MeshCNN: A Network with an Edge (1809.05910v2)

Abstract: Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networks that combine convolution and pooling operations. In this paper, we utilize the unique properties of the mesh for a direct analysis of 3D shapes using MeshCNN, a convolutional neural network designed specifically for triangular meshes. Analogous to classic CNNs, MeshCNN combines specialized convolution and pooling layers that operate on the mesh edges, by leveraging their intrinsic geodesic connections. Convolutions are applied on edges and the four edges of their incident triangles, and pooling is applied via an edge collapse operation that retains surface topology, thereby, generating new mesh connectivity for the subsequent convolutions. MeshCNN learns which edges to collapse, thus forming a task-driven process where the network exposes and expands the important features while discarding the redundant ones. We demonstrate the effectiveness of our task-driven pooling on various learning tasks applied to 3D meshes.

• The paper introduces edge-centric convolution and pooling operations that process 3D mesh data directly, bypassing traditional grid-based conversions.
• It leverages a task-driven edge collapse mechanism to selectively retain key geometric features, enhancing model flexibility for complex shapes.
• Empirical evaluations demonstrate superior performance on classification and segmentation tasks, confirming its efficacy on detailed 3D analyses.

MeshCNN: An Exploration of Convolutional Neural Networks on 3D Mesh Structures

The research paper "MeshCNN: A Network with an Edge" introduces an innovative application of Convolutional Neural Networks (CNNs) directly onto 3D mesh structures. Unlike traditional applications of CNNs on regular grid data, such as images, this method leverages the unique properties of triangular meshes to capture intricate geometric features without converting them into alternate representations like voxel grids or 2D projections.

Motivation and Challenges

Polygonal meshes offer an efficient way to represent 3D shapes due to their ability to maintain surface topology and handle non-uniform data distribution. This characteristic makes them suitable for applications requiring detailed geometric fidelity. However, the intrinsic irregularity of mesh structures presents a challenge to conventional neural network operations which are typically optimized for regular data grids.

Methodological Innovations

Edge-Based Convolution and Pooling:

MeshCNN introduces a suite of operations customized for triangular mesh geometries, including edge-centric convolution and pooling mechanisms. Each edge serves as a key computational unit, analogous to pixels in image data. Convolutions are performed on neighborhoods defined by mesh connectivity, specifically the edges of adjacent triangular faces.

The pooling operation harnesses an edge collapse mechanism, allowing the network to learn task-specific features by selectively retaining or collapsing edges based on their geometric significance. This ability to perform task-driven pooling distinguishes MeshCNN from traditional geometric simplifications that aim to minimize geometric distortion irrespective of task importance.

Invariance to Affine Transformations:

Further strengthening its design, MeshCNN employs a symmetric strategy in its feature extraction process to ensure invariance to transformations such as rotation, translation, and scaling. The convolutional operations are designed to be compatible with the inherent non-uniformity of meshes, promoting robustness across varied mesh samples with different vertex densities and edge count.

Empirical Evaluation

MeshCNN's capabilities are substantiated through rigorous evaluation on both classification and segmentation tasks. In classification scenarios, MeshCNN demonstrated superior accuracy, especially when significant geometric details differentiate class features, such as in the SHREC11 dataset. In segmentation tasks, the method outperformed several state-of-the-art techniques across diverse datasets including COSEG and human body models, emphasizing its adeptness at learning feature hierarchies directly from the mesh structures.

Implications and Future Directions

The presented approach of leveraging mesh structures opens new avenues for 3D shape analysis in computer graphics, computer vision, and related disciplines. By accurately preserving geometric and topological nuances within 3D data, MeshCNN can be beneficial in applications such as shape retrieval, object recognition, and digital fabrication where detail fidelity is paramount.

Furthermore, the flexibility exhibited through task-driven edge pooling shows promise for adaptive network designs in applications outside typical mesh processing, potentially influencing neural network architectures that operate on other irregular data forms, such as graph-based systems.

Future work may delve into optimizing mesh data handling, exploring adversarial robustness against mesh variations, and extending the MeshCNN framework to fully exploit generative scenarios, including mesh synthesis and refinement. These developments could extend the benefits of MeshCNN beyond traditional shape analysis into the burgeoning field of 3D content creation and augmentation.