AtlasNet: A Papier-Mâché Approach to Learning 3D Surface Generation

Abstract: We introduce a method for learning to generate the surface of 3D shapes. Our approach represents a 3D shape as a collection of parametric surface elements and, in contrast to methods generating voxel grids or point clouds, naturally infers a surface representation of the shape. Beyond its novelty, our new shape generation framework, AtlasNet, comes with significant advantages, such as improved precision and generalization capabilities, and the possibility to generate a shape of arbitrary resolution without memory issues. We demonstrate these benefits and compare to strong baselines on the ShapeNet benchmark for two applications: (i) auto-encoding shapes, and (ii) single-view reconstruction from a still image. We also provide results showing its potential for other applications, such as morphing, parametrization, super-resolution, matching, and co-segmentation.

• The paper presents a novel method using learnable parameterizations to transform 2D patches into detailed 3D surface representations.
• The approach employs multiple MLP-based patches and minimizes Chamfer distance, outperforming traditional voxel and point cloud methods.
• AtlasNet enables practical applications such as single-view reconstruction and shape interpolation, advancing efficient 3D modeling techniques.

Overview of AtlasNet: A Papier-Mâché Approach to Learning 3D Surface Generation

The paper "AtlasNet: A Papier-Mâché Approach to Learning 3D Surface Generation" introduces a novel framework for generating 3D surfaces with a specific emphasis on achieving high-quality and memory-efficient results. Unlike traditional voxel grids or point cloud methods, AtlasNet leverages a collection of parametric surface elements to infer a continuous and smooth surface representation of 3D shapes. This approach not only enhances precision and generalization capabilities but also facilitates the generation of shapes at arbitrary resolutions, circumventing memory constraints typically associated with high-resolution 3D shape generation.

Methodology

AtlasNet represents 3D shapes using a series of learnable parameterizations, essentially transforming 2D squares into 3D surface patches. These parameterizations are learned in such a way that, when combined, they form a continuous 2D manifold capable of representing detailed 3D surfaces. The fundamental aspects of this methodology include the following components:

1. Learnable Parametrizations: The core idea involves using multiple local parameterizations to map 2D points onto 3D surfaces. Each parameterization is modeled by a Multi-Layer Perceptron (MLP) with ReLU nonlinearities.
2. Surface Generation: By learning these mappings, the method ensures that each 2D point is accurately transformed into a corresponding point on the target 3D surface. Multiple such mappings (or patches) collectively represent complex 3D geometries.
3. Loss and Optimization: The learning process minimizes the Chamfer distance between generated and target point sets, ensuring high fidelity in surface reconstruction.

Applications and Experiments

AtlasNet's efficacy was rigorously tested through multiple applications:

1. Auto-Encoding 3D Shapes: AtlasNet was found to outperform traditional point cloud-based baselines in reconstructing 3D shapes from point clouds. The method demonstrated strong quantitative and qualitative results, preserving intricate details and generating high-resolution outputs.
2. Single-View Reconstruction: For the task of reconstructing 3D shapes from 2D images, AtlasNet exhibited superior performance compared to state-of-the-art methods, including voxel-based and point cloud-based approaches. The generated surfaces were more detailed and visually consistent with the input images.
3. Shape Interpolation and Correspondence: AtlasNet's latent space enables smooth interpolation between different shapes, facilitating applications such as morphing and shape interpolation. Moreover, the method inherently provides semantic correspondences across shapes, useful for tasks like mesh parameterization and co-segmentation.

Numerical Results

The performance of AtlasNet was validated through the ShapeNet benchmark and additional datasets. Key numerical outcomes include:

• Auto-Encoding: Demonstrated significant improvements in Chamfer distance and Metro distance over baseline methods, particularly when using multiple patches. For instance, AtlasNet with 25 patches achieved a Chamfer distance of 1.56 (x $10^{-3}$), outperforming the baseline's 1.91.
• Single-View Reconstruction: Compared to other methodologies like 3D-R2N2 and PointSetGen, AtlasNet consistently generated higher-quality meshes with a lower Chamfer distance, averaging 5.11 (x $10^{-3}$) over multiple categories.

Implications and Future Work

AtlasNet's approach to 3D surface generation has both practical and theoretical implications:

• Practical Implications: This method allows for the generation of highly detailed and high-resolution 3D shapes without significant memory overheads, a crucial advantage over voxel-based approaches. Similarly, the ability to generate a proper mesh directly reduces the need for post-processing steps, such as surface reconstruction from point clouds.
• Theoretical Implications: The framework establishes a novel way to think about 3D surface generation by approximating the target surface through local parameterizations. This perspective can influence future works in areas such as neural implicit representations and generative models for 3D data.

Future developments might explore the integration of global constraints to ensure patch continuity, thereby preventing issues such as overlapping or disconnected patches seen in some of the more complex geometries. Additionally, extending the method to handle real-world, densely cluttered 3D scenes or applying it to dynamic, deformable surfaces (e.g., human body poses) could yield interesting directions for further research.

In summary, AtlasNet provides a robust framework for generating high-quality 3D surfaces from point clouds and images. Its innovative use of learnable parameterizations offers both precision and efficiency, rendering it a valuable addition to the computational geometry and shape analysis toolkit.