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PCPNET: Learning Local Shape Properties from Raw Point Clouds
Paul Guerrero, Yanir Kleiman, Maks Ovsjanikov, Niloy J. Mitra
TL;DR
Robust estimation of local normals and curvature from imperfect raw point clouds remains difficult because existing approaches depend on data-sensitive local parameters. PCPNET learns these properties from local, multi-scale point patches using a PointNet-based architecture, achieving state-of-the-art results across challenging scenarios while also extracting oriented normals. Its scope is limited by failures on large flat areas where patch information cannot determine orientation.
Problem
Estimating local normals and curvature from noisy, incomplete point clouds with varying sampling density and feature scales remains unresolved by unified robust methods.
Method
PCPNET adapts PointNet into a multi-scale, patch-based neural network trained on perturbed point clouds from triangle meshes to learn local shape properties.
Results
PCPNET achieves state-of-the-art results across varied challenging scenarios and improves over recently proposed learning-based methods while estimating oriented normals and principal curvature values.
Takeaways & Limitations
The data-driven approach replaces difficult manual parameter tuning and supports unified estimation of normals, curvature, and normal orientation from raw point clouds.
Takeaways & Limitations
Large flat areas can defeat patch-based orientation inference, producing inconsistent oriented normals such as at the centers of cube faces.
Abstract
from arXiv · showhide
In this paper, we propose PCPNet, a deep-learning based approach for estimating local 3D shape properties in point clouds. In contrast to the majority of prior techniques that concentrate on global or mid-level attributes, e.g., for shape classification or semantic labeling, we suggest a patch-based learning method, in which a series of local patches at multiple scales around each point is encoded in a structured manner. Our approach is especially well-adapted for estimating local shape properties such as normals (both unoriented and oriented) and curvature from raw point clouds in the presence of strong noise and multi-scale features. Our main contributions include both a novel multi-scale variant of the recently proposed PointNet architecture with emphasis on local shape information, and a series of novel applications in which we demonstrate how learning from training data arising from well-structured triangle meshes, and applying the trained model to noisy point clouds can produce superior results compared to specialized state-of-the-art techniques. Finally, we demonstrate the utility of our approach in the context of shape reconstruction, by showing how it can be used to extract normal orientation information from point clouds.
1. Introduction
PCPNET addresses robust local shape-property estimation from raw point clouds, where noise, sampling variation, missing data, and scale choices challenge traditional methods. It learns normals and curvature from perturbed local neighborhoods and reports strong performance across difficult scenarios.
- Raw point clouds lack connectivity and commonly contain noise, incomplete regions, and varying sampling density.
- PCPNET jointly estimates surface properties from noisy point sets, including normals and curvature, without specific training on RGBD data.
- Traditional local fitting requires parameters that trade off feature preservation against noise stability and depend on unknown shape and noise characteristics.Small neighborhoods preserve sharp features but become noise-sensitive, whereas large neighborhoods are more stable but can oversmooth local detail.
- PCPNET learns local normals and curvatures from point neighborhoods under different input perturbations using a multi-scale PointNet-inspired architecture.
- Extensive tests indicate that PCPNET consistently produces superior normal and curvature estimates in challenging raw-point-cloud scenarios.The reported scope includes varied noise and sampling conditions, high-curvature regions, and oriented-normal extraction through cascaded local analysis.
2. Related Works
Prior methods estimate local properties through neighborhood statistics or fitted primitives, but they are sensitive to scale, noise, structure, or orientation ambiguities. PCPNET adapts PointNet to local differential properties and avoids manual parameter tuning through data-driven learning.
- PCA estimates normals from minimum neighborhood variance but depends heavily on neighborhood size and does not determine normal orientation.
- Robust geometric methods address noisy or complex data through weighted distances, higher-order primitives, algebraic fits, or neighborhood-cell distributions.
- Oriented-normal estimation combines local direction with global orientation, making greedy propagation vulnerable to noisy estimates and complex shapes.
- Jet fitting can be reliable on well-structured point sets but requires a scale parameter that is difficult to choose across noise and shape types.
- PCPNET modifies PointNet for local differential properties, including oriented normals and curvature, rather than global classification or semantic labeling.
3. Overview
The paper replaces parameter-sensitive local surface fitting with a deep network trained to estimate properties from local patches under varied conditions. PCPNET uses single- and multi-scale patch processing and reports strong normal-estimation performance without manual parameter adjustment.
- The proposed alternative uses a deep neural network trained on a relatively small set of shapes to remain robust across varied conditions with fixed parameter settings.
- Figure 3 compares single-scale, multi-scale, and joint normal-curvature PCPNET variants with geometric and deep-learning baselines across patch sizes and sampling conditions.
- PCPNET applies PointNet-inspired processing to local patches centered at points, using a radius proportional to the point cloud bounding-box extent.
4. Algorithm
PCPNet adapts PointNet to local point-cloud patches, using neighborhood features and multi-scale inputs to estimate local surface properties. Its architecture enforces order independence, canonicalizes patch pose with rotation-only transformations, and regresses properties from learned patch descriptors.
- Local architecture: PCPNet replaces PointNet’s global or single-point features with local neighborhood feature vectors better suited to estimating local surface properties.PointNet’s fully local and fully global representations omit the neighborhood information needed for properties depending on local context.
- Local architecture: Each patch is centered at a point, contains neighbors within radius r, is translated and radius-normalized, and targets properties at the center.Curvatures are rescaled to the original point-cloud scale; patches are padded or subsampled to provide a fixed input size.
- Spatial transformation: A rotation-constrained spatial transformer canonicalizes each patch, avoiding unstable scaling transformations and enabling inverse transformation of predicted geometric properties.The transformer outputs a quaternion, restricting the learned transformation to rotations.
- Point aggregation: The network applies shared point functions independently to points and combines their outputs with a symmetric operation, preserving invariance to input ordering.The paper uses summation rather than PointNet’s maximum, interpreting the resulting functions as density estimators for patch regions.
- Regression: The aggregated patch feature vector is used by a three-layer fully connected regressor to predict surface properties.A second spatial transformer operates on intermediate point features and introduces information from all points in the patch into the point functions.
- Multi-scale architecture: The multi-scale variant processes three differently sized regions, computes features separately per patch, and supplies the resulting nine-fold feature set to output regression.Scale normalization maps the patches to the same size while retaining differently sized point-cloud regions.
5. Evaluation and Discussion
PCPNET is evaluated on diverse mesh-derived and analytic point-cloud datasets under noise and sampling variation, against specialized baselines. It consistently improves local normal and curvature estimation, while showing limitations under non-uniform sampling and occasional reconstruction failures.
- Evaluation setup: PCPNET is evaluated against PCA, jet fitting, PointNet, and Boulch et al. across varied noise levels and sampling rates.The experiments include separate and joint prediction of normals and curvature.
- Dataset: The dataset combines simple and detailed shapes, analytic surfaces, Gaussian-noise variants, and non-uniformly sampled point clouds.Training uses eight triangular-mesh shapes; testing includes 19 additional shapes and three analytically sampled differentiable surfaces.
- Reconstruction and architecture: The multi-scale network can jointly output normals and curvature, although joint estimation is slightly inferior to separate normal estimation.Oriented normals support Poisson reconstruction, which succeeds on difficult cases but still includes failure cases.
- Normal estimation: PCPNET consistently outperforms competing techniques across all tested noise levels.Jet fitting requires noise-dependent patch sizes: small patches fail under strong noise, whereas large patches over-smooth clean data.
- Limitations: Performance decreases when sampling density changes because the network was trained only on uniformly sampled point sets.The method nevertheless achieves comparable results across most non-uniform sampling levels and shows overall improvement.
- Curvature estimation: PCPNET achieves significantly better performance than jet fitting on both principal curvature values, often by more than one order of magnitude.Curvature is trained with a relative rectified error and evaluated using RMS error, normalized by ground-truth curvature magnitude.
6. Conclusion, Limitations, and Future Work
PCPNet provides a unified, data-driven approach for estimating oriented normals and principal curvatures in noisy point clouds, achieving state-of-the-art results across challenging scenarios. The method can still fail on large flat areas, while future work targets additional differential and mid-level shape features.
- Conclusion: PCPNet unifies oriented-normal and principal-curvature estimation through a PointNet modification emphasizing local patch properties.
- Conclusion: Training on triangle-mesh point clouds corrupted by varied noise levels replaces difficult manual parameter tuning with data-driven learning.
- Conclusion: PCPNet achieves state-of-the-art results across diverse challenging scenarios and improves over recently proposed learning-based methods.
- Limitations: Large flat areas can produce inconsistent normal orientations because patch-based information may not determine the correct orientation.
- Future Work: Future work includes estimating principal-curvature directions, full first and second fundamental forms, and other mid-level features from noisy incomplete point clouds.