[Paper Review] PointManifold: Using Manifold Learning for Point Cloud Classification

Dinghao Yang, Wei Gao|arXiv (Cornell University)|Oct 14, 2020

3D Shape Modeling and Analysis27 references7 citations

TL;DR

This paper proposes PointManifold, a point cloud classification method that enhances feature representation by integrating manifold learning—via Locally Linear Embedding (LLE) and a neural network-based manifold projection—into a graph neural network framework. By preserving geometric continuity through low-dimensional manifold embeddings and concatenating them with 3D features, the method achieves state-of-the-art performance with 90.2% mean class accuracy and 93.2% overall accuracy on ModelNet40.

ABSTRACT

In this paper, we propose a point cloud classification method based on graph neural network and manifold learning. Different from the conventional point cloud analysis methods, this paper uses manifold learning algorithms to embed point cloud features for better considering the geometric continuity on the surface. Then, the nature of point cloud can be acquired in low dimensional space, and after being concatenated with features in the original three-dimensional (3D)space, both the capability of feature representation and the classification network performance can be improved. We pro-pose two manifold learning modules, where one is based on locally linear embedding algorithm, and the other is a non-linear projection method based on neural network architecture. Both of them can obtain better performances than the state-of-the-art baseline. Afterwards, the graph model is constructed by using the k nearest neighbors algorithm, where the edge features are effectively aggregated for the implementation of point cloud classification. Experiments show that the proposed point cloud classification methods obtain the mean class accuracy (mA) of 90.2% and the overall accuracy (oA)of 93.2%, which reach competitive performances compared with the existing state-of-the-art related methods.

Motivation & Objective

• To improve point cloud classification by leveraging geometric continuity through manifold learning, addressing limitations of Euclidean distance-based local feature analysis.
• To design a novel neural network architecture that integrates manifold learning into deep learning pipelines for 3D point cloud understanding.
• To enhance feature representation by combining low-dimensional manifold features with original 3D coordinates, improving classification performance.
• To validate the effectiveness of manifold learning in capturing intrinsic geometric structure compared to standard dimensionality reduction methods like PCA.
• To explore the complementary role of different manifold learning modules in boosting model performance through ablation studies.

Proposed method

• Proposes a Manifold Learning Module that uses Locally Linear Embedding (LLE) to preserve neighborhood relationships during dimensionality reduction from 3D to lower-dimensional space.
• Introduces a neural network-based Manifold Projection (MP) module that learns nonlinear 3D-to-2D mappings end-to-end to capture complex geometric structures.
• Concatenates the low-dimensional manifold features with original 3D coordinates to enrich input features for downstream classification.
• Constructs a k-nearest neighbors graph for point cloud representation, where edge features are aggregated via graph neural networks.
• Employs a channel control mechanism to regulate feature dimensionality and optimize representation learning.
• Uses the ModelNet40 dataset for training and evaluation, with ablation studies to analyze module interactions and hyperparameter sensitivity.

Experimental results

Research questions

• RQ1 Can manifold learning improve point cloud feature representation by capturing geometric continuity better than Euclidean distance-based methods?
• RQ2 How do LLE and neural network-based manifold projection compare in enhancing classification performance on point clouds?
• RQ3 Does concatenating manifold-learned features with original 3D features lead to significant performance gains over baseline models?
• RQ4 What is the optimal configuration of manifold learning modules and channel control parameters for maximum classification accuracy?
• RQ5 To what extent do the two manifold learning modules (LLE and MP) complement or overlap in their contributions to model performance?

Key findings

• The proposed PointManifold method achieves 90.2% mean class accuracy and 93.2% overall accuracy on the ModelNet40 dataset, outperforming the DGCNN baseline.
• The LLE-based manifold learning module improves classification accuracy to 90.0% mean class accuracy and 93.0% overall accuracy when using 1024 points.
• The neural network-based Manifold Projection (MP) module achieves 90.1% mean class accuracy and 93.0% overall accuracy on 1024-point inputs, demonstrating strong performance.
• Combining both LLE and MP modules does not yield a significant improvement over using either alone, indicating functional overlap between the two modules.
• The ablation study confirms that increasing the channel control parameter $ t $ improves performance, with optimal results at $ t = 4 $ when using 3 planes in MP.
• Compared to PCA, which shows no improvement over the baseline, LLE and MP modules significantly outperform standard linear dimensionality reduction by preserving geometric structure.