Variational Autoencoders for Deforming 3D Mesh Models (1709.04307v3)

Abstract: 3D geometric contents are becoming increasingly popular. In this paper, we study the problem of analyzing deforming 3D meshes using deep neural networks. Deforming 3D meshes are flexible to represent 3D animation sequences as well as collections of objects of the same category, allowing diverse shapes with large-scale non-linear deformations. We propose a novel framework which we call mesh variational autoencoders (mesh VAE), to explore the probabilistic latent space of 3D surfaces. The framework is easy to train, and requires very few training examples. We also propose an extended model which allows flexibly adjusting the significance of different latent variables by altering the prior distribution. Extensive experiments demonstrate that our general framework is able to learn a reasonable representation for a collection of deformable shapes, and produce competitive results for a variety of applications, including shape generation, shape interpolation, shape space embedding and shape exploration, outperforming state-of-the-art methods.

• The paper introduces a mesh VAE framework that employs a rotation-invariant mesh difference representation to capture non-linear deformations in 3D meshes.
• It integrates a fully connected neural network architecture with MSE and KL divergence losses to efficiently encode and reconstruct mesh features.
• The study demonstrates the method's potential for shape synthesis, interpolation, and low-dimensional embedding, outperforming traditional CNN-based approaches.

Variational Autoencoders for Deforming 3D Mesh Models

The paper authored by Qingyang Tan et al. presents an innovative framework titled "mesh variational autoencoders" (mesh VAE), aimed at effectively analyzing and synthesizing deforming 3D mesh models. This proposed framework largely focuses on exploring the complex probabilistic latent space of 3D surfaces.

Summary

The importance of deforming 3D meshes lies in their versatile representation of 3D animation sequences and collections of objects within a single category. Such representations are invaluable in fields such as computer animation and graphics, primarily due to their support for large-scale non-linear deformations. Previous efforts in 3D shape analysis using convolutional neural networks (CNNs) primarily concentrated on the voxel or geometry image representations. While these methods provide a bridge for CNN applications in 3D scenarios, they often suffer from inefficiencies, such as high computational costs and loss of complex surface details due to voxel limitations and parameterization distortions respectively.

The proposed mesh VAE circumvents these limitations by using a rotation-invariant mesh difference (RIMD) representation, expertly combined with a variational autoencoder (VAE) framework. The RIMD representation is noted for its ability to maintain the integral structure of 3D shapes while being invariant to translation and rotation, making it particularly suitable for shape analysis.

Techniques and Methodologies

1. Feature Representation: The paper emphasizes the novel use of RIMD as a feature representation, incorporating deformation gradient computations and rotation invariance to capture significant geometric differences across mesh deformations.
2. Mesh VAE Architecture: A fully connected neural network structure forms the basis of the proposed architecture. This is complemented by an MSE-based reconstruction loss and a KL divergence loss for the VAE's probabilistic nature. The encoder encodes the preprocessed RIMD features, while the decoder reconstructs these features into plausible mesh representations based on sampled latent vectors.
3. Conditional Mesh VAE: By incorporating label conditions, the conditional mesh VAE enhances control over the output shape generation, allowing targeted syntheses aligned with specific characteristics within the dataset.
4. Extended Models for Low-Dimensional Embedding: Adjusting the latent space's variation through tunable parameters facilitates improved low-dimensional embedding, making it suitable for visualization and exploration of the shape space.

Applications and Implications

The authors demonstrate the framework's capabilities through applications such as shape generation, interpolation, and dimensionally reduced embedding. The mesh VAE offers an avenue to generate entirely new 3D shapes that, while plausible, do not exist in the original dataset. Additionally, the interpolation between varied mesh models translates into coherent deformation sequences that outperform traditional data-driven methods.

The potential for using the mesh VAE in shape embedding applications allows for effective low-dimensional mapping and visualization. This functionality is crucial for tasks such as shape exploration in large datasets, where users can navigate the latent space to identify desired shape attributes or forms.

Future Prospects

While current iterations of the mesh VAE are optimized for homogeneous mesh collections, future work could broaden its applicability. This encompasses advancing the model’s adaptability to handle diverse topologies or heterogeneous mesh datasets, thereby extending its utility across broader application domains such as virtual reality, medical imaging, and real-time 3D animation.

In conclusion, the paper significantly contributes to the domain of 3D model representation and synthesis by advocating a robust framework that leverages variational autoencoders, combined with invariant feature encoding, to overcome extant constraints in 3D shape analysis and synthesis.