TRACE: Topology-Aware Reconnection via Prediction-Adaptive Connectivity Enforcement for Thin-Structure Segmentation

Junho Moon; Ikbeom Jang

cs.CVOct 15, 2026

TRACE: Topology-Aware Reconnection via Prediction-Adaptive Connectivity Enforcement for Thin-Structure Segmentation

Authors: Junho Moon, Ikbeom Jang

Organizations: Hanyang University, Seoul, Republic of Korea · Hankuk University of Foreign Studies, Yongin, Republic of Korea

Abstract

Thin, elongated structures are particularly sensitive to connectivity errors, as even a few local segmentation mistakes can disrupt otherwise continuous paths. Existing skeleton-based objectives typically supervise fixed centerline locations and do not account for alternative local routes that may restore connectivity. We propose TRACE, a topology-aware, prediction-adaptive objective that uses a target skeleton to define required local connections. For each connection, TRACE identifies the easiest valid reconnection under the current prediction and jointly supervises its bottleneck with the corresponding skeleton point. The supervision thus adapts to the evolving prediction rather than remaining fixed to the centerline. We further introduce a topology-aware skeleton carrier that preserves both foreground and class-specific topology, enabling reliable definition of these connections. Extensive experiments across six 2D and 3D benchmarks show that TRACE improves connectivity and topology while maintaining strong segmentation accuracy with low training overhead. Code will be released upon acceptance.

Figures & tables

Figure 1: Conventional target-skeleton supervision [ 13 ] relies on fixed skeleton locations and can alter the ground-truth topology (a). TRACE preserves it (b), selects the easiest valid reconnection among candidates (c, d), and supervises its bottleneck (d).

Figure 2: Prediction-adaptive local reconnection in TRACE. Step 1) Removing a carrier point exposes neighboring same-class branches that should remain connected. Step 2) Valid local reconnections reaching all exposed branches are considered. Step 3) Candidates are activated in ascending order of centered logit-margin score until a valid reconnection forms; the point activated at this threshold is the supervised bottleneck. The carrier is TASC ( Sec. 3.2 ), numbers indicate

g_{c}(x)

( Sec. 3.3 ), and

\tau

denotes the activation threshold.

Method	DRIVE [ 21 ]				DSCA [ 27 ]
Method	clDice $\uparrow$	$\beta\downarrow$	HD95 $\downarrow$	Dice $\uparrow$	clDice $\uparrow$	$\beta\downarrow$	HD95 $\downarrow$	Dice $\uparrow$
Dice + CE [ 12 ]	81.43 $\pm$ 3.56	115.90 $\pm$ 18.51	4.00 $\pm$ 2.05	82.04 $\pm$ 1.40	87.03 $\pm$ 14.95	62.07 $\pm$ 52.24	49.50 $\pm$ 161.24	86.62 $\pm$ 15.74
+ clDice [ 20 ]	81.97 $\pm$ 3.69	97.80 $\pm$ 27.52	4.00 $\pm$ 2.19	82.22 $\pm$ 1.37	87.71 $\pm$ 12.69	53.81 $\pm$ 47.27	29.01 $\pm$ 111.52	87.25 $\pm$ 13.56
+ Topo-clDice [ 17 ]	81.99 $\pm$ 3.60	82.50 $\pm$ 18.26	3.82 $\pm$ 2.22	82.10 $\pm$ 1.41	— Out of memory —
+ clCE [ 1 ]	81.88 $\pm$ 3.45	106.90 $\pm$ 18.81	4.09 $\pm$ 2.33	82.18 $\pm$ 1.31	87.53 $\pm$ 12.51	65.91 $\pm$ 55.25	41.77 $\pm$ 153.70	87.33 $\pm$ 13.36
+ cbDice [ 19 ]	81.65 $\pm$ 3.62	109.70 $\pm$ 24.70	4.06 $\pm$ 2.22	82.10 $\pm$ 1.37	87.52 $\pm$ 13.28	61.86 $\pm$ 54.68	41.62 $\pm$ 153.59	87.09 $\pm$ 14.00

Table 1: Comparison of training objectives on four 2D thin-structure datasets spanning binary and multiclass tasks under the same nnU-Net setup. Results are mean

\pm

standard deviation over test samples. Bold and underlined values indicate the best and second-best results.

Method	MSD Hepatic Vessel [ 2 ]				TopCoW [ 26 ]
Method	clDice $\uparrow$	$\beta\downarrow$	HD95 $\downarrow$	Dice $\uparrow$	clDice $\uparrow$	$\beta\downarrow$	HD95 $\downarrow$	Dice $\uparrow$
Dice + CE [ 12 ]	67.00 $\pm$ 16.61	40.90 $\pm$ 24.44	39.41 $\pm$ 34.79	58.90 $\pm$ 15.66	86.32 $\pm$ 9.39	0.32 $\pm$ 0.25	8.31 $\pm$ 6.00	80.57 $\pm$ 7.12
+ clDice [ 20 ]	68.73 $\pm$ 16.87	38.57 $\pm$ 22.26	28.09 $\pm$ 25.15	59.70 $\pm$ 16.11	85.49 $\pm$ 6.96	0.36 $\pm$ 0.26	7.97 $\pm$ 5.61	81.20 $\pm$ 5.45
+ Topo-clDice [ 17 ]	68.92 $\pm$ 16.82	35.67 $\pm$ 20.56	23.40 $\pm$ 27.98	62.83 $\pm$ 16.28	— Out of memory —
+ clCE [ 1 ]	68.38 $\pm$ 16.57	32.13 $\pm$ 20.32	28.84 $\pm$ 28.20	60.25 $\pm$ 15.51	86.27 $\pm$ 7.64	0.29 $\pm$ 0.21	7.71 $\pm$ 6.75	80.79 $\pm$ 6.08
+ cbDice [ 19 ]	67.61 $\pm$ 15.87	33.77 $\pm$ 22.43	23.33 $\pm$ 22.54	61.70 $\pm$ 15.96	86.19 $\pm$ 7.56	0.30 $\pm$ 0.28	7.30 $\pm$ 5.36	81.20 $\pm$ 6.76

Table 2: Comparison of training objectives on two 3D vessel datasets spanning binary and multiclass tasks under the same nnU-Net setup. Results are mean

\pm

standard deviation over test samples. Bold and underlined values indicate the best and second-best results.

Figure 3: Qualitative comparison across six 2D and 3D thin-structure datasets. Each row shows the ground truth, an enlarged region, and predictions from the compared methods. Yellow arrows highlight representative breaks, missing branches, and incorrect connections.

Figure 4: Topology preservation and training efficiency across six datasets. Target topology violation rate across deep-supervision scales (top); per-epoch training time and peak GPU memory on an NVIDIA H200 (middle/bottom). OOM denotes out of memory.

Dataset	Method	clDice $\uparrow$	$\beta\downarrow$	HD95 $\downarrow$	Dice $\uparrow$
DeepCrack [ 15 ]	Dice + CE	89.03	6.16	16.46	82.78
	+ clDice [ 20 ]	90.42	5.06	15.75	84.58
	+ SkelRecall [ 13 ]	90.07	4.74	15.68	84.26
	+ TRACE	91.10	3.69	15.04	85.20
DRIVE [ 21 ]	Dice + CE	82.19	88.80	4.56	82.27
	+ clDice [ 20 ]	82.58	73.90	4.04	82.64

Table 3: Backbone-transfer evaluation of TRACE using CS 2 -Net on DeepCrack and DRIVE. Results are averaged over test samples; bold and underlined values indicate the best and second-best results.

Dataset	Method	clDice $\uparrow$	$\beta\downarrow$	HD95 $\downarrow$	Dice $\uparrow$
DRIVE [ 21 ]	Dice + CE w/ SCNP [ 25 ]	80.10	98.20	6.90	81.54
DRIVE [ 21 ]	+ TRACE	81.48	90.20	4.60	81.99
DSCA [ 27 ]	Dice + CE w/ SCNP [ 25 ]	87.25	46.17	29.39	87.40
DSCA [ 27 ]	+ TRACE	88.44	38.47	27.01	88.07

Table 4: Effect of adding TRACE to SCNP on DRIVE and DSCA under the same nnU-Net setup. Results are averaged over test samples; bold values indicate the better result within each dataset.

Dataset	Variant	clDice $\uparrow$	$\beta\downarrow$	HD95 $\downarrow$	Dice $\uparrow$
DRIVE [ 21 ]	DCE [ 12 ]	81.43	115.90	4.00	82.04
	Skel [ 13 ]	81.89	97.00	4.00	82.18
	TASC	82.01	93.40	3.82	82.24
	TASC-R	82.23	86.70	3.58	82.31
	TRACE-U	82.48	82.60	3.51	82.35
	TRACE	82.65	79.30	3.45	82.38

Table 5: Cumulative ablation of TRACE components on DRIVE. Results are averaged over test samples; bold and underlined values indicate the best and second-best results.

Figure 5: Annotation-induced artifacts in TASC. Small isolated regions and local irregularities in the ground-truth masks (arrows) are retained as isolated points or short loops because TASC preserves the annotated topology.

Thin-Structure Segmentation

See all 12 papers

Widest-Path Reachability Fields for Connectivity-Preserving Slender Structure Segmentation
Jul 8, 2026Youcheng Zong, Runda Jia, Minxuan Hu +2Image Segmentation Topology-Preserving Image Segmentation
College of Information Science and Engineering, Northeastern University, Shenyang 110004, China · Changsha Stomatological Hospital, Changsha 410005, China
SEMIR: Topology-Preserving Graph Minors for Thin-Structure Segmentation
Jun 22, 2026Luke James Miller, Yugyung LeeImage Segmentation Thin-Structure Segmentation
University of Missouri-Kansas City, Kansas City MO 64110, USA
Skeleton-Guided Progressive Test-Time Adaptation for Thin Curvilinear Structures
Oct 8, 2026Boa Jang, JunGyu Lee, Gwanho Lee +2Image Segmentation Test-Time Adaptation
Seoul National University · Seoul National University Hospital · Yonsei University +1

Jul 8, 2026J/K move · Enter open · S save

Widest-Path Reachability Fields for Connectivity-Preserving Slender Structure Segmentation

Youcheng Zong, Runda Jia, Minxuan Hu, Weilan Su+1

College of Information Science and Engineering, Northeastern University, Shenyang 110004, China · Changsha Stomatological Hospital, Changsha 410005, China

Image Segmentation Topology-Preserving Image Segmentation Medical Image Segmentation Differentiable Optimization Thin-Structure Segmentation

Open paper AskPDF arXiv

Segmenting slender curvilinear structures such as retinal vessels, cracks, and roads demands topological correctness, as even a single-pixel discontinuity can fragment a continuous network and invalidate downstream analysis. Under standard binary-mask supervision, models optimized for pixel-level overlap frequently produce topologically broken predictions. We trace this to a fundamental mismatch: pixel-wise losses distribute gradients uniformly, yet connectivity hinges on a sparse set of bottleneck pixels. These pixels are vastly outnumbered by thick structures and background, rendering their aggregate gradient contribution negligible. We term this phenomenon topological gradient starvation (TGS). To address it, we propose Widest-Path Reachability Fields (WPRF), a differentiable Max-Min reachability objective that redirects gradient flow to connectivity bottlenecks. The module is plug-and-play, backbone-agnostic, and incurs no inference overhead. WPRF implements a differentiable Max-Min objective via dynamic programming on a domain-restricted graph, coupled with a bottleneck-aware observation term that balances gradient contributions across varying structures. Compared to prior topology-aware losses that rely on post-hoc skeletonization or homology computation, WPRF directly optimizes end-to-end reachability via differentiable Max-Min algebra, enabling gradient flow to concentrate on connectivity bottlenecks without auxiliary structures. We introduce OMVIS, a new oral microvessel segmentation dataset. Experiments across nine architectures and six datasets validate the bottleneck-focused gradient routing mechanism. WPRF improves 87% of experiments with fixed hyperparameters and achieves clDice gains of 7.2 percentage points on structurally fragile datasets.

Abstract

Thin-Structure Segmentation

Explore similar work

Widest-Path Reachability Fields for Connectivity-Preserving Slender Structure Segmentation

SEMIR: Topology-Preserving Graph Minors for Thin-Structure Segmentation

Skeleton-Guided Progressive Test-Time Adaptation for Thin Curvilinear Structures