Dual Octree Graph Networks for Learning Adaptive Volumetric Shape Representations (2205.02825v2)

Abstract: We present an adaptive deep representation of volumetric fields of 3D shapes and an efficient approach to learn this deep representation for high-quality 3D shape reconstruction and auto-encoding. Our method encodes the volumetric field of a 3D shape with an adaptive feature volume organized by an octree and applies a compact multilayer perceptron network for mapping the features to the field value at each 3D position. An encoder-decoder network is designed to learn the adaptive feature volume based on the graph convolutions over the dual graph of octree nodes. The core of our network is a new graph convolution operator defined over a regular grid of features fused from irregular neighboring octree nodes at different levels, which not only reduces the computational and memory cost of the convolutions over irregular neighboring octree nodes, but also improves the performance of feature learning. Our method effectively encodes shape details, enables fast 3D shape reconstruction, and exhibits good generality for modeling 3D shapes out of training categories. We evaluate our method on a set of reconstruction tasks of 3D shapes and scenes and validate its superiority over other existing approaches. Our code, data, and trained models are available at https://wang-ps.github.io/dualocnn.

• The paper introduces a novel dual octree graph network that uses graph convolutions over octree nodes to efficiently balance fine and coarse geometric details.
• The paper employs a multi-level partition of unity integrated with an MLP to create continuous volumetric fields that capture both occupancy and high-fidelity surface detail.
• The paper demonstrates state-of-the-art performance across reconstruction benchmarks, achieving significant metric improvements and 390× faster processing than traditional methods.

Analysis of Dual Octree Graph Networks for Adaptive Volumetric Shape Representations

The development of efficient, high-quality 3D shape reconstruction and autoencoding methods is a critical frontier in computer vision and graphics. The paper "Dual Octree Graph Networks for Learning Adaptive Volumetric Shape Representations" addresses pertinent aspects within this domain, introducing novel methodologies for representing and learning volumetric fields of 3D shapes. This research delineates a sophisticated approach employing dual octree graph networks, accommodating adaptive volumetric fields utilizing graph convolutions over octree nodes, and leveraging an innovative multilevel partition of unity (MPU).

Methodology and Contributions

The core contribution of this work is the design and implementation of dual octree graph networks to encode and reconstruct 3D shapes. The mechanism involves constructing an octree-based adaptive feature volume, effectively balancing the representation between fine and coarse details. The use of octrees allows efficient handling of feature volumes by adjusting the granularity of elements according to the shape's geometric detail — an approach that offers marked improvements in computational and memory efficiency.

1. Graph Convolution Design: The paper introduces a new graph convolution operator performing over the dual graph of octree nodes at varying levels, rather than the conventional convolution over regular grids. This design addresses the challenges of computational overhead in processing irregular octree structures by optimizing message passing only to relevant neighboring nodes, thereby enhancing feature learning efficacy without ballooning the computational load.
2. Neural MPU Framework: Another innovative aspect is the neural MPU (multi-level partition of unity) employed to interpolate feature contributions across different octree nodes, achieving a continuous representation of the volumetric field. This MPU, combined with an MLP, facilitates direct mapping from the input point clouds to volumetric fields which express both occupancy and high-fidelity surface detail.
3. Generality and Adaptivity: The presented method generalizes well across categories outside the training data, indicative of a robust learning framework. This adaptability underscores the potential of the proposed dual octree graph networks in extending beyond traditional, homogeneous data distributions.

Evaluation and Results

The approach is rigorously evaluated across several benchmarks and tasks, including reconstruction from noisy point clouds and unsupervised surface reconstruction, illustrating its superiority over extant methods. Significant results are observed, such as achieving state-of-the-art performance on multiple datasets with enhancements in Chamfer distance, IoU, and normal consistency metrics. Notably, the network's ability to rapidly process input — approximately 390 times faster than MLP-heavy counterparts — is compelling for real-time applications.

Practical Implications and Future Work

From a practical perspective, this development could augment the efficiency of 3D modeling workflows in areas such as computer-aided design, games, and augmented reality by enabling reliable autoencoding with substantially lower computational overhead. Implementations of such approaches could leverage dynamic graph models to enable on-the-fly adaptations to input volume, ensuring resource optimization in complex processing environments.

Potential future directions include expanding the adaptability of octree structures during network operation rather than pre-defining them, potentially leading the way for self-optimizing neural architectures tailored to specific task requirements. Moreover, exploration into applying these techniques in shape analysis could broaden their utility further, encompassing semantic segmentation or shape classification.

In summary, this paper makes a compelling case for dual octree graph networks in adaptive 3D shape representation. The implications of this work suggest substantial advancements in both the theoretical frameworks for convolutional operations over irregular structures and practical applications in high-fidelity, real-time 3D reconstruction.