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SpiralNet++: A Fast and Highly Efficient Mesh Convolution Operator
Shunwang Gong, Lei Chen, Michael Bronstein, Stefanos Zafeiriou
TL;DR
Mesh convolution on manifolds traditionally relies on learned kernel weights or pseudo-coordinates, motivating more efficient operators for aligned meshes. SpiralNet++ serializes local neighborhoods with fixed spiral sequences, then fuses the ordered features through a fully connected layer. Across dense correspondence, facial-expression classification, and shape reconstruction, it is faster and outperforms competitive baselines, while its scope assumes manifold triangle meshes and aligned topology.
Problem
Designing effective kernel weight functions and pseudo-coordinates for manifold convolution remains difficult, motivating efficient alternatives for aligned meshes.
Method
SpiralNet++ precomputes spiral neighborhood sequences and uses a fully connected layer to combine ordered neighboring features with local geometric information.
Results
Across dense correspondence, facial-expression classification, and shape reconstruction, SpiralNet++ is faster and outperforms competitive baselines without shape descriptors or pseudo-coordinate systems.
Takeaways & Limitations
Fixed mesh topology lets SpiralNet++ efficiently fuse neighboring features with local geometric structure across multiple 3D shape tasks.
Takeaways & Limitations
The approach assumes inputs are manifold triangle meshes and uses aligned or fixed mesh topology in its evaluation and design.
Abstract
from arXiv · showhide
Intrinsic graph convolution operators with differentiable kernel functions play a crucial role in analyzing 3D shape meshes. In this paper, we present a fast and efficient intrinsic mesh convolution operator that does not rely on the intricate design of kernel function. We explicitly formulate the order of aggregating neighboring vertices, instead of learning weights between nodes, and then a fully connected layer follows to fuse local geometric structure information with vertex features. We provide extensive evidence showing that models based on this convolution operator are easier to train, and can efficiently learn invariant shape features. Specifically, we evaluate our method on three different types of tasks of dense shape correspondence, 3D facial expression classification, and 3D shape reconstruction, and show that it significantly outperforms state-of-the-art approaches while being significantly faster, without relying on shape descriptors. Our source code is available on GitHub.
1. Introduction
The paper asks whether mesh convolution can avoid intricate kernel functions and pseudo-coordinates while efficiently learning manifold representations. SpiralNet++ serializes local neighborhoods into fixed spiral sequences and performs strongly across three 3D vision tasks.
- Intrinsic convolution operators aim to extract non-linear low-dimensional features from manifold data, which remains challenging compared with generic graph learning.
- The paper investigates whether efficient manifold convolution can avoid designing elusive kernel functions and pseudo-coordinates, leveraging aligned mesh data.
- SpiralNet++ captures local geometric structure by serializing each vertex’s local neighborhood into a spiral sequence.
- SpiralNet++ precomputes spiral sequences once rather than randomly regenerating them each epoch, improving robustness on fixed meshes.
- The method supports multiple neighborhood scales through a dilated SpiralNet++ variant for more detailed feature capture.
- Across dense correspondence, facial-expression classification, and shape reconstruction, SpiralNet++ outperforms competitive baselines by a large margin without shape descriptors or pseudo-coordinate systems.
2. Related Work
Related work applies geometric deep learning to graphs, meshes, correspondence, facial expression classification, and shape reconstruction. SpiralNet++ builds on these approaches by replacing randomly generated or manually calculated spirals with fixed mesh-aware sequences.
- Geometric deep learning: Geometric deep learning generalizes neural networks to structured non-Euclidean data, including graphs and 3D geometry.
- Dense Shape Correspondence: Dense shape correspondence methods include intrinsic patches, anisotropic patches, dynamic graph convolutions, and SpiralNet, whose per-epoch random spirals make training difficult.
- 3D Facial Expression Classification: The paper introduces SpiralNet++ and other geometric deep learning methods to 3D facial expression classification.
- Shape Reconstruction: For shape reconstruction, prior mesh autoencoders used spiral convolutions with manually selected references, geodesic ordering, and zero-padding for shorter spirals.
- Shape Reconstruction: SpiralNet++ argues that fixed mesh topology makes repeated spiral calculation unnecessary because corresponding mesh vertices share the same sequences.
3. Our Approach
SpiralNet++ represents mesh neighborhoods with fixed spiral orderings and applies a fully connected layer to the ordered features, avoiding trainable kernel weight functions. Its dilated variant expands receptive fields exponentially without increasing spiral length, while the overall operator is designed for efficient 3D shape analysis.
- Main Concept: The method assumes input domains are manifold triangle meshes represented by vertices, edges, and faces.
- Main Concept: SpiralNet++ explicitly orders neighboring vertex features in a precomputed spiral sequence, then uses a fully connected layer to encode the ordered information.The spirals are fixed after being generated once, using a chosen orientation and starting direction.
- Spiral Sequence: The k-ring is constructed from neighboring vertices around a center vertex, with N(V) denoting vertices adjacent to any vertex in V.
- Spiral Sequence: A spiral sequence concatenates vertices from successive rings around a center vertex and truncates the final ring to obtain a fixed length.The sequence length is denoted by l.
- Spiral Convolution: Unlike message-passing operators that use differentiable kernel functions and permutation-invariant aggregation, spiral convolution assigns neighbors by explicit order and concatenates their features before an MLP.This ordering makes the operator analogous to a Euclidean convolution while avoiding the need to calculate neighbor-to-weight assignments.
- Dilated Spiral Convolution: Dilated spiral convolution samples the spiral sequence uniformly to capture multi-scale context and exponentially expand the receptive field without increasing spiral length.The construction is intended to preserve resolution and coverage without increasing complexity.
4. Experiments
SpiralNet++ is evaluated on dense correspondence, facial-expression classification, and shape reconstruction under matched architectures and raw 3D-coordinate inputs. Across these tasks, it achieves strong accuracy, faster training, and lower reconstruction errors than competing approaches.
- Experimental setup: The experiments compare SpiralNet++ with FeaStNet, MoNet, ChebyNet, and SpiralNet using matched architectures, kernel sizes, and parameterization.All methods use raw 3D XYZ coordinates rather than preprocessed shape descriptors, with experiments run on a single NVIDIA RTX 2080 Ti.
- Dense Shape Correspondence: 99.88% exact-correspondence accuracy is achieved by SpiralNet++ on FAUST, with 0.98s average training time per epoch.SpiralNet++ converges within 100 epochs, whereas SpiralNet generally requires around 2500 epochs.
- 3D Facial Expression Classification: 78.59% average recognition accuracy is achieved by SpiralNet++ on 4DFAB, the highest among the evaluated methods.The authors report that all graph convolution operations outperform the baseline and that SpiralNet++ is faster than the other approaches.
- 3D Shape Reconstruction: SpiralNet++ and its dilated version outperform the other approaches on CoMA reconstruction errors and training time per epoch.The authors attribute the dilated operator’s higher capacity to its larger receptive field without increasing parameters, and report that SpiralNet++ is a few times faster with the same autoencoder architecture.
5. Conclusions
SpiralNet++ targets 3D shape meshes by efficiently fusing neighboring node features with local geometric structure information. Across dense shape correspondence, 3D facial expression classification, and 3D shape reconstruction, experiments show it is faster and outperforms competitive baselines.
- SpiralNet++ efficiently fuses neighboring node features with local geometric structure information on generally aligned 3D shape meshes.
- The method is applied to dense shape correspondence, 3D facial expression classification, and 3D shape reconstruction.
- Experimental results show that SpiralNet++ is faster and outperforms competitive baselines in all three tasks.