks, from shape generation (unconditional and single-image-to-3D) to 3D CLIP alignment and neural rendering, Shape Tokens exhibit competitive or superior performance compared to existing baselines. Notably, they match or exceed the chamfer distance accuracy of alternatives while using drastically fewer dimensions. This hints at the potential for Shape Tokens to become a generalized representation for diverse machine learning tasks involving 3D data.

In particular, the ShapeNet results show a chamfer distance improvement at lower latent dimensions compared to PointFlow and LION, validating the model’s efficiency and effectiveness in reconstructing high-fidelity shapes. When applied to tasks like zero-shot text classification, Shape Tokens outperform several established models, hinting at their versatility.

Implications and Future Work

The Shape Tokens concept offers practical benefits such as reduced computational overheads and simplified data processing pipelines. Theoretically, it presents a bridge between differential geometry-based methods and modern generative models. Future work could explore integrating color or texture information into Shape Tokens, further optimize sampling times, and adapt advanced techniques from diffusion models to enhance performance efficiency.

Conclusion

The paper successfully introduces Shape Tokens as an efficient and versatile framework for handling 3D shapes within machine learning contexts. With its minimal assumptions, high fidelity, and strong task performance, this method has the potential to streamline processes in various practical applications and inspire future research in 3D generative modeling and representation learning.