Channel-Coupled Vessel Consistency Loss

• The paper introduces an output-level anatomical consistency loss that fuses arterial, venous, and vessel predictions to enforce nested relations.
• The methodology employs a minimum operator on the fused maps to ensure coherence, particularly at crossing regions and bifurcations.
• Empirical results show significant improvements in accuracy, F1, and mIoU across datasets and varied segmentation backbones.

Channel-Coupled Vessel Consistency Loss, denoted $\mathcal{L}_{C^3}$, is a supervised loss for retinal artery/vein classification in which a network predicts three maps jointly—blood vessel (BV), artery (A), and vein (V)—and the training objective enforces the anatomical dependence among these outputs rather than treating them as three unrelated binary segmentation tasks. In this formulation, artery and vein pixels are subsets of the overall vessel map, crossing pixels require joint support, and uncertain/background regions are handled through the vessel channel. The resulting loss is an output-level anatomical consistency prior built from a fused prediction map defined by the minimum of the relevant predicted channels, and it is optimized together with baseline BCE and an intra-image pixel-level contrastive regularizer (Zeng et al., 31 Jul 2025).

1. Conceptual basis and problem setting

The loss was introduced for retinal artery/vein classification, where segmented vessels must be assigned to artery or vein classes while preserving consistency with the overall vessel tree. The central motivation is that existing methods often treat artery, vein, and overall vessel segmentation as three separate binary tasks, even though these labels are anatomically coupled. This independence permits contradictions that are locally acceptable under per-channel BCE yet visibly implausible in the final triplet of predictions, such as a pixel being strongly predicted as artery but weakly predicted as vessel, a crossing region activating only one vascular subtype, or distal fragments whose artery/vein assignment changes inconsistently along the vessel tree (Zeng et al., 31 Jul 2025).

The loss therefore encodes a structural prior rather than a generic multitask regularizer. Artery $\subseteq$ vessel and vein $\subseteq$ vessel are treated as explicit inclusion relations. Crossing pixels are handled separately because both artery and vein may be present there, while uncertain/background regions are not forced into artery/vein assignments beyond the vessel prediction. This makes the method specific to a multi-label formulation in which the three channels are semantically related but not mutually exclusive.

A useful way to characterize $\mathcal{L}_{C^3}$ is as a supervised fused-map constraint. It does not ask the network merely to predict three correct maps; it asks the network to predict three maps whose joint configuration is anatomically coherent. This suggests a shift from channelwise correctness to channelwise compatibility.

2. Formal definition

The network takes an image $\boldsymbol{X}\in \mathbb{R}^{C\times H\times W}$, extracts encoder features, and predicts a three-channel output

$$\boldsymbol{Y}=d(e(\boldsymbol{X}))=d\left(\left\{\boldsymbol{X}^1,\cdots,\boldsymbol{X}^L\right\}\right),$$

where the channels are $$\boldsymbol{Y}_{BV}, \boldsymbol{Y}_A, \boldsymbol{Y}_V$$ (Zeng et al., 31 Jul 2025).

The total objective is

$$\mathcal{L}_{all}=\mathcal{L}_{BCE}+\lambda_1 \times \mathcal{L}_{C^3} + \lambda_2 \times \mathcal{L}_{intra}.$$

Here $\mathcal{L}_{BCE}$ is the baseline BCE on the original output channels against their labels, $\mathcal{L}_{C^3}$ is the channel-coupled vessel consistency term, and $\subseteq$0 is an intra-image pixel-level contrastive loss.

The key construction is the fused map $\subseteq$1, defined conditionally on the ground-truth artery/vein semantic type: $\subseteq$2 with $\subseteq$3 the predicted maps and $\subseteq$4 the corresponding labels.

The consistency loss is then

$\subseteq$5

with BCE written as

$\subseteq$6

This formulation is neither an equality constraint nor a sum-to-one softmax constraint, and it is not an overlap penalty between channels. Instead, it is an inclusion-style consistency loss implemented through a minimum operator. For an artery pixel, for example, the fused confidence is $\subseteq$7, so the artery branch is considered well supported only when both artery and vessel predictions are high.

3. Optimization behavior and training integration

The loss is architecture-agnostic at the level of principle. The paper frames it as a general loss usable with multiple segmentation backbones rather than as a module tied to a single decoder design. It is applied on RRWNet and also tested on UNet, IterNet, CTFNet, AttUNet, UNet++, and RollingUNet. Training uses PyTorch, Adam optimizer, learning rate $\subseteq$8, $\subseteq$9, batch size $\subseteq$0, and early stopping if validation loss does not decrease for 200 epochs. Preprocessing and augmentation include global contrast enhancement, local intensity normalization, color/intensity perturbation, affine transforms, horizontal flip, and random cutout; input sizes are full resolution for RITE, width 576 for LES-AV, and width 1024 for HRF (Zeng et al., 31 Jul 2025).

The use of $\subseteq$1 has a specific optimization consequence. Although the paper does not provide an explicit derivative expression, the construction implies that BCE on $\subseteq$2 backpropagates most strongly through the branch that is currently the bottleneck under the minimum. On an artery pixel, if $\subseteq$3, the corrective signal acts primarily on the artery branch; if $\subseteq$4, the vessel branch receives the stronger update. At crossing pixels, all three channels can become bottlenecks. This creates cross-branch gradient coupling rather than three isolated per-channel training signals.

The paper studies the weight $\subseteq$5 of $\subseteq$6 over $\subseteq$7. Best settings vary by dataset; RITE and LES-AV often favor $\subseteq$8, whereas HRF often favors $\subseteq$9. The loss is complemented by $\mathcal{L}_{C^3}$0, adapted from SuperCL, which acts on the deepest encoder feature map and uses SLIC-based superpixels to define positive and negative pixel sets. In the paper’s description, $\mathcal{L}_{C^3}$1 operates at output level, while $\mathcal{L}_{C^3}$2 promotes feature-level discrimination.

A notable technical point is that the BCE formula is written in probability form with $\mathcal{L}_{C^3}$3 and $\mathcal{L}_{C^3}$4. This suggests operation on probability maps rather than logits, although the text does not explicitly state a sigmoid layer.

4. Empirical evidence

The clearest isolation of the effect of $\mathcal{L}_{C^3}$5 comes from RRWNet ablations comparing baseline BCE against BCE $\mathcal{L}_{C^3}$6. The reported improvements are as follows (Zeng et al., 31 Jul 2025).

Dataset	Baseline BCE	BCE + $\mathcal{L}_{C^3}$7
RITE Acc. / F1 / mIoU	95.99 / 95.47 / 91.33	96.73 / 96.27 / 92.81
LES-AV Acc. / F1 / mIoU	92.75 / 91.98 / 85.15	95.82 / 95.22 / 90.88
HRF Acc. / F1 / mIoU	97.90 / 97.67 / 95.45	98.27 / 98.07 / 96.20

On RITE, adding $\mathcal{L}_{C^3}$8 alone yields $\mathcal{L}_{C^3}$9 Acc, $\boldsymbol{X}\in \mathbb{R}^{C\times H\times W}$0 F1, and $\boldsymbol{X}\in \mathbb{R}^{C\times H\times W}$1 mIoU, with Sens. increasing from $\boldsymbol{X}\in \mathbb{R}^{C\times H\times W}$2 to $\boldsymbol{X}\in \mathbb{R}^{C\times H\times W}$3 and Spec. from $\boldsymbol{X}\in \mathbb{R}^{C\times H\times W}$4 to $\boldsymbol{X}\in \mathbb{R}^{C\times H\times W}$5. On LES-AV, the gains are larger: $\boldsymbol{X}\in \mathbb{R}^{C\times H\times W}$6 Acc, $\boldsymbol{X}\in \mathbb{R}^{C\times H\times W}$7 F1, and $\boldsymbol{X}\in \mathbb{R}^{C\times H\times W}$8 mIoU, with Sens. $\boldsymbol{X}\in \mathbb{R}^{C\times H\times W}$9 and Spec. $$\boldsymbol{Y}=d(e(\boldsymbol{X}))=d\left(\left\{\boldsymbol{X}^1,\cdots,\boldsymbol{X}^L\right\}\right),$$0. On HRF, the reported gains are $$\boldsymbol{Y}=d(e(\boldsymbol{X}))=d\left(\left\{\boldsymbol{X}^1,\cdots,\boldsymbol{X}^L\right\}\right),$$1 Acc, $$\boldsymbol{Y}=d(e(\boldsymbol{X}))=d\left(\left\{\boldsymbol{X}^1,\cdots,\boldsymbol{X}^L\right\}\right),$$2 F1, and $$\boldsymbol{Y}=d(e(\boldsymbol{X}))=d\left(\left\{\boldsymbol{X}^1,\cdots,\boldsymbol{X}^L\right\}\right),$$3 mIoU, with Sens. $$\boldsymbol{Y}=d(e(\boldsymbol{X}))=d\left(\left\{\boldsymbol{X}^1,\cdots,\boldsymbol{X}^L\right\}\right),$$4 and Spec. $$\boldsymbol{Y}=d(e(\boldsymbol{X}))=d\left(\left\{\boldsymbol{X}^1,\cdots,\boldsymbol{X}^L\right\}\right),$$5.

The paper also reports that the loss improves diverse backbones on RITE, including AttUNet ($$\boldsymbol{Y}=d(e(\boldsymbol{X}))=d\left(\left\{\boldsymbol{X}^1,\cdots,\boldsymbol{X}^L\right\}\right),$$6 F1 / $$\boldsymbol{Y}=d(e(\boldsymbol{X}))=d\left(\left\{\boldsymbol{X}^1,\cdots,\boldsymbol{X}^L\right\}\right),$$7 mIoU), RollingUNet ($$\boldsymbol{Y}=d(e(\boldsymbol{X}))=d\left(\left\{\boldsymbol{X}^1,\cdots,\boldsymbol{X}^L\right\}\right),$$8 F1 / $$\boldsymbol{Y}=d(e(\boldsymbol{X}))=d\left(\left\{\boldsymbol{X}^1,\cdots,\boldsymbol{X}^L\right\}\right),$$9 mIoU), and RRWNet ($$\boldsymbol{Y}_{BV}, \boldsymbol{Y}_A, \boldsymbol{Y}_V$$0 F1 / $$\boldsymbol{Y}_{BV}, \boldsymbol{Y}_A, \boldsymbol{Y}_V$$1 mIoU). This supports the claim that the consistency term is backbone-agnostic rather than RRWNet-specific.

Qualitative findings are aligned with the intended consistency mechanism. Early in training, models using the proposed loss detect more fine micro-vessels. Later in training, they reduce misclassification around crossings and bifurcations. The paper also states that crossing regions are better preserved as white pixels rather than collapsing into veins, and that the fused supervision helps avoid “manifest misclassification errors” while improving micro distal vessel classification.

5. Relation to other vessel-consistency and topology-aware methods

The exact term “Channel-Coupled Vessel Consistency Loss” belongs to the A/V classification setting above, but related vessel-learning literature contains several adjacent formulations that enforce consistency through different objects and different mathematical mechanisms.

A close but distinct example is the cascaded multitask U-Net for vessel segmentation and centerline extraction, where vessel-mask prediction is passed to a second network that predicts the skeleton, and the outputs are tied together through clDice plus task-specific Dice losses. There, the coupling is cross-task and topology-aware, but it is not a standalone channel-consistency penalty between parallel output channels (Rougé et al., 2023).

Another distinct line is uncertainty-guided conservative propagation, which refines vessel logits through a finite-step structured update in logit space. Its consistency mechanism is spatial neighbor coupling and iterative-state stabilization rather than an explicit cross-channel loss (Huang et al., 19 May 2026).

In IVUS lumen/EEM segmentation, GeoCat includes a topology penalty $$\boldsymbol{Y}_{BV}, \boldsymbol{Y}_A, \boldsymbol{Y}_V$$2 that penalizes lumen-outside-EEM violations and a geometry consistency loss supervising diameters, orientations, cross-sectional areas, and plaque burden. This is functionally close to channel coupling because it imposes an inter-channel enclosure relation, but it is not the same fused minimum-map construction used in $$\boldsymbol{Y}_{BV}, \boldsymbol{Y}_A, \boldsymbol{Y}_V$$3 (Chen et al., 17 Jun 2026).

Other vessel-consistency mechanisms are projection- or output-coupled rather than channel-coupled. VAMOS-OCTA defines a vessel-aware multi-axis orthogonal supervision loss for B-scan inpainting, combining vessel-weighted reconstruction with axial and lateral projection consistency to encourage vascular continuity across orthogonal planes (DiSanto et al., 1 Feb 2026). SPOCKMIP adds maximum-intensity projection loss along one or multiple axes to penalize discontinuity of 3D vessel predictions (Radhakrishna et al., 2024). VCC-DSA introduces a vascular consistency regularizer $$\boldsymbol{Y}_{BV}, \boldsymbol{Y}_A, \boldsymbol{Y}_V$$4 between two DSA reconstructions obtained from different mask-live pairings sharing the same live image, thereby distilling motion-invariant vascular structure rather than channelwise inclusion (Ge et al., 12 Apr 2026). A further related direction is topology-aware loss based on morphological closing, which emphasizes broken segments and false bridges by their impact on graph connectivity rather than on per-pixel overlap (Araújo et al., 2021).

Taken together, these works suggest a family resemblance rather than terminological identity. $$\boldsymbol{Y}_{BV}, \boldsymbol{Y}_A, \boldsymbol{Y}_V$$5 is specifically an output-level anatomical consistency prior over nested retinal A/V/BV channels; the other methods couple masks with centerlines, logits with neighbors, lumen with enclosing boundaries, or predictions with projections or alternate reconstructions.

6. Assumptions, limitations, and broader applicability

The method rests on three explicit assumptions: artery and vein are subsets of vessel, crossing pixels can belong to both artery and vein, and uncertain/background pixels should not force artery/vein consistency beyond vessel prediction (Zeng et al., 31 Jul 2025). These assumptions are well aligned with retinal A/V annotation schemes, but they also delimit the regime in which the loss is directly applicable.

Several limitations are explicit. Because the fusion rule depends on label cases $$\boldsymbol{Y}_{BV}, \boldsymbol{Y}_A, \boldsymbol{Y}_V$$6, the loss is supervised and tied to the dataset’s annotation schema; if explicit crossing or uncertain labels are absent, adaptation may be required. The hard $$\boldsymbol{Y}_{BV}, \boldsymbol{Y}_A, \boldsymbol{Y}_V$$7 operator means that only the lowest-confidence channel dominates the fused response at each pixel, which can under-utilize information from non-min branches. The paper also notes that the loss does not explicitly model long-range connectivity or tree topology; it enforces local channel agreement, not graph-level vessel continuity.

These limitations clarify a common misconception. $$\boldsymbol{Y}_{BV}, \boldsymbol{Y}_A, \boldsymbol{Y}_V$$8 is not itself a topology loss in the sense of clDice, persistent-homology objectives, or graph-based path constraints. It is a local anatomical consistency loss over related output channels. This suggests that channel coupling and topology preservation are complementary rather than interchangeable design choices.

The paper further suggests that the construction should generalize to other nested or related segmentation tasks, including organ/substructure segmentation, tumor whole-core-enhancing regions, vessel lumen/wall/whole vessel, and lesion subtype channels constrained by a parent lesion mask. In that sense, Channel-Coupled Vessel Consistency Loss can be understood more broadly as a template for supervising hierarchical label relations directly in prediction space, with the retinal artery/vein/vessel problem providing the canonical formulation (Zeng et al., 31 Jul 2025).