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Lighthouses reconnect broken skeletons via minimal-cost paths

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2026-07-05 05:33 UTC pith:3BXLLTP7

load-bearing objection Reasonable idea, competitive results, but the central two-part claim is under-evaluated — the repair step's impact on F-measure is never isolated. the 3 major comments →

arxiv 2604.20123 v2 pith:3BXLLTP7 submitted 2026-04-22 cs.CV

Topology-Aware Skeleton Detection via Lighthouse-Guided Structured Inference

Daoyong Fu , Xiang Zhang , Zhaohuan Zhan , Fan Yang , Ke Yang This is my paper
classification cs.CV
keywords skeletondetectionstructurallighthouse-guidedskeletonsaccuracyconfidencecontinuity
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper argues that object skeleton detection should not stop at pixel-level classification but must explicitly reason about connectivity. The authors propose Lighthouse-Skel, a framework with two core ideas. First, a dual-branch network jointly learns a dense skeleton confidence field and sparse structural anchors (endpoints and junction points), where the point branch steers attention toward topologically fragile regions. Second, a post-detection repair step treats junction points and breakpoints as 'lighthouses' and uses minimal-cost path inference on the learned confidence field to reconnect broken skeleton segments. The paper demonstrates that this two-stage approach yields competitive pixel accuracy while substantially improving skeleton continuity on four benchmarks.

Core claim

The central mechanism is the lighthouse-guided topology completion strategy. After an initial skeleton is extracted from a confidence field, the method identifies breakpoints (degree-1 pixels not near true endpoints) and uses them alongside detected junction points as navigation anchors. A cost map is built by negating the joint probability of skeleton and point heatmaps. For each breakpoint, the method searches a sector-shaped neighborhood for the cheapest path to a candidate lighthouse, accepting the path only if it passes mean-cost, max-cost, and junction-confidence thresholds. This converts skeleton reconnection from a local pixel decision into a global structured inference problem on a

What carries the argument

Lighthouse-guided minimal-cost path completion on a learned skeleton confidence field, with dual-branch joint learning of dense skeleton maps and sparse structural anchor points (endpoints and junctions)

Load-bearing premise

The topology completion step assumes the initial skeleton confidence field is accurate enough to build a reliable cost map. If the confidence field is noisy or misses large regions, the minimal-cost path inference will find spurious connections, potentially degrading the final skeleton rather than improving it.

What would settle it

Construct images where the skeleton confidence field has systematic low-confidence gaps at junctions (not just isolated pixel drops). If the cost map guides paths through incorrect low-cost regions, the reconnection will produce topologically wrong skeletons with higher fragmentation than before repair.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Skeleton connectivity metrics (single-connected ratio, fragment count) could become standard evaluation criteria alongside F-measure for skeleton detection benchmarks.
  • The lighthouse-anchor principle could transfer to other curvilinear structure extraction tasks such as blood vessel segmentation, road network extraction, or neuron tracing, where junctions and endpoints are similarly critical.
  • The cost-map formulation (Eq. 5) blending dense confidence with sparse point heatmaps is a general template for combining pixel-level and keypoint-level predictions in any task requiring connected output.
  • The path validation criteria (Eq. 9) suggest a principled way to trade off skeleton completeness against false-positive connections, which could be tuned per application.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes Lighthouse-Skel, a topology-aware skeleton detection method that combines a dual-branch network (skeleton confidence field + structural anchor points) with a post-hoc lighthouse-guided topology completion strategy. The completion strategy uses detected junction points and breakpoints as 'lighthouses' to reconnect discontinuous skeleton segments via minimal-cost path inference on a learned cost map. The method is evaluated on four public datasets (SK-LARGE, SK-SMALL, WH-SYMMAX, SYM-PASCAL), showing competitive F-measure and improved connectivity metrics. The core idea of using structural anchors to guide both training attention and post-hoc path reconnection is reasonable and addresses a real limitation of pixel-level skeleton detection methods.

Significance. The paper addresses a genuine problem: existing skeleton detection methods produce discontinuous skeletons because they lack explicit connectivity reasoning. The lighthouse-guided topology completion strategy is a reasonable approach that formulates reconnection as minimal-cost path inference on a learned cost field. The dual-branch design with point-guided attention is sensible. The parameter sensitivity analysis (Table III) and backbone ablation (Table IV) are welcome. However, the significance of the connectivity improvement is undermined by the limited evaluation scope (Table II covers only 100 samples from one dataset) and the absence of F-measure impact analysis for the repair step across all datasets.

major comments (3)
  1. §IV-D, Table II: The central claim is that the method achieves 'competitive detection accuracy while substantially improving skeleton connectivity.' However, the connectivity improvement (single-connected ratio 19%→44%) is reported only on 100 samples from WH-SYMMAX, and Table II does not report F-measure before and after the repair step. Without an ablation row showing F-measure with topology completion disabled across all four datasets, the reader cannot assess whether the repair step helps, is neutral, or hurts accuracy. The paper itself acknowledges (§IV-D) that 'when the skeleton probability map is poor, the skeleton repair step may reduce detection accuracy.' Adding a before/after F-measure comparison on each dataset would directly substantiate or qualify the central claim.
  2. §IV-E, Table VII: The ablation study isolates the effect of auxiliary tasks and point representations (REG, HM) on F-measure and OKS, but it does not isolate the contribution of the lighthouse-guided topology completion strategy itself. Table VII varies point representation choices but does not include a row with the full dual-branch network but topology completion disabled. This means the F-measure contribution of the repair step — a core contribution of the paper — is not separately quantified. A row showing F-measure with and without the repair step (on at least SK-LARGE, ideally all four datasets) would address this.
  3. §III-D, Eq. (9): The path validation thresholds q1, q2, and q3 are used to accept or reject candidate reconnection paths, but their values are never specified in the paper. These are load-bearing parameters: they directly control which paths are accepted and thus affect both F-measure and connectivity. The sensitivity analysis (Table III) covers α, θ, and R but omits q1, q2, q3 entirely. The method is not reproducible without these values.
minor comments (6)
  1. §III-D, Eq. (5): The cost map C blends S_P and P_HM, both predicted by the same network. The paper could briefly discuss whether this creates any dependency concern, or clarify that the point heatmaps provide spatial guidance distinct from the skeleton confidence (e.g., sparse peaks vs. dense field), which would strengthen the non-circularity argument.
  2. §III-C, Eq. (1): The notation S_P = Linear(F_S) × Einsum(F_FPN, MLP(F_S)) is unclear. What is the exact operation — element-wise multiplication? Broadcasting? Clarifying the dimensions and operation would improve readability.
  3. §IV-D: The paper states 'we prioritize skeleton integrity, since a discontinuous skeleton is not an effective representation.' This is a reasonable position, but it would be strengthened by reporting how often the repair step improves vs. degrades F-measure, even if only on the WH-SYMMAX subset where connectivity matters.
  4. Table I: The runtime for Lighthouse-Skel is 0.051s, which is 4× slower than BlumNet (0.031s) and comparable to ProMask (0.056s). The paper describes this as 'not particularly significant' but does not discuss the computational cost of the path inference step. A brief note on what fraction of runtime is spent on topology completion would be appropriate.
  5. §IV-E, Table III: The sensitivity analysis shows F-measure variations of ~0.001 across parameter settings, which is within noise for most evaluation protocols. The paper should discuss whether these differences are statistically significant or report variance across multiple runs.
  6. Fig. 2: The pipeline figure is referenced as illustrating the full method, but the text description of the architecture (§III-C) is somewhat dense. A clearer architectural diagram showing the data flow from backbone through FPN/Deformable DETR to the two branches would help readers follow the architecture.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review. The referee raises three major points: (1) the connectivity improvement in Table II is evaluated on only 100 samples from WH-SYMMAX and lacks before/after F-measure comparison across all datasets; (2) the ablation study (Table VII) does not isolate the contribution of the lighthouse-guided topology completion step; (3) the path validation thresholds q1, q2, q3 in Eq. (9) are never specified, making the method non-reproducible. We agree that all three points are valid and will be addressed in the revision. Specifically, we will expand the before/after F-measure comparison to all four datasets, add an ablation row isolating the topology completion contribution, and specify the values of q1, q2, and q3 along with adding them to the sensitivity analysis.

read point-by-point responses

  1. Referee: §IV-D, Table II: The connectivity improvement (19%→44%) is reported only on 100 samples from WH-SYMMAX, and Table II does not report F-measure before and after the repair step. Without an ablation row showing F-measure with topology completion disabled across all four datasets, the reader cannot assess whether the repair step helps, is neutral, or hurts accuracy.

    Authors: The referee is correct on both counts. The connectivity evaluation in Table II is limited to 100 samples from WH-SYMMAX, and the absence of before/after F-measure comparison across all datasets makes it impossible to assess the repair step's impact on detection accuracy. We will address this in the revision by: (1) expanding the before/after F-measure comparison to all four datasets (SK-LARGE, SK-SMALL, WH-SYMMAX, SYM-PASCAL), reporting F-measure with topology completion enabled and disabled; (2) expanding the connectivity statistics (single-connected ratio, average fragment count) to at least SK-LARGE in addition to WH-SYMMAX. We acknowledge that the repair step may reduce F-measure in some cases, as noted in §IV-D, and the expanded comparison will make this trade-off transparent. The revised Table II will include F-measure before/after repair for each dataset, allowing readers to directly assess the accuracy–connectivity trade-off. revision: yes

  2. Referee: §IV-E, Table VII: The ablation study isolates the effect of auxiliary tasks and point representations (REG, HM) but does not isolate the contribution of the lighthouse-guided topology completion strategy itself. A row showing F-measure with and without the repair step would address this.

    Authors: We agree that Table VII does not isolate the contribution of the topology completion step, which is a core contribution of the paper. In the revision, we will add a row to the ablation table showing the full dual-branch network with topology completion disabled (i.e., using only the initial skeleton S0 without the lighthouse-guided path reconnection). This will be reported on SK-LARGE at minimum, and ideally on all four datasets. This addition will directly quantify the F-measure contribution attributable to the repair step, separate from the point-guided attention and dual-branch design. We note that this is related to but distinct from the before/after comparison requested in the first major comment: the ablation isolates the repair step within the full pipeline, while the before/after comparison in Table II shows the effect on the final output. Both are informative and will be included. revision: yes

  3. Referee: §III-D, Eq. (9): The path validation thresholds q1, q2, and q3 are used to accept or reject candidate reconnection paths, but their values are never specified in the paper. The sensitivity analysis (Table III) covers α, θ, and R but omits q1, q2, q3 entirely. The method is not reproducible without these values.

    Authors: The referee is correct that the omission of q1, q2, and q3 values is a reproducibility gap. These are indeed load-bearing parameters that directly control which reconnection paths are accepted or rejected. In the revision, we will: (1) specify the exact values of q1, q2, and q3 used in all experiments in §III-D or §IV-C; (2) extend the sensitivity analysis in Table III to include these three thresholds, reporting F-measure under variations of each. Based on our preliminary checks, the method is reasonably stable across moderate changes to these thresholds (consistent with the stability observed for α, θ, and R), but we will provide the full sensitivity table to substantiate this claim. revision: yes

Circularity Check

0 steps flagged

No circularity found: the method is a standard multi-component architecture with independently trained branches and post-hoc path inference.

full rationale

The paper proposes Lighthouse-Skel, a dual-branch network that jointly learns a skeleton confidence field S_P and structural anchor points (endpoints E, junctions J), followed by a lighthouse-guided topology completion strategy. Walking the derivation chain: (1) The skeleton branch predicts S_P via Eq. 1 from backbone features; (2) the point branch predicts heatmaps P_HM via a separate MLP and linear classifier (Eq. 3); (3) the cost map C (Eq. 5) blends S_P and P_HM, both network outputs but from different branches with different supervision signals; (4) minimal-cost path inference (Eqs. 6-8) finds optimal reconnection paths on C; (5) path validation (Eq. 9) filters spurious connections. No step reduces to its own inputs by construction. The cost map C is a function of two independently supervised network outputs, not a self-referential definition. The path inference operates on C as a post-hoc algorithmic step, not a fitted prediction renamed as derivation. The F-measure results in Table I are evaluated against external ground truth on four public datasets. The connectivity metrics in Table II measure before/after repair on held-out test samples. There are no self-citations forming a load-bearing chain — the paper cites prior work (BlumNet [12], DeepFlux [7], ProMask [13], etc.) as related work and baselines, not as uniqueness theorems or ansatz justifications. The one self-citation is [40] (NDASPP, co-author Fu), but it appears only as a baseline in Table I, not as a load-bearing premise. The paper's acknowledgment that 'When the skeleton probability map is poor, the skeleton repair step may reduce detection accuracy' is an honest limitation statement, not evidence of circularity. The method's components are independently supervised, externally benchmarked, and algorithmically distinct. No fitted parameter is renamed as a prediction, no definition is circular, and no self-citation chain forces the conclusion. The derivation is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

7 free parameters · 3 axioms · 1 invented entities

The method relies on several hyperparameters (alpha, r, theta, sigma, q1-q3) that are tuned on the target datasets. The core axioms are standard domain assumptions for skeleton detection. The 'lighthouse' is a conceptual repackaging of seed points for path search.

free parameters (7)
  • alpha = 0.7
    Weight balancing skeleton confidence and point heatmaps in the cost map (Eq. 5). Selected via sensitivity analysis on SK-LARGE (Table III).
  • tau
    Global threshold for initial skeleton extraction (Eq. 2). Value not specified in paper.
  • r = 0.3
    Tolerance radius for excluding true endpoints from breakpoint set (Eq. 4). Selected via sensitivity analysis (Table III).
  • theta = 90 degrees
    Search sector angle for candidate connection points. Selected via sensitivity analysis (Table III).
  • sigma = 10
    Gaussian radius for heatmap generation. Selected via ablation (Table VI).
  • q1, q2, q3
    Path validation thresholds for mean cost, max cost, and mean junction confidence (Eq. 9). Values not specified in paper.
  • lambda_dice, lambda_focal, lambda_sk-p
    Loss weights in the skeleton branch loss (Eq. 13-14). Values not specified.
axioms (3)
  • domain assumption Skeletons can be meaningfully represented as a set of branches, endpoints, and junction points.
    Section III.A states S = {L, E, J}. This is a standard assumption in skeleton analysis.
  • domain assumption Minimal-cost paths on a learned confidence field correspond to true skeleton segments.
    The lighthouse-guided topology completion (Section III.D) relies on this assumption to reconnect broken segments.
  • standard math Lee-skeletonization produces a valid single-pixel-wide skeleton from a thresholded confidence map.
    Used in Eq. 2 and Eq. 11 to obtain initial and final skeletons.
invented entities (1)
  • Lighthouses independent evidence
    purpose: A metaphor for structural anchors (endpoints, junctions, breakpoints) used to guide path reconnection.
    These are not new physical entities but a conceptual framing for detected keypoints. Their effectiveness is validated by the connectivity improvement in Table II.

pith-pipeline@v1.1.0-glm · 15606 in / 2354 out tokens · 333764 ms · 2026-07-05T05:33:18.127797+00:00 · methodology

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read the original abstract

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.

Figures

Figures reproduced from arXiv: 2604.20123 by Daoyong Fu, Fan Yang, Ke Yang, Xiang Zhang, Zhaohuan Zhan.

Figure 1
Figure 1. Figure 1: Skeleton Detection. (a) Skeleton Generation based on the Incircle. (b) Differences in Point Detection Difficulty. (c) The Pixel-based Skeleton Detection using Deepflux [7]. (d) The Endpoint E and Junction Point J. (e) Using Lighthouse (e.g., J) along the Cost Path to Connect the Discontinuous Skeleton. (f) Lighthouse-based Continuous Skeleton Detection. detection as a pixel-level classification problem and… view at source ↗
Figure 2
Figure 2. Figure 2: The pipeline of the Lighthouse-Skel. We build a Transformer-based dual-branch collaborative network that outputs the object skeleton and the point set E, J (endpoints and junction points). The skeleton is often discontinuous. We then use this discontinuous skeleton and the point set to perform a lighthouse-guided topology completion, yielding a fully connected skeleton. the same category (either endpoints … view at source ↗
Figure 3
Figure 3. Figure 3: Lighthouse-Guided Topology Completion Strategy. By parsing the (a) Skeleton Confidence Field SP , we obtain the discontinuous (b) Initial Skeleton S0. We extract all endpoints in S0 (denoted as breakpoints B) and discard those with high overlap with the detected endpoints E; the remaining breakpoints together with the detected junction points J are treated as the “Lighthouse” as in (c) Candidate Points. Us… view at source ↗
Figure 4
Figure 4. Figure 4: Qualitative results of Deepflux, AdaLSN, BlumNet, NDASPP and Lighthouse-Skel on SK-LARGE dataset. Table II shows the connectivity and fragmentation statis￾tics before and after applying the lighthouse-guided topol￾ogy completion strategy. The simple connectivity property and the number of fragments can reflect the continuity of the skeleton. After connection repair, the number of single￾connected skeletons… view at source ↗
Figure 6
Figure 6. Figure 6: Qualitative results of Lighthouse-Skel on SYM-PASCAL dataset. TABLE III SENSITIVITY ANALYSIS OF KEY PARAMETERS ON THE SK-LARGE DATASET. Parameter Tested values F-measure α 0.5/0.7/0.9 0.8216∼0.8222 θ 60◦/90◦/120◦ 0.8217∼0.8221 R 0.1/0.2/0.3/0.4/0.5 0.8221∼0.8226 E. Ablation Study Table III summarizes the sensitivity of the proposed method to three key parameters of our method, including the cost weight α i… view at source ↗
Figure 5
Figure 5. Figure 5: Qualitative results of Lighthouse-Skel on WH-SYMMAX dataset. Lighthouse-Skel on the WH-SYMMAX dataset. We observe that the closer the initial skeleton is to the groundtruth, the better the repair by Lighthouse-Skel, reflecting the method’s reliance on the quality of the skeleton probability map. When the skeleton probability map is poor, the skeleton repair step may reduce detection accuracy. Hence, there … view at source ↗

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