Skeleton Recall Loss in Tubular Segmentation

• Skeleton Recall Loss (SRL) is a topology‐aware segmentation loss that leverages precomputed tubed skeletons to preserve connectivity in thin tubular structures.
• It efficiently augments a conventional segmentation loss by rewarding high predicted probabilities on the tubed skeleton, keeping computational overhead minimal.
• SRL balances connectivity preservation with volumetric overlap, though later studies question its gradient sensitivity and robustness across datasets.

Searching arXiv for the cited SRL papers and related topology-aware segmentation work. Tool call: arxiv_search(query="(Kirchhoff et al., 2024) Skeleton Recall Loss for Connectivity Conserving and Resource Efficient Segmentation of Thin Tubular Structures", max_results=5) Tool call: arxiv_search(query="(Arora et al., 15 Aug 2025) Does the Skeleton-Recall Loss Really Work?", max_results=5) Skeleton Recall Loss (SRL) is a topology-aware segmentation loss for thin tubular structures such as vessels, nerves, roads, and concrete cracks. It was introduced by Kirchhoff et al. as a resource-efficient alternative to differentiable skeleton-based losses: the method precomputes a tubed skeleton from the ground-truth mask, then adds a recall-style term that rewards high predicted probabilities on that skeleton while retaining a conventional segmentation loss for volumetric overlap (Kirchhoff et al., 2024). SRL is therefore positioned at the intersection of connectivity preservation and practical training efficiency. Subsequent work has both extended the broader design space of skeleton-focused supervision and challenged SRL’s optimization behavior and empirical robustness, making it a notable case study in topology-aware learning for curvilinear segmentation (Arora et al., 15 Aug 2025, Chen et al., 13 May 2025).

1. Origins and problem setting

SRL was proposed for segmentation regimes in which thin, elongated, low-contrast structures occupy few pixels or voxels and where connectivity errors are disproportionately harmful. The motivating applications listed for the method include blood vessels, nerves, roads, cracks, the inferior alveolar canal, and the Circle of Willis; in these settings, a small local omission can disconnect a branch even when the volumetric error is modest (Kirchhoff et al., 2024).

The method was introduced against two established baselines. First, overlap-based losses such as Cross-Entropy and Dice optimize pixel-wise or volumetric agreement, but they do not directly penalize broken centerlines, missing bridges, or incorrect branch splitting and merging. Second, topology-focused losses such as clDice preserve connectivity more explicitly but rely on differentiable skeletonization at training time, which the proposing paper characterizes as expensive in memory and runtime, particularly in 3D and in multi-class settings (Kirchhoff et al., 2024).

A later reevaluation by Arora et al. framed SRL more narrowly: rather than a full topological comparison between prediction and target, SRL is a recall-like objective defined only on a precomputed tubed skeleton derived from ground truth. That distinction became central to the subsequent criticism of its gradients and error sensitivity (Arora et al., 15 Aug 2025).

Paper	Main contribution	Relation to SRL
"Skeleton Recall Loss for Connectivity Conserving and Resource Efficient Segmentation of Thin Tubular Structures" (Kirchhoff et al., 2024)	Original SRL proposal	Defines tubed skeletonization and the recall term
"Dynamic Snake Upsampling Operater and Boundary-Skeleton Weighted Loss for Tubular Structure Segmentation" (Chen et al., 13 May 2025)	DSU and boundary-skeleton weighting	Closely related skeleton-focused supervision without explicit SRL naming
"Does the Skeleton-Recall Loss Really Work?" (Arora et al., 15 Aug 2025)	Theoretical and empirical reevaluation	Critiques SRL gradients and reported gains

2. Formal construction

SRL has two components: tubed skeletonization of the target mask and a class-wise recall term computed on that transformed target. In the original formulation, the hard target $Y$ is first binarized to foreground and background, skeletonized, dilated, and then multiplied by the original labels to recover class information (Kirchhoff et al., 2024).

For $K$-class targets, the preprocessing is:

1. $Y_{\text{bin}} \leftarrow (Y > 0)$
2. $$Y_{\text{skel}} \leftarrow \text{skeletonize}(Y_{\text{bin}})$$
3. $$Y_{\text{skel}} \leftarrow \text{dilate}(Y_{\text{skel}})$$
4. $$Y_{\text{mc-skel}} \leftarrow Y_{\text{skel}} \times Y$$

In the original paper, skeletonization is performed with Zhang–Suen thinning in 2D and 3D medial axis thinning in 3D, while dilation uses a diamond kernel of radius $2$ (Kirchhoff et al., 2024). The result is a tubed skeleton: a thin but slightly thickened centerline representation that preserves class labels.

The training loss augments a generic segmentation loss with a skeleton recall term. In the original notation,

$$\mathcal{L} = \mathcal{L}_{\text{generic}} + w \cdot \mathcal{L}_{\text{SkelRecall}}.$$

Algorithmically, $Y_{\text{mc-skel}}$ is one-hot encoded, and for each class $c$,

$K$0

The class losses are averaged to obtain $K$1 (Kirchhoff et al., 2024). Arora et al. restated the same idea in a compact form:

$K$2

where $K$3 denotes the tubed-skeleton target and $K$4 the predicted class score or probability at pixel $K$5 for class $K$6 (Arora et al., 15 Aug 2025).

Two structural features are notable. First, SRL does not skeletonize predictions online; only the ground truth is transformed. Second, the loss is recall-like rather than overlap-symmetric: it rewards coverage of tubed-skeleton voxels, while precision away from the skeleton is delegated to the generic loss.

3. Connectivity rationale and optimization behavior

The intended rationale is straightforward. Since the skeleton encodes the centerline topology of the target, low predicted probability on skeleton voxels corresponds to broken or missing centerline coverage. Penalizing such failures should favor continuous vessels, roads, cracks, or canals, while the generic loss maintains thickness and overall shape (Kirchhoff et al., 2024).

The tubed skeleton is central to that rationale. By dilating the skeleton with radius $K$7, the supervision is made less brittle to slight centerline offsets: the model need not hit a single-pixel centerline exactly to receive useful gradient. In the original presentation, this tubification is also what makes the method stable enough for multi-class and 3D training (Kirchhoff et al., 2024).

The reevaluation by Arora et al. focused on what SRL actually supervises during optimization. They derived the gradient

$K$8

which implies a constant negative gradient on tubed-skeleton pixels and zero gradient elsewhere (Arora et al., 15 Aug 2025). Written piecewise,

$K$9

On that analysis, SRL does not adapt its gradient to the current prediction quality. A tubed-skeleton true positive with score $Y_{\text{bin}} \leftarrow (Y > 0)$0 and one with score $Y_{\text{bin}} \leftarrow (Y > 0)$1 receive the same SRL gradient; non-skeleton pixels, including false positives, receive none (Arora et al., 15 Aug 2025). This led Arora et al. to argue that SRL functions less like an error-correcting topology loss and more like a fixed bias toward increased foreground probability on tubed-skeleton pixels.

A common misconception is therefore to treat SRL as though it were a symmetric skeleton-overlap loss. It is not. It does not compare predicted and target skeletons directly, and it does not explicitly penalize off-skeleton false positives. The original method relies on the generic loss for those corrections, while the SRL term itself is one-sided recall supervision.

4. Reported efficacy, topology metrics, and efficiency

The proposing paper evaluated SRL on five public datasets spanning 2D and 3D, binary and multi-class segmentation: Roads, DRIVE, Cracks, ToothFairy, and TopCoW. Metrics included Dice, clDice, and absolute Betti number errors for $Y_{\text{bin}} \leftarrow (Y > 0)$2 and $Y_{\text{bin}} \leftarrow (Y > 0)$3, computed on whole volumes rather than random patches in the 3D medical settings (Kirchhoff et al., 2024).

The reported results positioned SRL as competitive with or better than clDice loss across these benchmarks. On Roads, SRL reached Dice $Y_{\text{bin}} \leftarrow (Y > 0)$4, clDice $Y_{\text{bin}} \leftarrow (Y > 0)$5, $Y_{\text{bin}} \leftarrow (Y > 0)$6 error $Y_{\text{bin}} \leftarrow (Y > 0)$7, and $Y_{\text{bin}} \leftarrow (Y > 0)$8 error $Y_{\text{bin}} \leftarrow (Y > 0)$9, with the best values reported for Dice, clDice, and $$Y_{\text{skel}} \leftarrow \text{skeletonize}(Y_{\text{bin}})$$0 error. On DRIVE, it achieved Dice $$Y_{\text{skel}} \leftarrow \text{skeletonize}(Y_{\text{bin}})$$1, clDice $$Y_{\text{skel}} \leftarrow \text{skeletonize}(Y_{\text{bin}})$$2, $$Y_{\text{skel}} \leftarrow \text{skeletonize}(Y_{\text{bin}})$$3 error $$Y_{\text{skel}} \leftarrow \text{skeletonize}(Y_{\text{bin}})$$4, and $$Y_{\text{skel}} \leftarrow \text{skeletonize}(Y_{\text{bin}})$$5 error $$Y_{\text{skel}} \leftarrow \text{skeletonize}(Y_{\text{bin}})$$6, with the best values reported for clDice and both Betti-number errors. On Cracks, SRL reported Dice $$Y_{\text{skel}} \leftarrow \text{skeletonize}(Y_{\text{bin}})$$7 and clDice $$Y_{\text{skel}} \leftarrow \text{skeletonize}(Y_{\text{bin}})$$8, both the best in that comparison, while the Betti errors were close to clDice loss. On ToothFairy, SRL reported Dice $$Y_{\text{skel}} \leftarrow \text{skeletonize}(Y_{\text{bin}})$$9, clDice $$Y_{\text{skel}} \leftarrow \text{dilate}(Y_{\text{skel}})$$0, $$Y_{\text{skel}} \leftarrow \text{dilate}(Y_{\text{skel}})$$1 error $$Y_{\text{skel}} \leftarrow \text{dilate}(Y_{\text{skel}})$$2, and $$Y_{\text{skel}} \leftarrow \text{dilate}(Y_{\text{skel}})$$3 error $$Y_{\text{skel}} \leftarrow \text{dilate}(Y_{\text{skel}})$$4, all best or tied-best. On binary TopCoW, SRL reported Dice $$Y_{\text{skel}} \leftarrow \text{dilate}(Y_{\text{skel}})$$5, clDice $$Y_{\text{skel}} \leftarrow \text{dilate}(Y_{\text{skel}})$$6, $$Y_{\text{skel}} \leftarrow \text{dilate}(Y_{\text{skel}})$$7 error $$Y_{\text{skel}} \leftarrow \text{dilate}(Y_{\text{skel}})$$8, and $$Y_{\text{skel}} \leftarrow \text{dilate}(Y_{\text{skel}})$$9 error $$Y_{\text{mc-skel}} \leftarrow Y_{\text{skel}} \times Y$$0, again the best values in that comparison (Kirchhoff et al., 2024).

The same paper emphasized computational efficiency as a defining property. Averaged over four binary datasets, clDice loss was reported to add about $$Y_{\text{mc-skel}} \leftarrow Y_{\text{skel}} \times Y$$1 extra training time per epoch and about $$Y_{\text{mc-skel}} \leftarrow Y_{\text{skel}} \times Y$$2 extra GPU memory, whereas SRL added about $$Y_{\text{mc-skel}} \leftarrow Y_{\text{skel}} \times Y$$3 training time and about $$Y_{\text{mc-skel}} \leftarrow Y_{\text{skel}} \times Y$$4 VRAM. In that framing, SRL preserved topology-awareness with more than $$Y_{\text{mc-skel}} \leftarrow Y_{\text{skel}} \times Y$$5 reduction in additional computational overhead relative to clDice loss (Kirchhoff et al., 2024).

The multi-class claim was even stronger. On TopCoW with 13 vessel classes, the paper reported Dice $$Y_{\text{mc-skel}} \leftarrow Y_{\text{skel}} \times Y$$6 versus $$Y_{\text{mc-skel}} \leftarrow Y_{\text{skel}} \times Y$$7 for the baseline and clDice metric $$Y_{\text{mc-skel}} \leftarrow Y_{\text{skel}} \times Y$$8 versus $$Y_{\text{mc-skel}} \leftarrow Y_{\text{skel}} \times Y$$9, while clDice loss itself was reported as out of memory on a 40GB NVIDIA A100. SRL, by contrast, was presented as trainable at batch size $2$0, leading the authors to describe it as the first multi-class capable loss function for thin structure segmentation (Kirchhoff et al., 2024).

5. Reassessment, controversy, and limitations

The principal controversy around SRL comes from the 2025 reevaluation by Arora et al., which revisited both theory and experiments using nnU-Net on tubular and non-tubular datasets. Their overall conclusion was that SRL-based segmentation models did not exceed traditional baseline models, and that the original claims were not robustly reproduced (Arora et al., 15 Aug 2025).

On the tubular datasets DRIVE, Roads, and Cracks, the reevaluation found at most mixed gains. For DRIVE, vanilla nnU-Net reported DSC $2$1, clDice $2$2, JSI $2$3, FNR $2$4, and FPR $2$5, while SRL reported DSC $2$6, clDice $2$7, JSI $2$8, FNR $2$9, and FPR $$\mathcal{L} = \mathcal{L}_{\text{generic}} + w \cdot \mathcal{L}_{\text{SkelRecall}}.$$0. For Roads, vanilla reported DSC $$\mathcal{L} = \mathcal{L}_{\text{generic}} + w \cdot \mathcal{L}_{\text{SkelRecall}}.$$1, clDice $$\mathcal{L} = \mathcal{L}_{\text{generic}} + w \cdot \mathcal{L}_{\text{SkelRecall}}.$$2, JSI $$\mathcal{L} = \mathcal{L}_{\text{generic}} + w \cdot \mathcal{L}_{\text{SkelRecall}}.$$3, FNR $$\mathcal{L} = \mathcal{L}_{\text{generic}} + w \cdot \mathcal{L}_{\text{SkelRecall}}.$$4, and FPR $$\mathcal{L} = \mathcal{L}_{\text{generic}} + w \cdot \mathcal{L}_{\text{SkelRecall}}.$$5, whereas SRL reported DSC $$\mathcal{L} = \mathcal{L}_{\text{generic}} + w \cdot \mathcal{L}_{\text{SkelRecall}}.$$6, clDice $$\mathcal{L} = \mathcal{L}_{\text{generic}} + w \cdot \mathcal{L}_{\text{SkelRecall}}.$$7, JSI $$\mathcal{L} = \mathcal{L}_{\text{generic}} + w \cdot \mathcal{L}_{\text{SkelRecall}}.$$8, FNR $$\mathcal{L} = \mathcal{L}_{\text{generic}} + w \cdot \mathcal{L}_{\text{SkelRecall}}.$$9, and FPR $Y_{\text{mc-skel}}$0. For Cracks, vanilla reported DSC $Y_{\text{mc-skel}}$1, clDice $Y_{\text{mc-skel}}$2, JSI $Y_{\text{mc-skel}}$3, FNR $Y_{\text{mc-skel}}$4, and FPR $Y_{\text{mc-skel}}$5, while SRL reported DSC $Y_{\text{mc-skel}}$6, clDice $Y_{\text{mc-skel}}$7, JSI $Y_{\text{mc-skel}}$8, FNR $Y_{\text{mc-skel}}$9, and FPR $c$0 (Arora et al., 15 Aug 2025).

The pattern highlighted in that study was consistent: SRL could slightly reduce false negatives or improve centerline-oriented metrics, but often at the cost of higher false positive rate. Across 15 tubular scores summarized in their analysis, SRL was significantly better in 3 metrics and significantly worse in 3 metrics, with all significant degradations occurring in FPR (Arora et al., 15 Aug 2025). On non-tubular datasets such as BoMBR, Drone, and ACDC, the reevaluation was more negative: out of 15 summarized scores, vanilla was significantly better in 7, and SRL was never clearly superior (Arora et al., 15 Aug 2025).

The same paper also questioned the value of tubed skeletonization itself. In their ablation, using SRL with or without the tubed skeleton transformation changed DSC, clDice, and JSI on DRIVE and Cracks by at most about $c$1–$c$2 points, with negligible and inconsistent changes in FNR and FPR (Arora et al., 15 Aug 2025). This directly challenged the idea that the transformed mask adds substantial additional supervisory structure beyond the original target.

Taken together, these results define the main limitations currently associated with SRL. It depends on ground-truth skeleton quality; it encodes recall more directly than precision; its gradients do not depend on prediction error magnitude; and its benefits appear dataset-dependent rather than universal. A plausible implication is that SRL is best understood as a lightweight connectivity bias, not as a complete topological objective.

6. Related formulations and subsequent directions

A closely related development is the boundary-skeleton weighted loss introduced alongside the Dynamic Snake Upsampling operator for tubular segmentation. That paper did not name its loss SRL, but it explicitly situated its formulation in the same context of clDice, skeleton preservation, and continuity of thin curvilinear structures (Chen et al., 13 May 2025).

Its weighting scheme computes a ground-truth skeleton $c$3 with Zhang–Suen thinning, a boundary set $c$4 with Canny edge detection, and distance fields $c$5 and $c$6. The resulting weight map

$c$7

assigns weight near $c$8 at skeleton pixels and weight near $c$9 at boundary pixels, with continuous interpolation in between (Chen et al., 13 May 2025). Used inside a weighted Dice loss, this yields a skeleton-focused but boundary-aware objective that, unlike explicit SRL, does not require skeletonization of predictions.

The paper explicitly stated that this boundary-skeleton weighted loss is not a pure Skeleton Recall Loss, because it has no explicit skeleton overlap term, but it is “a weighted segmentation loss where skeleton pixels are heavily emphasized,” and it was presented as strongly correlated with improving skeleton recall (Chen et al., 13 May 2025). On DeepCrack, BCE alone reported mIoU $K$00, clDice $K$01, and Assd $K$02; BSWL reported $K$03, $K$04, and $K$05; clDiceLoss alone reported $K$06, $K$07, and $K$08; and clDiceLoss + BSWL reported $K$09, $K$10, and $K$11 (Chen et al., 13 May 2025).

This later line of work suggests a broader lesson about the SRL family of ideas. Topology preservation in thin-structure segmentation is not only a loss-design problem; it is also an architectural and sampling problem. The same paper paired skeleton-focused supervision with Dynamic Snake Upsampling, a geometry-aware upsampler designed to reconstruct features along serpentine paths rather than fixed square neighborhoods, and reported gains in mIoU, clDice, and Assd on DeepCrack and DRIVE (Chen et al., 13 May 2025). A plausible implication is that skeleton-aware supervision is most effective when the network’s feature reconstruction mechanism is also biased toward curvilinear continuity.

In current usage, SRL therefore occupies a specific place in the topology-aware segmentation literature. It remains important because it demonstrated that offline skeleton preprocessing and a simple recall term can dramatically reduce training overhead relative to differentiable skeleton losses, especially in 3D and multi-class regimes (Kirchhoff et al., 2024). At the same time, its later critique established that efficiency does not guarantee superior optimization behavior or superior segmentation quality across datasets (Arora et al., 15 Aug 2025). The resulting consensus is not that skeleton-focused losses are unworkable, but that recall-only formulations must be interpreted carefully, balanced with volumetric supervision, and evaluated against strong baselines with metrics that expose both connectivity and false-positive behavior.