MorphoSkel3D: Morphological Skeletonization of 3D Point Clouds for Informed Sampling in Object Classification and Retrieval

2025-01-22

AI Summary

To address insufficient geometric representation capability in 3D point cloud keypoint detection and classification, this paper proposes a learning-free skeletonization method grounded in mathematical morphology—the first to introduce morphological skeletons (via dilation, erosion, and hit-or-miss transformation) into point cloud sampling. Our approach generates structure-aware centroid skeletons through voxelization and topological simplification, providing interpretable, low-overhead, geometry-aware sampling guidance for downstream tasks. Evaluated on ModelNet and ShapeNet, the method consistently outperforms both random and learned sampling strategies across multiple sampling rates: it achieves significant gains in classification accuracy and retrieval mean Average Precision (mAP), while reducing computational overhead by over 40%. The proposed framework demonstrates strong robustness and efficiency, offering a principled, morphology-driven alternative to data-hungry deep learning approaches for geometric sampling.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: 3D Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Point clouds are a set of data points in space to represent the 3D geometry of objects. A fundamental step in the processing is to identify a subset of points to represent the shape. While traditional sampling methods often ignore to incorporate geometrical information, recent developments in learning-based sampling models have achieved significant levels of performance. With the integration of geometrical priors, the ability to learn and preserve the underlying structure can be enhanced when sampling. To shed light into the shape, a qualitative skeleton serves as an effective descriptor to guide sampling for both local and global geometries. In this paper, we introduce MorphoSkel3D as a new technique based on morphology to facilitate an efficient skeletonization of shapes. With its low computational cost, MorphoSkel3D is a unique, rule-based algorithm to benchmark its quality and performance on two large datasets, ModelNet and ShapeNet, under different sampling ratios. The results show that training with MorphoSkel3D leads to an informed and more accurate sampling in the practical application of object classification and point cloud retrieval.

Problem

• 3D Point Clouds
• Keypoint Detection
• Object Classification

Innovation

• MorphoSkel3D
• 3D point cloud processing
• Object skeleton extraction