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

TL;DR

MorphoSkel3D presents a shape-agnostic, morphology-based skeletonization pipeline that extracts a fixed-size set of skeletal points by locating centers of maximal inscribed balls via a dilated unsigned distance function. The skeleton informs a sampling prior through Local Feature Size, enabling geometry-aware point selection that improves downstream tasks. Across ShapeNet and ModelNet40, MS3D yields superior Chamfer distances for skeleton extraction and enhances object classification and retrieval performance, particularly at higher sampling ratios. The approach relies on simple, train-free morphological operations, enabling scalable integration of geometric priors into learning-based 3D understanding with practical impact on large-scale point cloud processing.

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.

Figures (12)

• Figure 1: Overview of the proposed shape-agnostic skeletonization pipeline, illustrated with the Stanford dragon 10.1145/237170.237269. In the MorphoSkel3D module, the local maxima on the unsigned distance function of inner points reveal the set of maximal balls. The local neighbourhood of points is encoded by a structuring element $\text{SE}$.
• Figure 2: Occupancy function used to retain the inner points from the bounding box points. A case for 10000 points in the bounding box (left). Inner points extracted for the case with 1M points within the box volume (right).
• Figure 3: Transformed distance function by dilation (left) and its initial unsigned distance function (right). Brighter points indicate greater distances, while darker areas correspond to points closer to the surface.
• Figure 4: Based on 1M bounding box points, $\text{MS3D}(x)$ as the difference between the dilated and original UDF (left). The 1024 inner points with lowest $\text{MS3D}(x)$ values are retained to form the skeleton with point colors based on their original UDF to the surface (right).
• Figure 5: The 1024 inner points selected by $\text{MS3D}(x)$, color-coded by their original UDF to the surface (up). Distribution of $\text{MS3D}(x)$ for 1024 skeletal points (down), contingent to the density of 1M (left) to 10M (right) bounding box points.