Source-linked AI summary
Morphing and Sampling Network for Dense Point Cloud Completion
Minghua Liu, Lu Sheng, Sheng Yang, Jing Shao, Shi-Min Hu
TL;DR
Dense point-cloud completion must recover missing geometry while avoiding structural loss, blurred details, and uneven point distributions. The paper proposes a two-stage surface-based network with input-aware sampling and refinement, and reports better EMD and CD than existing methods.
Problem
3D point-cloud completion seeks to infer complete geometry from partial scans whose limited views can cause structural loss and poor-quality reconstructions.
Method
The method first predicts a coarse complete cloud with parametric surface elements, then merges it with the input, samples an even subset, and learns point-wise residuals.
Results
The method outperforms existing methods on both EMD and CD, achieving the lowest EMD across all object categories.
Takeaways & Limitations
The approach preserves known structures and generates realistic, continuous, smooth details in dense point clouds with even distributions.
Takeaways & Limitations
Chamfer Distance can overlook visual inferiority, while EMD is more discriminative but traditionally costly for dense point clouds.
Abstract
from arXiv · showhide
3D point cloud completion, the task of inferring the complete geometric shape from a partial point cloud, has been attracting attention in the community. For acquiring high-fidelity dense point clouds and avoiding uneven distribution, blurred details, or structural loss of existing methods' results, we propose a novel approach to complete the partial point cloud in two stages. Specifically, in the first stage, the approach predicts a complete but coarse-grained point cloud with a collection of parametric surface elements. Then, in the second stage, it merges the coarse-grained prediction with the input point cloud by a novel sampling algorithm. Our method utilizes a joint loss function to guide the distribution of the points. Extensive experiments verify the effectiveness of our method and demonstrate that it outperforms the existing methods in both the Earth Mover's Distance (EMD) and the Chamfer Distance (CD).
Introduction
Partial scans can lose structures and produce uneven or blurred completions, motivating a two-stage network that combines coarse surface-based prediction with input-aware sampling and refinement.
- Motivation: High-fidelity 3D reconstruction is difficult because real-world scans provide limited sensor views and restricted raw data.Shape completion compensates for structural loss and supports downstream tasks such as classification and registration.
- Motivation: Existing completion methods can distort results or omit structures already visible in the input, such as chair-leg connectors.Chamfer Distance can also encourage uneven density and blurred details, while EMD is more detail-sensitive but computationally expensive for dense clouds.
- Approach: The proposed network completes partial point clouds in two stages using parametric surface elements followed by input-aware sampling and point-wise refinement.The first stage predicts a coarse complete cloud; the second merges it with the input, samples an even subset, and learns residuals for fine-grained detail.
- Approach: An expansion penalty regularizes surface elements, while an auction algorithm approximates EMD for dense point-cloud comparison.The penalty discourages overlapping elements, and the auction-based approximation makes EMD applicable to dense point clouds.
- Results: The method outperforms existing methods on both EMD and CD in extensive experiments.The paper also presents realistic structures, continuous and smooth details, preserved known structures, and evenly distributed dense outputs as core contributions.
Related Work
Prior 3D shape-completion work uses geometric assumptions, examples, volumetric or projected representations, meshes, implicit fields, and point-cloud networks, each addressing different representation challenges.
- 3D Shape Completion: Geometry-based methods interpolate surfaces or impose assumptions such as symmetry, but large-scale incompleteness and real-world violations limit these approaches.Example-based methods provide another conventional strategy for shape completion.
- Learning-Based Completion: Learning-based methods map partial shapes to completions using volumetric grids, 2D projections, polygon meshes, or continuous implicit fields.These representations support convolutional, graph-convolutional, or implicit-field completion strategies.
- Point Cloud Analysis: Point clouds avoid discretization artifacts and preserve geometric information, but their unordered structure and varying density complicate deep learning.Traditional convolution cannot be applied directly to irregular point clouds.
- Point Cloud Generation: Point-cloud generation methods decode latent features through coordinate branches, 2D deconvolution, plane deformation, or coarse-to-fine generation.FoldingNet favors continuous and smooth structures, while PCN combines fully connected and FoldingNet-style generation.
Approach
The approach completes partial point clouds in two stages: morphing parameterized unit squares into coarse surface elements, then merging, sampling, and refining the result. Expansion and density-aware sampling address overlap and uneven distributions while EMD-based training emphasizes local detail and density.
- The supervised pipeline takes a partial point cloud and predicts a dense, evenly distributed complete shape end-to-end.
- Morphing-Based Prediction: A morphing-based auto-encoder maps sampled unit-square points into K local surface elements that assemble the coarse output.The decoder uses K=16 elements and samples N=512 points per element in experiments.
- Merging and Refining: A residual network refines the sampled combination, while the joint loss balances EMD coverage with expansion-based compactness.The loss combines coarse-output EMD, the expansion penalty, and final-output EMD; α=0.1 and β=1.0 in experiments.
- Morphing-Based Prediction: The penalty mitigates overlaps, helping individual elements cover local regions that can correspond to semantic object parts.
- Morphing-Based Prediction: The expansion penalty uses directed minimum spanning trees to shrink sparsely distributed boundary points toward their neighbors, concentrating each surface element.It penalizes directed edges longer than λl_i, with λ=1.5 in experiments.
- Merging and Refining: Minimum density sampling selects an evenly distributed subset from the merged coarse prediction and input, outperforming FPS and PDS in global uniformity.
Experiments
Experiments evaluate the method on ShapeNet using 8,192-point outputs and compare it with existing and ablated methods. The results show advantages in EMD and CD, while ablations associate key components with point distribution, structure preservation, and detail quality.
- Data Generation and Model Training: The evaluation uses 30,974 ShapeNet CAD models across eight categories, with 8,192 sampled points for each complete point cloud.Partial clouds are generated from 50 camera poses per model and unified to 5,000 points for training.
- Comparison with Existing Methods: Each qualitative output in Figure 7 contains 8,192 points for comparison across completion methods.
- Comparison with Existing Methods: Our method achieves the lowest EMD across all object categories, with average EMD equal to 57.9% of AtlasNet and 51.5% of PCN.It also outperforms existing methods on CD, while Ours-CD achieves lower CD results.
- Comparison with Existing Methods: Qualitatively, the method predicts realistic structures, continuous smooth details, preserves known structures, and supports arbitrary-resolution dense point clouds.FCAE and PCN more often produce blurred details or distort structures revealed in the input.
- Ablation Study: The expansion penalty limits surface-element coverage, while merging, MDS sampling, and refining contribute to structure preservation, even distribution, and fine-grained details.The ablation analysis links removal of the expansion penalty to significantly larger surface-element areas.
- Ablation Study: Removing the expansion penalty, merging and refining operations, or the EMD-based metric generally produces larger EMD and CD, with metric-specific trade-offs for FPS.Replacing MDS with FPS causes significantly larger EMD but smaller CD, while replacing EMD with CD produces larger EMD and smaller CD.
Conclusion
The paper concludes that its two-stage point cloud completion approach controls point distribution, preserves known structures, and supports evenly distributed dense outputs. It also presents an efficient EMD approximation for dense point clouds.
- Conclusion: The two-stage approach completes partial point clouds while controlling point distribution through the expansion penalty.
- Conclusion: The sampling operation preserves known structures and helps generate dense point clouds with even point distributions.
- Conclusion: An efficient EMD approximation is implemented for calculating similarity on dense point clouds.