skeletonization

Existing skeletonization algorithms face a fundamental trade-off between computational efficiency and topological fidelity: morphological methods are fast but prone to skeletal fragmentation, whereas topology-preserving approaches achieve high accuracy at prohibitive computational cost—particularly challenging for clinical applications such as vascular structure extraction from medical images. Method: We propose the first fully differentiable, lightweight iterative skeletonization framework tailored for curve-like anatomical structures (e.g., vasculature). Our approach integrates synthetic data training, task-aware augmentation, and knowledge distillation for end-to-end optimization, and supports unified 2D/3D processing with built-in post-processing. Contribution/Results: Our method accelerates state-of-the-art topology-preserving algorithms by 100× while significantly improving skeletal connectivity. It generalizes zero-shot across imaging centers and modalities without fine-tuning, and demonstrates strong efficacy and robustness in downstream tasks—including vessel segmentation—validating its clinical applicability.

The medial axis (Hamilton–Jacobi skeleton) suffers from poor robustness against boundary noise, hindering reliable multi-scale shape analysis. Method: We propose the first scale-space framework for the medial axis based on synergistic sparse–dense evolution: we unify the modeling of the Hamilton–Jacobi partial differential equation in both continuous and discrete domains, yielding a theoretically guaranteed, invertible hierarchical representation system. Contribution/Results: Our framework achieves, for the first time, geometric equivariance, controllable simplification, and reversible refinement of the medial axis, enabling overcomplete multi-scale reconstruction and overcoming the expressive limitations of conventional pruning methods. Experiments demonstrate significant improvements in robust skeleton extraction, shape compression, and stiffness optimization for additive manufacturing—highlighting enhanced performance and generalization capability.

To address the lack of objective, reproducible geometric evaluation for point-cloud skeletonization in robotics applications, this work introduces the first systematic, multi-dimensional evaluation framework. It comprises four geometric quality metrics: topological similarity, boundedness, centrality, and smoothness, unified within a single numerical scoring scheme. Methodologically, the framework integrates point-cloud topological analysis, signed distance field modeling, quantitative centrality deviation estimation, and curvature-driven smoothness measurement. We implement an open-source Python evaluation toolkit to support reproducible assessment. Extensive validation on real-world point-cloud data across robotic tasks—including grasping and navigation—demonstrates that our framework significantly improves skeleton quality discrimination accuracy and interpretability. It enables cross-task performance sensitivity analysis and has been adopted by the research community for algorithm development and benchmarking.

This work addresses the limitation of existing graph analysis methods that often neglect geometric structure, thereby failing to capture the joint variation of topology and shape in shape graphs. To overcome this, the authors propose an explicit feature framework that integrates topological, geometric, and directional information to construct a multidimensional representation invariant to transformations such as rotation and translation. This approach transcends the traditional reliance on connectivity alone and enables effective grouping, clustering, and classification of shape graphs. Evaluated on real-world datasets—including urban road networks, neuronal trajectories, and astrocyte images—the method significantly outperforms both feature-based and non-feature baselines, demonstrating its efficacy for statistical analysis and pattern recognition in complex shape graphs.

Existing graph-based skeletonization methods, such as Local Separators, struggle to simultaneously preserve topological fidelity and geometric detail in complex 3D shapes due to their discrete representations. This work proposes CSCD, a continuous-domain curve skeletonization framework that unifies processing of meshes (CSCD-M) and point clouds (CSCD-PC) directly on the intrinsic geometry of manifolds. CSCD-M leverages intrinsic triangulation, while CSCD-PC introduces a tufted Laplacian operator, both overcoming the expressiveness limitations of discrete approaches. Experiments demonstrate that CSCD-M outperforms Local Separators on benchmarks like Thingi10k, and CSCD-PC qualitatively surpasses CoverageAxis++ and EPCS. Furthermore, the resulting skeletons exhibit strong performance in downstream tasks including shape classification, segmentation, and topological recognition.

This study addresses the fragmented conceptualization and inconsistent implementation standards of existing watershed segmentation algorithms, which hinder research reproducibility and application efficiency. To overcome these limitations, this work presents the first compact integration of diverse watershed theories and algorithms. By leveraging weighted graphs, Kruskal-based minimum spanning trees, and connected component analysis, it constructs an end-to-end segmentation pipeline encompassing both supervised and unsupervised paradigms alongside multiple seed computation variants. The primary contribution lies in establishing a clear, unified implementation standard that serves as a highly reproducible framework guide for watershed segmentation. Ultimately, this systematic consolidation significantly enhances both the theoretical understanding and the engineering implementation efficiency of watershed algorithms within the field.

该研究解决了自动骨架生成中分支结构编码和测试时计算效率问题，通过引入以分支为中心的标记化和视图增强生成方法提高了预测准确性。

This work addresses the challenge of topological errors—such as spurious connections and centerline fractures—in automatic extraction of 3D tubular structure skeletons, which commonly arise from noise or missing data and are inefficient and error-prone to correct manually. The authors propose a lightweight semi-automatic correction method: given user-specified start and end points, it performs locally stable propagation via component-wise minimum spanning trees and bridges gaps or resolves ambiguous connections using filtered 3D Delaunay edge graphs. Candidate paths are ranked through a scoring mechanism that integrates directional continuity, spatial proximity, component consistency, and goal-directedness. Implemented in C++ with Libigl, the interactive system effectively repairs typical artifacts like “crossings” and “breaks” in cerebral vasculature data, producing ordered polylines suitable for downstream processing and demonstrating both practical utility and robustness.

Existing CAD learning approaches discretize B-Rep models into triangle meshes, thereby discarding the analytical surface representations and topological information essential for consistent instance-level analysis. This work proposes STEP-Parts, a deterministic pipeline that directly extracts geometric instance partitions from native STEP B-Rep data. The method defines partitions based on intrinsic B-Rep topology, merges faces using analytical surface types and near-tangent plane continuity criteria, and transfers labels to triangulated meshes via face-to-mesh correspondence mapping. STEP-Parts ensures boundary consistency across varying triangulations and processes the DeepCAD subset of the ABC dataset—comprising approximately 180,000 models—in under six hours. The resulting labels significantly enhance performance in implicit reconstruction-segmentation tasks and point cloud networks. Code and precomputed labels are publicly released.

This work addresses the sensitivity of the Mapper algorithm to lens functions, cover parameters, and clustering strategies, for which no systematic evaluation framework previously existed. The authors propose the first triaxial assessment framework that comprehensively evaluates Mapper variants across three complementary dimensions: stability, cluster quality, and topological shape preservation. Experiments on synthetic data and the UCI handwritten digits dataset reveal inherent trade-offs among these dimensions, demonstrating that no single configuration achieves optimal performance across all metrics simultaneously. The study further identifies a “topological explosion” phenomenon at high resolutions, offering practical guidance for parameter selection in real-world applications and highlighting key challenges for future research in Mapper-based topological data analysis.