Multi-chart Generative Surface Modeling (1806.02143v3)

Abstract: This paper introduces a 3D shape generative model based on deep neural networks. A new image-like (i.e., tensor) data representation for genus-zero 3D shapes is devised. It is based on the observation that complicated shapes can be well represented by multiple parameterizations (charts), each focusing on a different part of the shape. The new tensor data representation is used as input to Generative Adversarial Networks for the task of 3D shape generation. The 3D shape tensor representation is based on a multi-chart structure that enjoys a shape covering property and scale-translation rigidity. Scale-translation rigidity facilitates high quality 3D shape learning and guarantees unique reconstruction. The multi-chart structure uses as input a dataset of 3D shapes (with arbitrary connectivity) and a sparse correspondence between them. The output of our algorithm is a generative model that learns the shape distribution and is able to generate novel shapes, interpolate shapes, and explore the generated shape space. The effectiveness of the method is demonstrated for the task of anatomic shape generation including human body and bone (teeth) shape generation.

• The paper introduces a tensor-based multi-chart representation that enables effective use of standard convolutions for modeling complex 3D shapes.
• The paper establishes scale-translation rigidity to guarantee unique embeddings and high-fidelity 3D reconstructions from latent vectors.
• The paper adapts GAN architecture with modifications like periodic convolutions and symmetry layers to generate diverse and plausible 3D models.

Multi-chart Generative Surface Modeling

The research presented in "Multi-chart Generative Surface Modeling" addresses the challenge of developing effective generative models for 3D shapes, particularly focusing on genus-zero surfaces. Utilizing deep neural networks, the authors propose a new data representation for 3D shapes, facilitating efficient learning by leveraging Generative Adversarial Networks (GANs).

Overview

The paper introduces a method that uses a multi-chart structure for 3D surface representation. This approach involves multiple parameterizations or charts, each covering different parts of the shape, and collectively offering a comprehensive representation. The multi-chart system demonstrates properties including scale-translation rigidity, vital for reliable reconstruction from latent space vectors. The authors show this method's applicability in generating anatomical shapes like human bodies and bones (teeth).

Key Contributions

1. Tensor Representation: The authors devised a tensor-based data format that captures complex 3D shapes using a set of smooth, bijective, and conformal charts. These properties allow standard convolution operations usable in image data to be applied here.
2. Scale-Translation Rigidity: Ensuring that the multi-chart structure is scale-translation rigid guarantees a unique embedding and reconstruction of shapes, which is crucial for post-generation shape fidelity. Rigidity is backed by theoretical proofs, further establishing the model's robustness.
3. Generative Model using GAN: The research effectively adapts GANs, well-established for image generation, to operate on this novel multi-chart representation of 3D shapes. This adaptation includes architectural modifications such as periodic convolutions to respect topological properties and symmetry layers for ensuring consistency across chart copies.

Numerical Results

The authors demonstrate strong numerical performance with the method generating a diverse set of plausible human body models in various poses (1024 models). The approach compares favorably to existing baselines and previous approaches in 3D shape generation, showcasing its efficacy in preserving intricate details and achieving variety across generated instances.

Implications and Future Directions

This research has significant implications for applications requiring automatic content creation in computer graphics, such as in synthetic data generation for simulations and virtual environments. The theoretical guarantee of scale-translation rigidity further enhances its potential for robust physical simulations where topological consistency is critical.

For theoretical developments, exploring adaptations for shapes beyond genus-zero surfaces can expand the model's applicability. Future work may also delve into point cloud integration and more generalized shape reconstruction mechanisms without reliance on fixed templates. Additionally, incorporating conditional generation capabilities could enhance control over model outputs, catering to specific user requirements.

In summary, the paper proposes a substantial advancement in 3D shape generative modeling with practical utility and robust theoretical underpinnings. It sets a foundation for further exploration in multi-chart methods and their applications in AI-driven shape generation.