Curve Skeletonization in Continuous domain for Meshes and Point Clouds

In natural images, object skeletons are used to represent geometric shapes. However, even slight variations in pose or movement can cause noticeable changes in skeleton structure, increasing the difficulty of detecting the skeleton and often resulting in discontinuous skeletons. Existing methods primarily focus on point-level skeleton point detection and overlook the importance of structural continuity in recovering complete skeletons. To address this issue, we propose Lighthouse-Skel, a topology-aware skeleton detection method via lighthouse-guided structured inference. Specifically, we introduce a dual-branch collaborative detection framework that jointly learns skeleton confidence field and structural anchors, including endpoints and junction points. The spatial distributions learned by the point branch guide the network to focus on topologically vulnerable regions, which improves the accuracy of skeleton detection. Based on the learned skeleton confidence field, we further propose a lighthouse-guided topology completion strategy, which uses detected junction points and breakpoints as lighthouses to reconnect discontinuous skeleton segments along low-cost paths, thereby improving skeleton continuity and structural integrity. Experimental results on four public datasets demonstrate that the proposed method achieves competitive detection accuracy while substantially improving skeleton connectivity and structural integrity.

Topological features play an essential role in ensuring geometric plausibility and structural consistency in image analysis tasks such as segmentation and skeletonization. However, integrating topology-preserving learning based on simple points into deep learning tasks remains challenging, as existing simple point detection methods are confined to binary images and are non-differentiable, rendering them incompatible with gradient-based optimization in modern deep learning. Moreover, morphological and purely data-driven approaches often fail to guaranty topological consistency. To address these limitations, we propose a novel method that directly computes simple points on continuous-valued images, enabling differentiable topological inference. Building on this theory, we develop an efficient skeleton extraction algorithm that preserves topological structures in binary and continuous-valued images. Furthermore, we design a variational model that enforces topological constraints by preserving topologically non-removable (i.e., non-simple) points, which can be seamlessly integrated into any deep neural network segmentation with softmax or sigmoid outputs. Experimental results demonstrate that the proposed approach effectively improves topological integrity and structural accuracy across multiple benchmarks. The codes are available in https://github.com/levnsio/CSP.

Superquadrics have proven to provide a compact, geometrically meaningful representation for 3D objects. However, existing methods suffer from limited reconstruction accuracy, are restricted to rigid primitives, and lack robustness to partial point clouds. In this work, we present SuperFlex, an enhanced framework that expands the expressive power and applicability of superquadric decompositions. First, we introduce a novel loss formulation which significantly improves reconstruction accuracy. Second, we include bending and tapering deformations, enabling high-fidelity representation of curved and asymmetric geometries. Finally, we leverage these high-quality decompositions as supervision to train a model that is robust to partial real-world point clouds. Experiments demonstrate substantial improvements in reconstruction accuracy over both optimization- and learning-based baselines while maintaining a highly compact primitive representation.