DualConvMesh-Net: Joint Geodesic and Euclidean Convolutions on 3D Meshes

CVPR, pp. 8609-8619, 2020.

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The convolutional kernels are applied to local point neighborhoods obtained from spherical or k-nn neighborhoods defined over the Euclidean distance between pairs of points

Abstract:

We propose DualConvMesh-Nets (DCM-Net) a family of deep hierarchical convolutional networks over 3D geometric data that combines two types of convolutions. The first type, geodesic convolutions, defines the kernel weights over mesh surfaces or graphs. That is, the convolutional kernel weights are mapped to the local surface of a given m...More

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Introduction
  • Geometric deep learning [3, 4, 12, 26, 36, 44] aims at transferring the successes of CNNs from regular, discrete domains, e.g., 1D audio, 2D images or 3D voxel grids, onto irregular data representations such as graphs, point clouds or 3D meshes.
  • Geometric deep learning is divided into two main areas relying on different data representations: 3D scene understanding and 3D shape analysis.
  • The convolutional kernels are applied to local point neighborhoods obtained from spherical or k-nn neighborhoods defined over the Euclidean distance between pairs of points.
  • The authors refer to these convolutions as Euclidean convolutions.
  • Regardless of point cloud or voxel representations, these convolutions are agnostic to the surface information and, sensitive to surface deformations
Highlights
  • Geometric deep learning [3, 4, 12, 26, 36, 44] aims at transferring the successes of CNNs from regular, discrete domains, e.g., 1D audio, 2D images or 3D voxel grids, onto irregular data representations such as graphs, point clouds or 3D meshes
  • The convolutional kernels are applied to local point neighborhoods obtained from spherical or k-nn neighborhoods defined over the Euclidean distance between pairs of points
  • 4 We present a thorough ablation study, which empirically proves that combining Euclidean and geodesic convolutions provides a consistent benefit using radius neighborhoods, regardless of the pooling method used in the architecture
  • We propose Random Edge Sampling which is similar in spirit to [37] but has a special appeal in its probabilistic interpretation of reducing the neighborhood size
  • SparseConvNet [21] and MinkowskiNet [7] use Voxelized Sparse Convolutions, which currently perform best on ScanNet, but which are inherently limited for other tasks in that they cannot make use of detailed surface information
  • We provide our results on Scale 3D Indoor Spaces in the k-fold test setting, as well as detailed descriptions of our models
Methods
  • The authors propose a novel family of deep hierarchical network architectures. DCM-Nets combine the previously mentioned benefits of geodesic graph convolutions on 3D surface meshes and Euclidean graph convolutions on 3D vertices in the spatial domain.
  • Dual convolutions perform geodesic and Euclidean convolutions in parallel, and subsequently concatenate the resulting feature maps.
  • As suggested by He et al [25], the authors add residual connections such that gradients can by-pass the convolutions for better convergence.
  • Despite training on cropped meshes, the authors can perform inference on full meshes as the model is invariant to absolute vertex positions.
  • PointNet [39] PointNet++ [40]
Results
  • Table 1 shows the performance of the approach compared to recent competing approaches on the ScanNet benchmark test dataset as well as S3DIS Area 5, grouped by the approaches’ inherent categories.
  • The authors are able to report state-of-the-art results for graph convolutional approaches by a significant margin of 4 % mIoU for the ScanNet benchmark, as well as 2.1 % mIoU for S3DIS Area 5.
  • The authors provide the results on S3DIS in the k-fold test setting, as well as detailed descriptions of the models
Conclusion
  • The authors have motivated a mesh-centric view on 3D scene segmentation and the authors have proposed DCM-Nets to take advantage of the geometric surface information available in meshes.
  • The authors hope that the work encourages fellow researchers to perform convolutions in both the geodesic and Euclidean domain, as the authors have empirically shown that this combination brings significant improvements independent to the architecture used.
  • Future work might include incorporating geodesic convolutions for better separating instances in the task of 3D instance segmentation, as well as extending the work for leveraging point convolutions.
  • The experiments were performed with computing resources granted by RWTH
Summary
  • Introduction:

    Geometric deep learning [3, 4, 12, 26, 36, 44] aims at transferring the successes of CNNs from regular, discrete domains, e.g., 1D audio, 2D images or 3D voxel grids, onto irregular data representations such as graphs, point clouds or 3D meshes.
  • Geometric deep learning is divided into two main areas relying on different data representations: 3D scene understanding and 3D shape analysis.
  • The convolutional kernels are applied to local point neighborhoods obtained from spherical or k-nn neighborhoods defined over the Euclidean distance between pairs of points.
  • The authors refer to these convolutions as Euclidean convolutions.
  • Regardless of point cloud or voxel representations, these convolutions are agnostic to the surface information and, sensitive to surface deformations
  • Methods:

    The authors propose a novel family of deep hierarchical network architectures. DCM-Nets combine the previously mentioned benefits of geodesic graph convolutions on 3D surface meshes and Euclidean graph convolutions on 3D vertices in the spatial domain.
  • Dual convolutions perform geodesic and Euclidean convolutions in parallel, and subsequently concatenate the resulting feature maps.
  • As suggested by He et al [25], the authors add residual connections such that gradients can by-pass the convolutions for better convergence.
  • Despite training on cropped meshes, the authors can perform inference on full meshes as the model is invariant to absolute vertex positions.
  • PointNet [39] PointNet++ [40]
  • Results:

    Table 1 shows the performance of the approach compared to recent competing approaches on the ScanNet benchmark test dataset as well as S3DIS Area 5, grouped by the approaches’ inherent categories.
  • The authors are able to report state-of-the-art results for graph convolutional approaches by a significant margin of 4 % mIoU for the ScanNet benchmark, as well as 2.1 % mIoU for S3DIS Area 5.
  • The authors provide the results on S3DIS in the k-fold test setting, as well as detailed descriptions of the models
  • Conclusion:

    The authors have motivated a mesh-centric view on 3D scene segmentation and the authors have proposed DCM-Nets to take advantage of the geometric surface information available in meshes.
  • The authors hope that the work encourages fellow researchers to perform convolutions in both the geodesic and Euclidean domain, as the authors have empirically shown that this combination brings significant improvements independent to the architecture used.
  • Future work might include incorporating geodesic convolutions for better separating instances in the task of 3D instance segmentation, as well as extending the work for leveraging point convolutions.
  • The experiments were performed with computing resources granted by RWTH
Tables
  • Table1: Comparison to state-of-the-art. Semantic segmentation mIoU scores on the offical ScanNet benchmark [<a class="ref-link" id="c8" href="#r8">8</a>] and S3DIS Area-5 [<a class="ref-link" id="c1" href="#r1">1</a>]. We outperform other graph convolutional approaches on all benchmarks. * indicates concurrent work. Full network definitions in the supplementary. ScanNet benchmark was accessed on 11/15/2019. S3DIS results as reported in original publications
  • Table2: Mean class accuracy scores on Matterport3D Test [<a class="ref-link" id="c5" href="#r5">5</a>]. We outperform other approaches in 11 out of 21 classes. We use the same network definition as for the ScanNet v2 benchmark. Scores from [<a class="ref-link" id="c30" href="#r30">30</a>]
  • Table3: Comparison of pooling methods. We compare Vertex Clustering (VC), Farthest Point Sampling (FPS), and Quadric Error Metrics (QEM) as pooling methods
  • Table4: Combining geodesic and Euclidean convolutions in our DCM-Net brings significant performance improvements, especially compared to solely geodesic convolutions
  • Table5: Architectural influence. For the DCM-Net, we see improvements when using geodesic and Euclidean neighborhoods in parallel, in contrast to only using the same neighborhood notion
  • Table6: Geodesic/Euclidean filter ratio per mesh level. Geodesic convolutions are particularly useful in early mesh levels, when high frequency signals of the mesh are still preserved. In later levels, we benefit from Euclidean convolutions for localizing objects better. To this end, we use a larger ratio of geodesic filters in early levels, whereas we use more Euclidean ones in later levels. (Level 1-2 use 64 and level 3-4 use 96 filters in total.)
  • Table7: Influence of the number of mesh levels. We observe that the multi-scale architecture has a strong impact on the performance. With decreasing effect, more mesh levels bring performance gains. (Experiments where conducted with QEM pooling and geodesic/radius neighborhoods in our DCM-Net.)
  • Table8: Comparison of activation functions. As Leaky ReLU gains popularity, we compare it with standard ReLU activation functions. We conclude that default ReLU units work significantly better for our architecture. (Experiments are conducted with QEM pooling and geodesic/radius neighborhoods in a DCM-Net.)
  • Table9: Majority voting. By using majority voting with 100 runs on augmented scenes, we experience performance gains up to 0.5 % mIoU on ScanNet and S3DIS. Our scores on Matterport3D increase by 0.7 % mAcc compared to the single run variant with no test time augmentations
  • Table10: Architectures for the ablation study. In our ablation study, we experimentally prove the effectiveness of combining geodesic and Euclidean convolutions. We propose SCM-Nets for applying convolutions either in the geodesic or Euclidean space and DCM-Nets which jointly perform convolutions in the geodesic and Euclidean space
  • Table11: Architectures for benchmarks. We present two slightly different architectures for S3DIS and ScanNet/Matterport, respectively. This is due to the comparably lower mesh quality of S3DIS
  • Table12: Semantic segmentation IoU scores on S3DIS Area 5. We furthermore provide mean class accuracy scores. Among all approaches, we perform third best only outperformed by KPConv [<a class="ref-link" id="c57" href="#r57">57</a>] and MinkowskiNet [<a class="ref-link" id="c7" href="#r7">7</a>]. Among graph convolutional approaches, we clearly report state-of-the-art with a gap of 2.1% to HPEIN [<a class="ref-link" id="c33" href="#r33">33</a>]
  • Table13: Semantic segmentation IoU scores on S3DIS k-fold. We furthermore provide mean class accuracy scores. Among all approaches, we perform second best only outperformed by KPConv [<a class="ref-link" id="c57" href="#r57">57</a>]. Among graph convolutional approaches, we report state-of-the-art with a gap of 0.8% to the concurrent work SPH3D-GCN [<a class="ref-link" id="c37" href="#r37">37</a>]
  • Table14: Data representations and input features. We show the data representation and input features of each approach
Related work
  • Convolutions on point clouds. A simple way of handling point clouds is to transform them into a voxel grid representation that enables standard CNNs to be applied [8, 10, 43, 64, 65]. By construction, such approaches are limited to applying convolutional kernels on voxel neighborhoods, as it is not trivial to define geodesic neighborhoods on regular grids. Even recent methods focusing on efficient sparse voxel convolutions [7, 21] have similar limitations. Numerous other approaches operate directly on raw point clouds using convolutional kernels that are applied to the local neighborhoods of points obtained using k-nn or spherical neighborhoods [2, 39, 40, 47, 59]. Alternative methods define the position of the kernel weights explicitly in the Euclidean space relative to point positions [2, 29, 57, 66]. In both cases, the convolutional kernels are defined over the Euclidean space and are independent of the actual underlying object surface. In contrast, we additionally consider surface information using geodesic convolutions in combination with the Euclidean convolutions.
Funding
  • This work was supported by the ERC Consolidator Grant DeeViSe(ERC-2017-COG-773161)
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