PaperlayerView exact revision on arXiv

Source-linked AI summary

Adaptive O-CNN: A Patch-based Deep Representation of 3D Shapes

Peng-Shuai Wang, Chun-Yu Sun, Yang Liu, Xin Tong

arXiv:1809.07917v1cs.CVcs.GR

TL;DR

3D shape learning faces varied representations, and dense voxels require substantial memory and computation while making high-resolution outputs difficult. Adaptive O-CNN uses an adaptive octree of planar patches for encoding and decoding shapes. It reports efficiency gains and better shape-generation quality than existing methods, while planar patches do not approximate curved features very well.

  • Problem

    3D shapes have varied representations, and dense voxels’ high memory and computational costs make high-resolution outputs difficult in practice.

    Source: §1 · p. 1

  • Method

    Adaptive O-CNN adaptively subdivides octants, represents local shape with planar patches, and encodes patch normals and displacements across octree levels.

    Source: §1 · p. 2, §4.1 · p. 4

  • Results

    Adaptive O-CNN reports high memory and computational efficiency and superiority over state-of-the-art methods on several 3D learning tasks.

    Source: §6 · p. 9

  • Takeaways & Limitations

    The framework is evaluated for classification, autoencoding, single-image shape prediction, and completion of noisy or incomplete point clouds.

    Source: §1 · p. 2

    Planar patches do not approximate curved features very well.

    Source: §6 · p. 9

Abstract

from arXiv · show

We present an Adaptive Octree-based Convolutional Neural Network (Adaptive O-CNN) for efficient 3D shape encoding and decoding. Different from volumetric-based or octree-based CNN methods that represent a 3D shape with voxels in the same resolution, our method represents a 3D shape adaptively with octants at different levels and models the 3D shape within each octant with a planar patch. Based on this adaptive patch-based representation, we propose an Adaptive O-CNN encoder and decoder for encoding and decoding 3D shapes. The Adaptive O-CNN encoder takes the planar patch normal and displacement as input and performs 3D convolutions only at the octants at each level, while the Adaptive O-CNN decoder infers the shape occupancy and subdivision status of octants at each level and estimates the best plane normal and displacement for each leaf octant. As a general framework for 3D shape analysis and generation, the Adaptive O-CNN not only reduces the memory and computational cost, but also offers better shape generation capability than the existing 3D-CNN approaches. We validate Adaptive O-CNN in terms of efficiency and effectiveness on different shape analysis and generation tasks, including shape classification, 3D autoencoding, shape prediction from a single image, and shape completion for noisy and incomplete point clouds.

1 INTRODUCTION

3D shape learning uses varied representations, each with trade-offs, while dense voxels incur high memory and computational costs and are difficult to produce at high resolution. Adaptive O-CNN uses patches in an adaptively subdivided octree and reports efficiency gains and improved shape quality across shape analysis and generation tasks.

1 INTRODUCTION

  • Dense voxels fit existing CNN frameworks but require high memory and computation, making high-resolution outputs difficult in practice.Multi-view representations face view-selection, consistency, and occlusion challenges; point outputs are limited by point count and require additional processing for high-quality surfaces.Source: §1 · p. 1
  • Octree generation can stop subdivision early when a stored patch approximates the local shape, yielding a more compact adaptive representation than uniform finest-level samples.The stored patch also has higher-order approximation accuracy than sampling the surface at an octant center or corner.Source: §1 · p. 2
  • Adaptive O-CNN estimates local patches and occupancy at octants, subdividing those labeled as poorly approximated; its encoder also supports classification and 3D autoencoding.The non-empty leaf patches form a multiscale, adaptive representation of the predicted shape.Source: §1 · p. 2
  • Adaptive O-CNN gains memory and computational efficiency over existing octree-based CNNs and reports superior shape quality over state-of-the-art learning-based generation methods.The evaluated tasks include classification, autoencoding, single-image shape prediction, and completion of incomplete data.Source: §1 · p. 2

2 RELATED WORK

Prior 3D CNN work uses dense or sparse voxels, multi-view images, points, meshes, and primitives, with each representation offering different capabilities and constraints. Adaptive O-CNN is positioned among sparse representations and treats shapes as locally fitted patches organized by an adaptive octree.

2 RELATED WORK

  • Sparse-voxel CNNs exploit octree structures for efficient processing, and Adaptive O-CNN adds adaptiveness and patch fitting for greater sparsity and accuracy.Its octree subdivision follows local patch-fitting error, and leaf patches approximate the shape with a bounded Hausdorff distance.Source: §2 · pp. 2–3
  • Voxel, multi-view, point, graph, and manifold representations serve different input and task needs, with no universal representation for 3D learning.Point-based CNNs suit point-cloud inputs such as LiDAR scans, while graph- and manifold-based CNNs leverage mesh neighborhoods for shape analysis.Source: §2 · p. 2
  • Dense voxel decoders reconstruct shapes but retain low-resolution limitations, whereas octree-based decoders enable greater efficiency and higher-resolution outputs.Prior octree work made outputs of 128^3, 256^3, and higher resolutions possible; Adaptive O-CNN is described as further improving efficiency and prediction accuracy.Source: §2 · pp. 2–3
  • Multi-view decoders infer views or depth maps and fuse them, while point-based decoders predict point sets from images and may use Chamfer or Earth Mover’s distance losses.The related-work discussion notes that multi-view representations can miss shape information through occlusion or insufficient views, while generated point sets roughly approximate the expected shape.Source: §2 · pp. 2–3
  • Mesh decoders deform template vertices or map 2D patches into 3D, but topology constraints or distorted mesh elements can limit output quality.The discussion notes genus-zero or disk-topology assumptions in some methods and uncontrolled distortion in deformation or mapping approaches.Source: §2 · p. 3
  • Primitive decoders generate hierarchical structures or sets of primitives, while Adaptive O-CNN organizes simple planar surface patches in an octree.The paper frames patches as local approximations of shape rather than as points or voxels.Source: §2 · p. 3

3 PATCH-GUIDED ADAPTIVE OCTREE

Patch-guided partitioning fits a planar patch to each non-empty octant and subdivides octants when the local approximation error exceeds a threshold. The resulting leaf patches provide an adaptive approximation, although adjacent patches may leave gaps that require mesh repair or reconstruction.

3 PATCH-GUIDED ADAPTIVE OCTREE

  • For each non-empty octant, the method fits a planar patch by minimizing approximation error to the local surface.The plane is represented by a unit normal and displacement, with its normal oriented consistently with the underlying shape normals.Source: §3 · p. 3
  • An octant is subdivided when it is below maximum depth, contains surface, and its patch’s Hausdorff error exceeds the threshold.The local patch is the planar patch restricted to the octant, and the error compares that patch with the surface within the octant.Source: §3 · p. 3
  • The leaf patches approximate the input shape with Hausdorff distance bounded by the subdivision threshold.The octree’s patch sizes vary with its adaptive subdivision.Source: §3 · p. 3
  • Figure 2 shows Bunny patches at depths four through seven and together; facet colors encode the depth level of each patch.The illustration uses a maximum octree depth of seven.Source: Figure 2 · p. 4
  • Adjacent leaf patches can leave boundary gaps, so watertight mesh output requires surface reconstruction or polygonal repair.The text identifies gaps as an approximation artifact between non-empty leaf octants.Source: §3 · p. 4

4 ADAPTIVE O-CNN

This section describes an Adaptive O-CNN encoder and decoder for processing adaptive octrees whose octants carry local planar patches. The encoder processes features across octree levels, while the decoder predicts octant status and plane parameters to construct the adaptive structure.

4.1 3D Encoder of Adaptive O-CNN

  • Adaptive O-CNN uses estimated local planes at all octants as input, encoding each plane with its normal and center-relative displacement; empty octants receive zeros.The relative displacement is bounded by the grid size at that level, unlike displacement measured from the origin.Source: §4.1 · p. 4
  • Shared convolutions process octants at each level, then pooled features are fused across levels by element-wise maximum up to the coarsest level.The coarsest level is set to 2, where octants are enforced to be full so the features have the same dimension.Source: §4.1 · pp. 4–5

4.2 3D Decoder of Adaptive O-CNN

  • At each level, the decoder predicts whether an octant is empty, surface-well-approximated, or surface-poorly-approximated, and regresses its local plane parameters.Poorly approximated octants are subdivided and pass features to their children by deconvolution; well-approximated octants become leaves when patch error is bounded by δ.Source: §4.2 · p. 5
  • The decoder combines a weighted cross-entropy structure loss across octree levels with a patch loss on plane parameters at leaf octants.Adaptive splitting begins above level 4; wrongly generated octants receive structure loss only, and predicted plane displacement is constrained so the plane passes through its octant.Source: §4.2 · p. 6

5 EXPERIMENTS AND COMPARISONS

Experiments evaluate shape classification, 3D autoencoding, single-image reconstruction, and completion of noisy, incomplete car shapes. Across these tasks, Adaptive O-CNN combines competitive or improved shape quality with lower classification memory and computation costs.

5.1 Shape classification

  • On ModelNet40, Adaptive O-CNN's classification accuracy is better or comparable to SubVolSup, PointNet, OctNet, and O-CNN, but lower than PointNet++, Kd-Network, and VRN Ensemble.The benchmark table compares classification accuracy across learning-based methods.Source: Table 2 · p. 6
  • At 2563 resolution, Adaptive O-CNN achieves about a 4-times speedup and reduces GPU memory consumption by 73% versus O-CNN, with comparable accuracy across resolutions.The classification table reports GPU memory and time for batch size 32.Source: §5.1 · p. 6, Table 1 · p. 6
  • When resolution exceeds 1283, classification accuracy drops slightly; from 323 to 1283, training loss falls from 0.168 to 0.146 while testing loss rises from 0.372 to 0.375.The authors interpret this pattern as overfitting and report a 0.2% accuracy increase at 1283 when each training object is rotated 24 times.Source: §5.1 · p. 7

5.2 3D Autoencoding

  • Adaptive O-CNN achieves the best average autoencoding quality against AtlasNet with 25 or 125 mesh patches, and it and AtlasNet outperform PSG.The comparison reports Chamfer distance; AtlasNet uses that loss directly, while Adaptive O-CNN is not specified for it.Source: §5.2 · p. 7, Table 3 · p. 7
  • Adaptive subdivision stops when a coarse patch approximates the shape well, focusing finer layers on detail and reducing holes compared with fixed finest-level subdivision.Patch regression also enables sub-voxel precision, and hierarchical patch supervision improves reconstruction over finest-level patch prediction alone.Source: §5.2 · p. 8
  • For completion, the authors train on cars assembled from 3 to 5 randomly selected views, with cropped regions and perturbed point positions; Adaptive O-CNN fills holes better than O-CNN(patch).The reported examples are closer to ground truth; their Chamfer distances are 0.0713 and 0.0349 for O-CNN(patch), versus 0.0626 and 0.0306 for Adaptive O-CNN.Source: §5.2 · pp. 8–9, Figure 8 · p. 9

5.3 Shape reconstruction from a single image

  • Adaptive O-CNN performs best on 8 of 13 single-image reconstruction categories, especially objects with large flat regions such as cars and cabinets.Reconstruction quality is relatively lower for flip phones across all methods, which the authors attribute to their rarity in the training dataset.Source: §5.3 · p. 9
  • Against OctGen, Adaptive O-CNN has a lower Chamfer distance error, 0.274 vs. 0.294, and preserves more detail, especially on flat regions.The evaluation densely samples points from OctGen's boundary octant boxes.Source: §5.3 · p. 9

6 CONCLUSION

Adaptive O-CNN uses a patch-guided adaptive octree for 3D encoding and decoding, with reported efficiency and task performance advantages. Its implementation has limitations at patch seams and curved features.

6 CONCLUSION

  • The patch-guided adaptive octree supports compact, adaptive shape approximation; the method reports high memory and computational efficiency and superiority on several 3D learning tasks.Evaluated tasks include autoencoding, completion from noisy and incomplete point clouds, and prediction from images.Source: §6 · p. 9
  • Adjacent patches are not seamless, so producing a well-connected mesh requires mesh repair or surface reconstruction techniques.The authors observe that snapping nearby vertices can stitch most seams and propose seam-reducing regularization and post-processing to stitch all gaps.Source: §6 · p. 9
  • Planar patches do not approximate curved features well, as illustrated by a car wheel; non-planar patches and topology-aware subdivision guidance are proposed future directions.Quadratic, parabolic, and ellipsoidal patches are suggested, alongside fitting metrics that consider geometric and topological similarity.Source: §6 · p. 9

APPENDIX: PARAMETER SETTING OF ADAPTIVE O-CNN

The appendix specifies the encoder and decoder configuration for a max-depth-7 octree and gives training settings for classification, autoencoding, and single-image shape prediction.

PARAMETER SETTING OF ADAPTIVE O-CNN

  • For max-depth 7, the decoder uses a 128-dimensional latent code; from level 4, seven outputs predict octant fitting status and plane parameters.The first two levels where adaptation is introduced use two outputs to predict whether to split; from level 4, three outputs classify fitting status and four regress plane parameters.Source: APPENDIX: PARAMETER SETTING OF… · p. 12, Figure 11 · p. 12
  • The encoder-decoder diagram defines data[d] as the input feature at octree level d and specifies convolution, deconvolution, pooling, fully connected, and prediction operations.Convolution and deconvolution use kernel size 3; deconvolution has stride 2, while pooling uses kernel size and stride 2.Source: APPENDIX: PARAMETER SETTING OF… · p. 12, Figure 11 · p. 12
  • Training uses SGD with batch size 32; classification runs 40 epochs, autoencoding 350k iterations, and single-image prediction 400k iterations.Each task starts at learning rate 0.1, with reductions scheduled at task-specific epochs or iterations.Source: APPENDIX: PARAMETER SETTING OF… · p. 12
Loading 1809.07917v1…