Airway Structure Awareness Loss

• Airway structure awareness loss is a family of objective functions designed to enforce continuity, completeness, and anatomical plausibility in airway segmentation.
• These techniques address challenges like class imbalance, fragmented distal bronchioles, and incomplete annotations by integrating centerline, connectivity, and boundary information.
• Methodologies such as gradient rebalancing, curriculum learning, and weak supervision improve structural metrics in CT and bronchoscopy applications.

Airway structure awareness loss denotes a family of objective functions and closely related supervision mechanisms that optimize for continuity, completeness, connectivity, and anatomical plausibility of airway predictions, rather than only voxel-wise overlap. In airway CT segmentation, these formulations are motivated by discontinuity in peripheral bronchioles, severe class imbalance between foreground and background, intra-class imbalance between large and small branches, incomplete annotations, and heterogeneity across centres and disease cohorts. Closely related ideas also appear in bronchoscopy and bronchoscopic depth estimation, where the relevant structural prior is not a full airway tree but the geometric organization of airway orifices or the lumen itself (Tang et al., 2022, Zheng et al., 2020, Wang et al., 2023, Zhang et al., 15 Sep 2025).

1. Motivation and problem setting

Airway segmentation differs from many organ segmentation tasks because the principal failure mode is often topological rather than regional. Several studies state that small distal airways, peripheral bronchioles, and higher-generation bronchioles are easily missed, fragmented, or disconnected, even when global overlap remains acceptable. One paper explicitly states that airway segmentation focuses on topology rather than pure pixel-wise accuracy, while another identifies discontinuity in the delineation of peripheral bronchioles as a direct obstacle to clinical deployment. These problems are compounded by low contrast, pathological abnormalities, blurred CT detail, and severe imbalance across airway generations (Wang et al., 2022, Tang et al., 2022, Yang et al., 2024).

The optimization difficulty has been analyzed at the gradient level. “Alleviating Class-wise Gradient Imbalance for Pulmonary Airway Segmentation” attributes the poor parsing of distal small airways to gradient erosion and dilation of neighborhood voxels during back-propagation. When the ratio of foreground gradient to background gradient is small while class imbalance is local, the foreground gradients can be eroded by their neighborhoods, progressively increasing noise in the gradient flow and limiting the learning of small structures. A separate line of work emphasizes that incomplete labeling is also structural: one study notes that most existing airway datasets are incompletely labeled and that manual or semi-automatic annotation can require up to 7 or 3 hours per case, which in turn constrains the completeness of computer-segmented airway trees (Zheng et al., 2020, Wang et al., 2023).

2. Centerline-, skeleton-, and breakage-sensitive objectives

A dominant strategy is to encode airway topology through centerlines or skeletons. In “Adversarial Transformer for Repairing Human Airway Segmentation,” the refinement network combines a voxel-wise term, a continuity term, a Dice/clDice hybrid, and an adversarial term at each supervised layer,

$$L_j = \alpha L_1 + \beta L_{CCF} + \gamma L_D + \delta L_{cGAN},$$

with the continuity and completeness F-score loss

$$L_{CCF} = 1 - \frac{\sum X \cdot Y_{CL}}{\sum Y_{CL}},$$

and the topology-aware hybrid

$$L_D = (1-\alpha)(1-\mathrm{Dice}) + \alpha(1-\mathrm{clDice}).$$

Here, clDice emphasizes centerline overlap, while the patch-scale discriminator penalizes locally implausible or discontinuous branches. The same paper states that patch-scale discrimination and centreline objective functions are effective in detecting discontinuities and missing bronchioles (Tang et al., 2022).

“Fuzzy Attention Neural Network to Tackle Discontinuity in Airway Segmentation” makes the continuity term even more explicit through the Jaccard Continuity and Accumulation Mapping loss,

$$L_\text{JCAM} = \alpha L_\mathcal{J}(X,Y) + \beta L_C(X,Y_{CL}) + \varphi L_{CE}(X,Y) + \gamma L_{LAM}(X,Y) + \delta L_{nLAM}(X,Y),$$

where $L_C$ measures prediction overlap with the skeletonized centerline of the ground truth, and $L_{LAM}$ and $L_{nLAM}$ compare axial projections to encourage volumetric consistency and emphasize small structures. The same work proposes the CCF-score,

$$\mathrm{CCF}_s = (1+\omega^2)\frac{J \times C}{\omega^2 J + C},$$

with $\omega$ set to 0.9, to jointly evaluate continuity and completeness (Nan et al., 2022).

Other formulations isolate branch breakage more aggressively. “BREAK: Bronchi Reconstruction by gEodesic transformation And sKeleton embedding” introduces a breakage-sensitive regularization term

$L_{BS} = 1 - \frac{1}{M+\epsilon}\sum_i p_i c_i,$

which depends only on centerline voxels and is therefore highly sensitive to missed or disconnected branches regardless of branch thickness. In the fine-tune branch, the overall loss is

$$L_{CCF} = 1 - \frac{\sum X \cdot Y_{CL}}{\sum Y_{CL}},$$0

“NaviAirway” adopts a related but differentiable skeleton-space formulation,

$$L_{CCF} = 1 - \frac{\sum X \cdot Y_{CL}}{\sum Y_{CL}},$$1

where Skeleton Dice Loss optimizes overlap of semi-skeletonized prediction and label, and Penalty Dice Loss amplifies low-confidence, bronchiole-weighted errors. In both works, structure awareness is achieved by making breaks in thin branches disproportionately costly during optimization (Yu et al., 2022, Wang et al., 2022).

3. Gradient imbalance, anatomy-aware decomposition, and curriculum design

A second family of airway structure awareness losses addresses the fact that topology errors are often induced by imbalance rather than by the absence of a structural term per se. “Alleviating Class-wise Gradient Imbalance for Pulmonary Airway Segmentation” proposes General Union Loss,

$$L_{CCF} = 1 - \frac{\sum X \cdot Y_{CL}}{\sum Y_{CL}},$$2

where $$L_{CCF} = 1 - \frac{\sum X \cdot Y_{CL}}{\sum Y_{CL}},$$3 is a distance-based weight linked to the airway centerline, $$L_{CCF} = 1 - \frac{\sum X \cdot Y_{CL}}{\sum Y_{CL}},$$4 controls focal strength, and $$L_{CCF} = 1 - \frac{\sum X \cdot Y_{CL}}{\sum Y_{CL}},$$5 adapt the recall–precision tradeoff. The key claim is that the loss allocates more gradient to misclassified or uncertain airway voxels and gives higher weight to small or peripheral branches through centerline-distance weighting. This directly targets both inter-class imbalance and intra-class imbalance between large and small airways (Zheng et al., 2020).

“Accurate Airway Tree Segmentation in CT Scans via Anatomy-aware Multi-class Segmentation and Topology-guided Iterative Learning” decomposes the airway into three anatomical classes: large branches $$L_{CCF} = 1 - \frac{\sum X \cdot Y_{CL}}{\sum Y_{CL}},$$6, medium branches $$L_{CCF} = 1 - \frac{\sum X \cdot Y_{CL}}{\sum Y_{CL}},$$7, and small branches $$L_{CCF} = 1 - \frac{\sum X \cdot Y_{CL}}{\sum Y_{CL}},$$8. The multi-class loss is the sum of segmentation losses over these three subspaces, and the full objective further adds General Union Loss with $$L_{CCF} = 1 - \frac{\sum X \cdot Y_{CL}}{\sum Y_{CL}},$$9. This anatomy-aware decomposition is paired with topology-guided iterative self-learning, including a breakage attention map

$$L_D = (1-\alpha)(1-\mathrm{Dice}) + \alpha(1-\mathrm{clDice}).$$0

and normalized attention

$$L_D = (1-\alpha)(1-\mathrm{Dice}) + \alpha(1-\mathrm{clDice}).$$1

to reconnect breaking branches in pseudo-label refinement. The paper frames this as a way to segment toward the complete airway tree despite incomplete reference labels (Wang et al., 2023).

A curriculum-based variant appears in “Progressive Curriculum Learning with Scale-Enhanced U-Net for Continuous Airway Segmentation.” Its pipeline has three stages: extracting main airways, identifying small airways, and repairing discontinuities. The third stage introduces an Adaptive Topology-Responsive Loss; the detailed formulation is a weighted Breakage-Aware Loss focused on airway centerline voxels,

$$L_D = (1-\alpha)(1-\mathrm{Dice}) + \alpha(1-\mathrm{clDice}).$$2

with hybrid stage-three objective

$$L_D = (1-\alpha)(1-\mathrm{Dice}) + \alpha(1-\mathrm{clDice}).$$3

The adaptive weight combines local-imbalance and breakage-aware components, so the curriculum and the loss are aligned: first separate scales, then repair topology (Yang et al., 2024).

4. Connectivity prediction and boundary emphasis

Some methods replace centerline overlap by explicit local connectivity modeling. “AirwayNet: A Voxel-Connectivity Aware Approach for Accurate Airway Segmentation Using Convolutional Neural Networks” converts binary segmentation into 26 directional connectivity tasks in a $$L_D = (1-\alpha)(1-\mathrm{Dice}) + \alpha(1-\mathrm{clDice}).$$4 neighborhood. For each voxel, the network predicts a 26-dimensional binary vector indicating whether that voxel is connected to each immediate neighbor. The loss is the average Dice loss across the 26 connectivity channels,

$$L_D = (1-\alpha)(1-\mathrm{Dice}) + \alpha(1-\mathrm{clDice}).$$5

The method further concatenates lung distance map and voxel coordinates as semantic context and enforces bidirectional consistency in post-processing, so connectivity is learned both as supervision target and as a structural constraint on candidate generation (Qin et al., 2019).

A different direction is to emphasize the airway boundary rather than the centerline. “Boundary-Emphasized Weight Maps for Distal Airway Segmentation” defines Boundary-Emphasized Loss as a weighted non-linear extension of Root Tversky loss,

$$L_D = (1-\alpha)(1-\mathrm{Dice}) + \alpha(1-\mathrm{clDice}).$$6

with the weight map

$$L_D = (1-\alpha)(1-\mathrm{Dice}) + \alpha(1-\mathrm{clDice}).$$7

and soft breakage term

$$L_D = (1-\alpha)(1-\mathrm{Dice}) + \alpha(1-\mathrm{clDice}).$$8

This formulation is explicitly described as differing from centerline-based approaches: it prioritizes boundary voxels to reduce misclassification, improve topology, and enhance structural consistency, especially on distal airway branches. A plausible implication is that the field contains two complementary geometric emphases—centerline integrity and boundary fidelity—rather than a single canonical definition of structural awareness (Keshavarzi et al., 28 Feb 2025).

5. Beyond explicit topological loss: architecture, weak supervision, and depth geometry

Not all structure-aware airway methods rely on a dedicated topological loss. “Topology-Aware Wavelet Mamba for Airway Structure Segmentation in Postoperative Recurrent Nasopharyngeal Carcinoma CT Scans” states that topology is enforced implicitly through architectural design, not via a dedicated loss. The model uses Dice loss plus Cross-Entropy loss,

$$L_D = (1-\alpha)(1-\mathrm{Dice}) + \alpha(1-\mathrm{clDice}).$$9

while topology awareness is induced by SnakeVSS, Wavelet-based Mamba Blocks, and spatial and channel attention. SnakeVSS uses serpentine scan patterns to follow curvilinear anatomical paths, and WMB combines low-frequency global context with high-frequency boundary detail. The paper explicitly notes that it does not incorporate an explicit topological loss such as Betti number matching, persistent homology, or connectivity constraints (Huang et al., 20 Feb 2025).

Weakly supervised bronchoscopy provides another contrast case. “Weakly Supervised Airway Orifice Segmentation in Video Bronchoscopy” does not introduce a novel airway-specific loss; instead, structure awareness is embedded in the labels. A depth-image pipeline combining $$L_\text{JCAM} = \alpha L_\mathcal{J}(X,Y) + \beta L_C(X,Y_{CL}) + \varphi L_{CE}(X,Y) + \gamma L_{LAM}(X,Y) + \delta L_{nLAM}(X,Y),$$0-means clustering and a compact marker-based watershed algorithm generates binary and instance airway segmentation maps, which then serve as weak supervision for a shallow CNN trained on RGB images. The corresponding structure-sensitive evaluation metric is the Average Minimum Centroid Distance,

$$L_\text{JCAM} = \alpha L_\mathcal{J}(X,Y) + \beta L_C(X,Y_{CL}) + \varphi L_{CE}(X,Y) + \gamma L_{LAM}(X,Y) + \delta L_{nLAM}(X,Y),$$1

which measures localization of airway orifices rather than contour overlap alone (Keuth et al., 2022).

In bronchoscopic depth estimation, structure awareness becomes a geometric prior on disparity. “BREA-Depth: Bronchoscopy Realistic Airway-geometric Depth Estimation” extracts an airway lumen mask by thresholding grayscale bronchoscopy images,

$$L_\text{JCAM} = \alpha L_\mathcal{J}(X,Y) + \beta L_C(X,Y_{CL}) + \varphi L_{CE}(X,Y) + \gamma L_{LAM}(X,Y) + \delta L_{nLAM}(X,Y),$$2

computes mean disparity inside and outside the mask,

$$L_\text{JCAM} = \alpha L_\mathcal{J}(X,Y) + \beta L_C(X,Y_{CL}) + \varphi L_{CE}(X,Y) + \gamma L_{LAM}(X,Y) + \delta L_{nLAM}(X,Y),$$3

and penalizes violations of the anatomical prior that the lumen should be deeper than non-lumen regions,

$$L_\text{JCAM} = \alpha L_\mathcal{J}(X,Y) + \beta L_C(X,Y_{CL}) + \varphi L_{CE}(X,Y) + \gamma L_{LAM}(X,Y) + \delta L_{nLAM}(X,Y),$$4

The full objective adds this term to adversarial, cycle-consistency, and identity losses. This extends airway structure awareness loss from volumetric tree segmentation to monocular depth estimation (Zhang et al., 15 Sep 2025).

6. Evaluation criteria and reported effects

The evaluation of airway structure awareness losses is itself structure-aware. Common metrics include Dice and IoU for global overlap, but airway-specific studies repeatedly emphasize Detected Length Ratio, Detected Branch Ratio, Airway Missing Ratio, tree length detection, branch detection, continuity indices, HD95, and task-specific structure metrics such as CCF-score, AMCD, DepthCon, and LocalAccu. This reflects a recurrent claim across the literature: high overlap does not guarantee continuous, anatomically plausible airways or realistic bronchoscopic depth (Tang et al., 2022, Nan et al., 2022, Keuth et al., 2022, Zhang et al., 15 Sep 2025).

The reported gains are typically largest on structural metrics. The adversarial refinement network of (Tang et al., 2022) reports more than a 15% rise in detected length ratio and detected branch ratio, with best-performing settings including BAS DLR $$L_\text{JCAM} = \alpha L_\mathcal{J}(X,Y) + \beta L_C(X,Y_{CL}) + \varphi L_{CE}(X,Y) + \gamma L_{LAM}(X,Y) + \delta L_{nLAM}(X,Y),$$5, DBR $$L_\text{JCAM} = \alpha L_\mathcal{J}(X,Y) + \beta L_C(X,Y_{CL}) + \varphi L_{CE}(X,Y) + \gamma L_{LAM}(X,Y) + \delta L_{nLAM}(X,Y),$$6, AMR $$L_\text{JCAM} = \alpha L_\mathcal{J}(X,Y) + \beta L_C(X,Y_{CL}) + \varphi L_{CE}(X,Y) + \gamma L_{LAM}(X,Y) + \delta L_{nLAM}(X,Y),$$7; Fibrosis DLR $$L_\text{JCAM} = \alpha L_\mathcal{J}(X,Y) + \beta L_C(X,Y_{CL}) + \varphi L_{CE}(X,Y) + \gamma L_{LAM}(X,Y) + \delta L_{nLAM}(X,Y),$$8, DBR $$L_\text{JCAM} = \alpha L_\mathcal{J}(X,Y) + \beta L_C(X,Y_{CL}) + \varphi L_{CE}(X,Y) + \gamma L_{LAM}(X,Y) + \delta L_{nLAM}(X,Y),$$9, AMR $L_C$0; and COVID-19 DLR $L_C$1, DBR $L_C$2, AMR $L_C$3. The JCAM-based fuzzy attention network of (Nan et al., 2022) raises BAS DBR from $L_C$4 in the baseline 3D U-Net to $L_C$5 in the full method and CCF-score from $L_C$6 to $L_C$7; on COVID-19 it reports DLR $L_C$8, DBR $L_C$9, CCF-score $L_{LAM}$0; on pulmonary fibrosis, DLR $L_{LAM}$1, DBR $L_{LAM}$2, CCF-score $L_{LAM}$3. General Union Loss in (Zheng et al., 2020) reaches branch detected rate $L_{LAM}$4, length detected rate $L_{LAM}$5, precision $L_{LAM}$6 on EXACT’09, and length detected $L_{LAM}$7, branch detected $L_{LAM}$8, precision $L_{LAM}$9 on the Binary Airway Segmentation Dataset.

Comparable patterns appear in later work. The anatomy-aware multi-class and topology-guided iterative framework of (Wang et al., 2023) ranks 1st in both EXACT’09 and ATM’22 and reports at least $L_{nLAM}$0 more detected tree length and $L_{nLAM}$1 more tree branches than previous leading approaches while maintaining similar precision. The progressive curriculum method of (Yang et al., 2024) reports ATM22 TD $L_{nLAM}$2 and BD $L_{nLAM}$3, while removing the weighted Breakage-Aware Loss lowers TD from $L_{nLAM}$4 to $L_{nLAM}$5 and BD from $L_{nLAM}$6 to $L_{nLAM}$7. AirwayNet reports DSC $L_{nLAM}$8 and TPR $L_{nLAM}$9, with ablations showing that removing connectivity modeling drops DSC to $$\mathrm{CCF}_s = (1+\omega^2)\frac{J \times C}{\omega^2 J + C},$$0 and TPR to $$\mathrm{CCF}_s = (1+\omega^2)\frac{J \times C}{\omega^2 J + C},$$1 (Qin et al., 2019). BEL improves over GUL by $$\mathrm{CCF}_s = (1+\omega^2)\frac{J \times C}{\omega^2 J + C},$$2 DLR and $$\mathrm{CCF}_s = (1+\omega^2)\frac{J \times C}{\omega^2 J + C},$$3 DBR on AIIB23, and by $$\mathrm{CCF}_s = (1+\omega^2)\frac{J \times C}{\omega^2 J + C},$$4 DLR and $$\mathrm{CCF}_s = (1+\omega^2)\frac{J \times C}{\omega^2 J + C},$$5 DBR on ATM22, although IoU, precision, and leakage-related measures can be slightly worse, indicating a topology-versus-overlap tradeoff (Keshavarzi et al., 28 Feb 2025). TopoWMamba reaches mean Dice $$\mathrm{CCF}_s = (1+\omega^2)\frac{J \times C}{\omega^2 J + C},$$6 on NPCSegCT and trachea Dice $$\mathrm{CCF}_s = (1+\omega^2)\frac{J \times C}{\omega^2 J + C},$$7 on SegRap 2023, with the lowest reported HD95 values in those comparisons (Huang et al., 20 Feb 2025). In bronchoscopic depth estimation, BREA-Depth reports DepthCon $$\mathrm{CCF}_s = (1+\omega^2)\frac{J \times C}{\omega^2 J + C},$$8 and LocalAccu $$\mathrm{CCF}_s = (1+\omega^2)\frac{J \times C}{\omega^2 J + C},$$9 with the airway structure loss, versus DepthCon $\omega$0 and LocalAccu $\omega$1 without it, showing that airway structure awareness can be quantified even when the target is depth rather than segmentation (Zhang et al., 15 Sep 2025).

Taken together, the literature does not present a single canonical airway structure awareness loss. Instead, it presents a technically coherent family of formulations: centerline-aware, skeleton-aware, connectivity-aware, boundary-aware, anatomy-aware, breakage-aware, curriculum-aware, and geometry-aware. What unifies them is the optimization target: preserving the connected, fine-scale, clinically relevant structure of the airway system under severe imbalance, annotation incompleteness, and modality-specific ambiguity.