Semi-Automatic Correction of 3D Tubular Structure Skeletons via Component-Wise MST and Filtered Delaunay Triangulation

Chuan Li; Ruoxuan Yang

arxiv: 2606.19949 · v1 · pith:BKLVKLFCnew · submitted 2026-06-18 · 💻 cs.CG

Semi-Automatic Correction of 3D Tubular Structure Skeletons via Component-Wise MST and Filtered Delaunay Triangulation

Ruoxuan Yang , Chuan Li This is my paper

Pith reviewed 2026-06-26 15:10 UTC · model grok-4.3

classification 💻 cs.CG

keywords skeleton correctiontubular structuresminimum spanning treeDelaunay triangulation3D imagingvascular networkssemi-automatic correction

0 comments

The pith

A method reconstructs plausible centerline connections in 3D tubular skeletons from user-selected source and target points using component-wise MST and filtered Delaunay triangulation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a semi-automatic method for correcting artifacts like erroneous connections and fragments in skeletons of tubular structures from 3D images. Given minimal user input of source and target points, it traces a path using component-wise minimum spanning trees for local stability and a filtered 3D Delaunay edge graph for bridging gaps. Candidate paths are ranked by a score incorporating direction continuity, proximity, consistency, and progress toward the target. This produces an ordered polyline suitable for integration into post-processing workflows. The approach is demonstrated qualitatively on brain vessel data for common crossing and dotted artifacts.

Core claim

Given a user-selected source and target point, the method traces a path by combining component-wise minimum spanning trees for stable local propagation and a filtered 3D Delaunay edge graph for bridging gaps and handling ambiguous junctions, with candidates ranked by a multi-factor score.

What carries the argument

The combination of component-wise minimum spanning trees and filtered 3D Delaunay triangulation to generate and rank candidate connections between user points.

If this is right

Corrected centerlines can be used directly in morphometric analysis and flow simulations.
The method handles both crossing errors and fragmentation artifacts in input skeletons.
Output polylines integrate into existing skeleton post-processing pipelines.
The lightweight implementation supports interactive correction in biomedical imaging applications.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The approach could extend to other graph-based structures beyond tubular skeletons if similar ranking criteria apply.
Quantitative validation metrics would strengthen claims about topological correctness.
Integration with automatic skeletonization tools might reduce the need for manual intervention in large datasets.

Load-bearing premise

The ranking score based on direction continuity, spatial proximity, component consistency, and target-directed progress will select a topologically correct connection even when the input skeleton contains crossing or fragmentation artifacts.

What would settle it

A set of test cases where the top-ranked path connects incorrect branches despite the presence of a better topological alternative that the score misses.

read the original abstract

Skeletonization of tubular structures from 3D imaging is essential for tasks such as morphometric analysis, transport or flow simulation, and procedural planning in domains including vascular networks, plant root systems, and neural connectomes. However, automatic skeleton extraction often introduces topological artifacts, such as erroneous connections between nearby branches and fragmented centerlines caused by noise or missing data. Correcting these artifacts manually can be time-consuming and error-prone, especially when precise interaction is required. We present a semi-automatic correction method that reconstructs a plausible centerline connection from minimal user input. Given a user-selected source and target point, our method traces a path by combining (i) component-wise minimum spanning trees for stable local propagation and (ii) a filtered 3D Delaunay edge graph for bridging gaps and handling ambiguous junctions. Candidate steps are ranked using a score that accounts for direction continuity, spatial proximity, component consistency, and target-directed progress. The output is an ordered polyline (or edge sequence) that can be used as a suggested correction and integrated into downstream skeleton post-processing workflows. We implement the system in C++ with an interactive viewer based on Libigl and demonstrate representative qualitative results on brain vessel datasets, including correction of typical "crossing" and "dotted" artifacts. While our current validation is qualitative, the method is lightweight and serves as a practical building block toward more comprehensive interactive correction pipelines in biomedical imaging and related domains.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

A lightweight heuristic for user-guided skeleton repair that stays practical but offers no numbers to back its reliability claims.

read the letter

The paper gives a concrete way to fix broken or crossed centerlines in 3D tubular data with just two clicks. It builds local minimum spanning trees inside each connected component, adds edges from a filtered 3D Delaunay graph to jump gaps, and then ranks possible steps by direction continuity, distance, component match, and progress toward the target point. The result is a suggested polyline that can be accepted or rejected in an interactive viewer.

The implementation is straightforward: C++ with Libigl, no heavy dependencies, and the authors show it handling the usual crossing and dotted artifacts on brain vessel scans. That combination is not a standard off-the-shelf fix, and the focus on minimal user input plus downstream integration is useful for people already running skeletonization pipelines.

The main weakness is the complete absence of quantitative checks. Validation is stated as qualitative only, with no success rates, no comparison to manual correction or other interactive tools, and no examination of cases where several high-scoring paths exist at a junction. The ranking score is presented as a linear combination of four terms, but nothing shows why that particular weighting prefers the correct topology when the input is noisy or ambiguous.

This is aimed at imaging groups that need a quick post-processing step rather than a new theory of geometry or reconstruction. It is solid enough on the algorithmic description to go to referees, provided the authors are asked to add controlled tests and failure cases. I would send it out.

Referee Report

2 major / 0 minor

Summary. The paper presents a semi-automatic method for correcting topological artifacts (such as erroneous crossings and fragmentation) in 3D skeletons of tubular structures extracted from imaging data. Given minimal user input in the form of a source point and a target point, the algorithm traces a connecting polyline by (i) building component-wise minimum spanning trees for local propagation and (ii) using a filtered 3D Delaunay edge graph to bridge gaps and resolve ambiguous junctions; candidate steps are ranked by a composite heuristic score that combines direction continuity, spatial proximity, component consistency, and target-directed progress. The method is implemented in C++ with a Libigl-based viewer and is illustrated qualitatively on brain-vessel datasets.

Significance. If the ranking heuristic were shown to be reliable, the work would supply a lightweight, practical building block for interactive post-processing pipelines in biomedical imaging, vascular analysis, and related domains, reusing standard CG primitives (MST, Delaunay) without introducing new theoretical machinery. The current absence of any quantitative evaluation, however, prevents assessment of whether the approach improves upon existing correction techniques or generalizes beyond the demonstrated cases.

major comments (2)

[Abstract] Abstract and validation description: the central claim that the composite ranking score selects topologically correct connections rests on untested assumptions about its behavior at junctions and gaps; the manuscript supplies only qualitative demonstrations on brain-vessel data and explicitly states that validation is qualitative, with no error metrics, failure-mode analysis, or baseline comparisons. This is load-bearing for the contribution.
[Method] Method section (ranking-score definition): no derivation, sensitivity analysis, or bound is provided showing why the particular linear combination of the four heuristics must prefer ground-truth topology when multiple high-scoring paths exist; the skeptic's concern about reliability in ambiguous cases is therefore unaddressed by the text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We agree that the manuscript's validation is qualitative and that claims about the ranking score require careful qualification to avoid overstatement. We will revise the abstract, method description, and add a limitations discussion to clarify the heuristic nature of the approach and its intended use as a practical suggestion tool. Point-by-point responses follow.

read point-by-point responses

Referee: [Abstract] Abstract and validation description: the central claim that the composite ranking score selects topologically correct connections rests on untested assumptions about its behavior at junctions and gaps; the manuscript supplies only qualitative demonstrations on brain-vessel data and explicitly states that validation is qualitative, with no error metrics, failure-mode analysis, or baseline comparisons. This is load-bearing for the contribution.

Authors: We agree that the validation is qualitative, as already stated in the manuscript. However, the abstract does not assert that the score 'selects topologically correct connections'; it describes the output as a suggested correction. We will revise the abstract to explicitly frame the ranking as a heuristic for generating candidate paths and add a limitations paragraph noting the absence of quantitative metrics or baselines. This addresses the load-bearing concern by tempering the contribution to a lightweight practical method rather than a validated selector of ground truth. revision: yes
Referee: [Method] Method section (ranking-score definition): no derivation, sensitivity analysis, or bound is provided showing why the particular linear combination of the four heuristics must prefer ground-truth topology when multiple high-scoring paths exist; the skeptic's concern about reliability in ambiguous cases is therefore unaddressed by the text.

Authors: The composite score is a heuristic combining standard terms (direction continuity, proximity, consistency, progress) with empirically selected weights to favor plausible connections in the demonstrated vessel data. We do not claim or derive that it must prefer ground-truth topology, as the underlying problem is ambiguous at junctions and gaps. We will revise the method section to state this explicitly, note the empirical weight selection, and discuss ambiguous cases qualitatively. A formal derivation, bound, or sensitivity analysis is outside the paper's scope and would require extensive ground-truth annotations not available here. revision: partial

Circularity Check

0 steps flagged

No circularity: algorithmic construction with independent heuristics

full rationale

The paper describes a semi-automatic path-tracing algorithm that builds a graph from component-wise MSTs plus filtered Delaunay edges and ranks candidates via an explicit composite heuristic (direction continuity + spatial proximity + component consistency + target-directed progress). No equations, fitted parameters, or self-citations are presented that reduce the output path to the input by construction. The method is a procedural construction whose correctness is asserted via qualitative demonstration rather than a closed-form derivation; the ranking criteria are stated as independent design choices, not derived from the target result itself. This is the normal case of a self-contained algorithmic contribution.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; any thresholds in the filtered Delaunay or scoring weights would be free parameters if present in the full text.

pith-pipeline@v0.9.1-grok · 5796 in / 1096 out tokens · 26887 ms · 2026-06-26T15:10:17.522461+00:00 · methodology

discussion (0)

Reference graph

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