A Geometric Algorithm for Tubular Shape Reconstruction from Skeletal Representation

TL;DR

This work addresses tubular shape reconstruction from skeletal representations by introducing a purely geometric pipeline that treats skeleton points as unordered slices and computes a truncated signed distance function ($TSDF$) through a fast, surface-sampling-free process. An adaptive graph construction over the skeletal points, a geometric $f_{SDF}$ between adjacent slices, and a voxel-hashing storage enable efficient TSDF evaluation, followed by parallel marching cubes for dense surface extraction. Experiments on five public datasets demonstrate superior reconstruction quality and lower runtime compared with traditional surface-based baselines, with a fast $SDF$ variant offering substantial speedups while preserving accuracy. The approach provides a practical, topology-preserving method to reconstruct complex tubular structures from centerlines, with clear applicability to vascular and airway modeling.

Abstract

We introduce a novel approach for the reconstruction of tubular shapes from skeletal representations. Our method processes all skeletal points as a whole, eliminating the need for splitting input structure into multiple segments. We represent the tubular shape as a truncated signed distance function (TSDF) in a voxel hashing manner, in which the signed distance between a voxel center and the object is computed through a simple geometric algorithm. Our method does not involve any surface sampling scheme or solving large matrix equations, and therefore is a faster and more elegant solution for tubular shape reconstruction compared to other approaches. Experiments demonstrate the efficiency and effectiveness of the proposed method. Code is avaliable at https://github.com/wlsdzyzl/Dragon.

Figures (6)

• Figure 1: Overview of our shape reconstruction algorithm. Left: original shape and sampled skeletal points. Middle: Constructed graph. Right: recovered shape from slices.
• Figure 2: Illustration of different skeletal representations. Left: original shape. Middle: the input skeletal points are a thinner representation of the original shape, but not a string-like structure. Right: the ideal skeletal points forms a string-like structure.
• Figure 3: The geometric view of SDF computing.
• Figure 4: A failure case when faced with poor sampling.
• Figure 5: Surface extraction using different SDF values.