A self-supervised depth-aware method for pose optimization in hybrid bronchoscopic navigation

Abstract

Pose optimization is essential for aligning bronchoscopic views with preoperative CT scans in hybrid vision–electromagnetic navigation systems. It helps eliminate the discrepancies between the virtual and actual bronchoscope positions in the navigation process. However, a large modality gap between virtual (CT-rendered) and real bronchoscopic scenes introduces appearance and scale ambiguities that hinder robust pose estimation. This paper presents a self-supervised pose estimation method, named Depth-aware Attention Pose Network (DaAPNet). In particular, DaAPNet integrates a Depth-aware Attention module to resolve structural ambiguities by leveraging depth information to guide attention towards geometrically consistent regions, such as bronchial bifurcations. To further suppress unreliable appearance cues, an entropy-based uncertainty-weighted masking mechanism dynamically attenuates low-confidence regions in the attention process. A dedicated scale prediction module further enforces geometric consistency to recover cross-modality scale factor, while a pose consistency loss promotes temporal stability. Extensive experiments on virtual and phantom bronchus datasets show that DaAPNet achieves improved estimated performance. Qualitative results indicate that it effectively mitigates appearance ambiguity by capturing clear representations of bronchial bifurcations. Quantitatively, it restores scale consistency along the forward direction, reducing translation error by 35.99%.

Introduction

Lung cancer remains a leading cause of global cancer mortality¹. The prognosis for patients is significantly improved when pulmonary lesions are detected and diagnosed at an early stage². Transbronchial needle aspiration (TBNA)³ is a common biopsy technique for early diagnosis. This procedure is performed under bronchoscopic guidance to access lymph nodes for biopsy. The variations in lung conformation between the preoperative CT scan and the intraoperative ventilated lung cause a misalignment between the virtual camera location and the real camera position⁴. This misalignment manifests as a visual divergence between the real bronchoscopic view and the CT-rendered camera view, creating uncertainty in identifying the correct route for physicians. Therefore, a robust bronchoscopic navigation system is critical to the success of TBNA.

Bronchoscopic navigation systems have attracted significant research interest for providing real-time surgical guidance^5–7. They are mainly classified into electromagnetic (EM) navigation, vision-based navigation, and hybrid navigation. In electromagnetic navigation bronchoscopy (ENB)⁸, a virtual 3D model of the bronchi is created from the patient’s chest CT scans using image segmentation and 3D reconstruction. This model provides anatomical reference and path planning⁹ for navigation. During navigation, doctors determine the bronchoscope’s position by observing real-time electromagnetic tracking data displayed on the virtual 3D model. However, it is highly susceptible to disturbances such as respiratory motion and changes in body posture¹⁰, making it particularly challenging for inexperienced operators. Vision-based navigation bronchoscopy (VNB)^11–14 uses real-time images captured by the bronchoscope to perform localization through computer vision and image processing methods. Instead of relying on external sensors, VNB analyzes anatomical features, or optical flow in the images to help determine the bronchoscope’s position within the airways. However, because the pose from the previous frame is used as the initial estimate for the current frame, occlusion in the previous frame can cause a sudden shift in the estimated pose, negatively impacting the navigation results in subsequent frames. Therefore, hybrid navigation^15,16 has gained increasing attention. It typically uses EM for coarse pose estimation and visual modules for fine pose alignment. For instance, Liu et al.¹⁵ employed swarm intelligence to refine pose estimation based on the initial ENB, enabling accurate alignment between the bronchoscopic views from the virtual CT model and the real bronchus.

The hybrid navigation system faces two challenges, as shown in Fig. 1. The first challenge is appearance ambiguity, caused by texture and illumination differences, which undermines the reliability of vision-based localization. It motivates the integration of depth estimation networks, which have demonstrated strong geometric perception capabilities in medical imaging^17,18. Consequently, monocular depth estimation has been applied to bronchoscopic images to support more robust pose estimation^15,19. Their training heavily relies on ground truth (GT) depth maps, which are difficult to obtain in real bronchial environments due to hardware limitations. Conventional depth sensors (e.g., structured light or Time-of-Flight) require specific imaging distances ()^20,21, which are not feasible in the confined anatomy of the bronchial airways. This data scarcity has motivated the adoption of self-supervised learning strategies, such as Monodepth2²², SfMLearner²³, and LiteMono²⁴, which learn depth from monocular video by minimizing a photometric reconstruction loss without the need for GT depth maps.

Fig. 1.

Overview of the proposed hybrid navigation pipeline for bronchoscopic procedures. The 6-DoF pose represents the bronchoscope pose measured by the electromagnetic (EM) navigation system, and the corresponding video image is captured. In the CT-based virtual bronchial model, represents an initial camera pose used to render the virtual image. DaAPNet estimates the relative pose transformation between the virtual and real views, which is then used to refine the initial pose , yielding the optimized pose .

Furthermore, the second challenge arises from scale ambiguity. Monocular depth estimation networks predict depth only up to an unknown scale factor because a single image does not contain absolute metric information²⁵. So, multiplying the entire depth map by any positive constant yields an equally valid output. Consequently, while depth maps are internally coherent within each modality, their scales differ across modalities, leading to scale ambiguity. This ambiguity is especially pronounced along the z-axis, since forward translation dominates in the tubular environment and lateral translations are limited. Although existing methods^15,19,26 enhance robustness to blur and visual artifacts, they do not consider the scale mismatch across modalities.

These depth-enhanced methods^15,19 treat depth maps as direct inputs for pose estimation without modeling depth reliability. In contrast, we design the depth-aware attention module (DaA) based on attention mechanism²⁷ to learn robust structural cues from cross-modality depth maps, which are incorporated into the pose estimation process. This enables the network to focus on reliable bifurcation regions, thereby mitigating the impact of cross-modality appearance ambiguity. We also introduce a scale prediction head to address the forward-motion scale ambiguity inherent in hybrid bronchoscopic navigation. Together, the depth-aware attention and the scale prediction are designed to handle these specific challenges. Furthermore, we leverage self-supervised frameworks²², which do not require ground truth supervision. Accordingly, we propose a self-supervised pose estimation method, Depth-aware Attention Pose Network (DaAPNet), as illustrated in Fig. 2. The main contributions are summarized as follows:

• We introduce a Depth-aware Attention module that leverages depth information to focus on robust structural cues, such as bronchial bifurcations, mitigating appearance ambiguity. An entropy-based uncertainty-weighted masking mechanism further suppresses unreliable appearance cues by attenuating low-confidence regions during attention computation.

• A dedicated scale prediction module recovers cross-modality scale factor by enforcing geometric consistency between depth maps from different modalities. Additionally, a pose consistency loss ensures temporal coherence across consecutive frames, promoting stable pose estimation.

• Extensive experiments on virtual and phantom bronchus datasets show that DaAPNet achieves improved estimated performance.

Fig. 2.

Overview of the self-supervised pose estimation method—DaAPNet.

Related work

Image-feature-based navigation methods

Traditional image-feature-based methods such as SIFT²⁸ and visual SLAM²⁹ have also been applied to extract and match feature points of bronchial lumens for real-time navigation. Luo et al.³⁰ extract structural patches from video and virtual images and then employ the enhanced particle swarm algorithm and adaptive differential evolution³¹ for pose optimization. Soper et al.³² convert video and virtual images into the pq space, where p and q approximate the 3D surface gradients and in the camera coordinate system, and subsequently adopt the CONDOR optimization algorithm. Sganga et al.³³ leverage ResNet-34 backbones to extract visual features from bronchoscope camera images and simulated data to perform frame-to-frame pose refinement. Gu et al.³⁴ propose a visual kinematic interaction (VKI) method that utilizes a visual similarity network (VSN) to extract modality-invariant features representing bifurcation structures and modality-relevant features describing surface textures and imaging artifacts. While image-feature-based methods can achieve frame-to-frame pose estimation, they often struggle in bronchoscopic scenarios due to illumination variations and texture sparsity, motivating the integration of depth information to provide more robust spatial information for pose estimation.

Depth-enhanced navigation methods

Compared with 2D image features, depth maps provide more robust spatial information. Shen et al.³⁵ obtain depth maps of video and virtual images using shape-from-shading (SFS) and a perspective-based method, and subsequently apply the Powell optimization algorithm for pose estimation. Building on this idea, Shen et al.¹⁹ propose a context-aware depth estimation network based on conditional GANs to alleviate image artifacts in video frames, followed again by Powell optimization for registration. Banach et al.¹¹ propose the 3cGAN network to perform style transfer and depth estimation, where the predicted depth maps are converted into point clouds and registered to a CT bronchial model via ICP for pose optimization. More recently, Liu et al.²⁶ combine structural-depth features with boundary constraints to refine continuous-frame pose estimation. Another study by Liu et al.¹⁵ introduce a two-stage pose optimization method that incorporates spatial geometric awareness derived from depth maps, leveraging surface normal and gradient constraints to improve robustness in blurred or degraded scenes.

Methods

DaAPNet overview

Fig. 2 illustrates the proposed DaAPNet, which comprises a DepthNet and a Depth-aware Attention PoseNet. DepthNet estimates depths from two inputs: a virtual image () acquired by the simulated camera, and a video image () captured by a real bronchoscopic camera. Depth-aware Attention PoseNet takes an image pair and their corresponding estimated depth maps as input and predicts the 6-DoF relative pose transformation between the two camera views, denoted as . is used to optimize the pose of simulated camera. This optimization ensures visual consistency between the real camera view and the simulated camera view, thereby facilitating accurate identification of the correct route by physicians. For clarity, we summarize the notations used in this work in Table 1.

Table 1.

Summary of notations.

Notation	Description	Acquisition
	6-DOF pose of the real bronchoscopic camera	Acquired from the EM tracking system
	6-DOF pose of the simulated camera	Rendered from the virtual bronchial model
	6-DOF relative pose transformation	Predicted by DaAPNet
	6-DOF pose of the simulated camera	Acquired after optimization
	Video image	Acquired by a real bronchoscopic camera at
	Original Virtual image	Acquired by a simulated camera at
	Optimized Virtual image	Acquired by a simulated camera at
	Depth map of	Predicted by DepthNet
	Depth map of	Predicted by DepthNet
	Attention mask of	Predicted by DaA
	Attention mask of	Predicted by DaA
	Scale factor for z-axis	Predicted by the Scale Prediction module
	Confidence weight	Predicted by Uncertainty-weighted Map in DaA

DepthNet

DepthNet adopts an encoder-decoder architecture with skip connections to enhance feature fusion. The encoder is based on ResNet-18³⁶ with the fully connected layers removed, while the decoder follows the design of Monodepth2²². The sigmoid output σ of the decoder is converted to depth using the formula where the constants a and b are chosen to constrain the depth values within a range of 0.005 to 200 units. Both the images, and are passed through the same DepthNet to estimate the depth maps and . Each depth map has the shape (B, 1, H, W), where B is the batch size, H and W denote the height and width, respectively.

Depth-aware attention PoseNet

In the Depth-aware Attention PoseNet, and are fed into the Depth-aware Attention (DaA) module, as shown in Fig. 3. This module utilizes a depth-guided mechanism to generate attention masks and . In addition, the module predicts a cross-modality scale factor based on features extracted from .

Fig. 3.

Overview of the proposed DaA’s architecture.

The DaA module is designed with a depth-guided cross-attention mechanism to focus on regions that are structurally consistent across different modalities. Specifically, the input depths and are passed through a shared depth encoder composed of three convolutional layers to extract depth features and , both with shape (B, C, H, W), where C is the number of feature channels. Here, is used as the query. serves as the key and value in the attention mechanism²⁷. Informative structures in bronchoscopic images usually appear in regions with significant depth variations. To capture them, DaA divides and into N = (H//h) × (W//w) non-overlapping windows, where each window is of size h × w (h, w = 7). These windows are then reshaped into tensors of shape , denoted as Q, K and V. And the local cross-attention is computed within each window to generate attention-enhanced features, which are reshaped back to the original spatial dimensions. This process yields the depth-guided attention feature , computed using the Dot-Product Attention formula in Equation (1).

1

To generate a pixel-level attention mask, DaA designs a lightweight self-attention mask prediction module composed of two convolutional layers followed by ReLU and Sigmoid activations. It takes as input the concatenated feature map of and and outputs a single-channel attention mask . Meanwhile, to enhance the adaptive adjustment capability in uncertain regions, we introduce an uncertainty weighting module that takes as input and outputs a non-negative uncertainty map, denoted as U. Its complement is then used to compute the confidence weight :

2

which is multiplied with to obtain the final attention mask . and are computed following the procedure described above.

We introduce a dedicated scale prediction module that recovers the cross-modality scale factor in the depth direction by exploiting the correlation between real bronchoscopic and virtual images. This module processes through a lightweight convolutional pipeline to predict a scale factor . A Softplus activation is applied to ensure non-negativity. The scale prediction estimates a scale factor from depth features to compensate for the monocular scale ambiguity. We restrict scale estimation to the z-axis only. This is motivated by the motion characteristics of bronchoscopic navigation, where forward translation dominates due to the constrained tubular environment. Lateral translations are limited and largely correlated with rotational motion, making them less suitable for independent scale adjustment. Rather than recovering an absolute metric scale, it adjusts the magnitude of the predicted translation to better align the estimated pose with the scale of the virtual bronchial model.

Finally, and are pixel-wise weighted by and , respectively, and then concatenated to form enhanced inputs:

3

The enhanced input is fed into a lightweight pose regression network adapted from Monodepth2. The network adopts a ResNet-18 backbone with the fully connected layers removed to extract spatial features, which are further processed by subsequent convolutional layers to regress the 6-DoF relative pose transformation.

4

where is the axis-angle representation of rotation, and is the translation vector.

Losses function

The DaAPNet is trained in an end-to-end self-supervised manner, leveraging view synthesis as supervision and requiring no GT depth or pose labels. The overall loss function integrates a photometric reprojection loss, an edge-aware depth smoothness loss, and a pose consistency loss.

Photometric Reprojection Loss (PR Loss). We follow Monodepth2²² in using L1 and SSIM³⁷ to make the photometric error function . During training, for each monocular video sequence, the frame at time step t is treated as the virtual image . Its temporally adjacent frames are used as real images after applying appearance perturbations (e.g., texture shifts of the bronchial wall). Given the source view (the frames aligned with ) and the target image , Monodepth2 generates the warped image by first back-projecting each pixel of the target frame into 3D using its predicted depth . The resulting 3D points are then transformed into the source camera coordinate system via the relative pose (obtained from the relative pose via the exponential map) and re-projected onto the source image plane to obtain 2D coordinates. Sampling the source image at these projected coordinates produces the synthesized target view . The photometric reprojection loss is then computed between the synthesized image and the actual target image . To mitigate the impact of occluded regions, a minimum reprojection error strategy²² is employed across multiple frames , using the frame that yields the lowest error for supervision:

5

6

where μ is a per-pixel auto-mask that suppresses pixels whose appearance can be explained without camera motion. [· ] is the Iverson bracket.

Edge-aware Depth Smoothness Loss (EDS Loss). To smooth the predicted depth, an edge-aware smoothness loss is computed:

7

where and represent the image gradients in the x and y directions, respectively.

Pose Consistency Loss (PC Loss). To enhance temporal consistency between consecutive frames, a pose composition constraint among three frames is introduced. The estimated relative poses from to are mapped to transformation matrices via the exponential map. These matrices are expected to approximately satisfy the following pose composition constraint: . By mapping the transformation matrices into vectors in the Lie algebra space via logarithmic mapping (), the constraint is enforced through an L2 loss:

8

Finally, the total loss can be written as:

9

Here, and . The method predicts depths at multiple scales . The corresponding image dimensions are and .

Results

Dataset

For the pose estimation task, we use two datasets: the Virtual Bronchus Dataset and the Phantom Bronchus Dataset. Their details are summarized in Table 2 and illustrated in Fig. 4.

Table 2.

Statistics of the virtual and phantom dataset.

Purpose	Dataset	Images		Image Size	Number	GT Pose	GT Depth
		I'	I
Train	Virtual Bronchus Dataset	Virtual image (texture)		480 × 480	3942	Yes	Yes
		Virtual image (texture)
		Virtual image (texture)
Test		Virtual image (texture)	Virtual image (texture)		700
	Phantom Bronchus Dataset	Virtual image (texture)	Vedio image	400 × 400	265	No	No

Fig. 4.

Illustrations of the lung dataset. On the left are samples from the Virtual Bronchus Dataset, and on the right are samples from the Phantom Bronchus Dataset.

The Virtual Bronchus Dataset is built upon a virtual 3D bronchial model proposed in Ref³⁸. (Fig. 4, left). A total of 23 virtual camera trajectories were selected to capture monocular video sequences inside the bronchial lumen. To simulate variations in bronchial inner wall appearance, three different surface textures (Texture, Texture, and Texture) were applied to the bronchial model, thereby increasing the appearance diversity of the virtual images. In total, training image sequences were generated from 18 trajectories, while testing image sequences were obtained from the remaining 5 trajectories, as shown in Fig. 5.

Fig. 5.

Illustrations of the selected trajectories used for testing in the virtual (left, 5 trajectories) and phantom (right, 2 trajectories) bronchial models.

The Phantom Bronchus Dataset is provided by Ref³⁹. It comprises a 3D bronchial model reconstructed from CT scans, camera poses tracked by an electromagnetic (EM) tracking system, and corresponding phantom images captured during the tracking procedure. The 3D bronchial model was imported into Blender to render virtual images associated with the two selected EM trajectories, while the phantom images served as the corresponding real images (Fig. 4, right). Testing image sequences were obtained from two selected trajectories, as shown in Fig. 5.

In addition to the virtual and phantom datasets, publicly available clinical images from Ref⁴⁰. are included for evaluation. As this dataset was originally collected for bronchial disease detection and lacks GT pose annotations and a bronchial CT model, it is only used to visually assess the generalization ability of DaAPNet on clinical images.

Implementation details

The proposed DaAPNet is implemented in PyTorch and trained on a single NVIDIA A100 GPU. The batch size is 8, and the optimizer is Adam with an initial learning rate of 1e-5. The model was trained for 20 epochs, and the learning rate was reduced by a factor of 0.1 at the 15th epoch. To evaluate pose estimation performance, seven self-supervised methods were selected for comparison: Monodepth2²², EDM⁴¹, ESM⁴², AF-SfMLearner²³, LiteMono²⁴, EndoDAC⁴³, and SPIdepth⁴⁴. Among these, Monodepth2, LiteMono, and SPIdepth are methods that perform well in general scenarios, while EDM, AF-SfMLearner, ESM, and EndoDAC are specifically designed for endoscopic environments. For a fair comparison, all methods were trained using the original hyperparameters reported in their respective papers on lung datasets. The best performance achieved by each method during evaluation was reported.

Translation and rotation errors along the x, y, and z axes are computed between the predicted relative pose transformation and the GT pose transformation ¹⁵ to evaluate the method’s performance.

Ablation studies

Ablation studies were conducted to evaluate the contribution of each component in DaAPNet. The evaluation results on the Virtual Bronchus Dataset, which provides GT poses, are presented in Table 3. Using all four modules together yields the best performance, reducing rotation error by 4.14% and translation error by 36.00% compared to the baseline. These results demonstrate the synergistic effect of the modules in improving the accuracy of self-supervised pose estimation under simulated conditions.

Table 3.

6-DOF pose estimation error for modules ablation studies (mean ± standard deviation). Bold font denotes the best performance, while underlining indicates the second-best result.

Uw	DaA		PC Loss	/mm↓	/mm↓	/mm↓	/mm↓	↓	↓	↓	↓
				0.54 ± 0.67	0.45 ± 0.46	4.77 ± 3.19	1.92 ± 1.25	3.09 ± 4.91	3.29 ± 3.33	1.44 ± 1.69	2.60 ± 2.25
	\checkmark		\checkmark	0.54 ± 0.67	0.45 ± 0.46	4.78 ± 3.19	1.92 ± 1.25	3.09 ± 4.90	3.15 ± 3.25	1.43 ± 1.69	2.56 ± 2.25
	\checkmark	\checkmark	\checkmark	0.54 ± 0.67	0.45 ± 0.46	2.86 ± 2.88	1.28 ± 1.13	3.04 ± 4.89	3.16 ± 3.27	1.40 ± 1.70	2.53 ± 2.25
\checkmark	\checkmark		\checkmark	0.54 ± 0.67	0.45 ± 0.46	4.78 ± 3.19	1.92 ± 1.25	3.05 ± 4.89	3.12 ± 3.27	1.44 ± 1.69	2.54 ± 2.22
\checkmark	\checkmark	\checkmark		0.54 ± 0.67	0.45 ± 0.46	2.75 ± 2.72	1.25 ± 1.07	3.05 ± 4.90	3.06 ± 3.20	1.41 ± 1.69	2.51 ± 2.24
\checkmark	\checkmark	\checkmark	\checkmark	0.54 ± 0.67	0.45 ± 0.46	2.70 ± 2.72	1.23 ± 1.07	3.05 ± 4.91	3.04 ± 3.32	1.40 ± 1.69	2.50 ± 2.26

When removing from the DaA module, the rotation error and translation error increase by 1.40% and 4.09%, respectively. The attention masks generated by the “DaA wo ” and by the full “DaA” module are shown in Fig. 6. These virtual, phantom, and clinical images exhibit varying illumination and specular reflections, which present challenges for reliably detecting bifurcation regions. As highlighted by the blue outline, the full DaA module more effectively captures these regions. Guided by , the DaA module learns robust structural cues by dynamically suppressing low-confidence regions.

Fig. 6.

The depth maps and attention masks generated by full DaA (“DaA”) and DaA without Uw (“DaA wo Uw”). Blue boxes indicate the regions in the attention masks where the contour information of the lumen is emphasized.

When removing from the DaA module, the rotation error increases by 1.58%, and the translation error increases by 36.04%, with the most pronounced degradation observed in translation estimation along the forward (z-axis) direction. As shown in Table 4, incorporating improves cross-modality scale recovery, resulting in more accurate pose estimation when evaluated on the 5 trajectories of the Virtual Bronchus Dataset.

Table 4.

Absolute Trajectory Error (ATE) evaluation on 5 trajectories for the ablation experiment. Bold font denotes the best performance.

Trajectory Num	RMSE			MEAN			MAX
	(xyz)	(z)	wo	(xyz)	(z)	wo	(xyz)	(z)	wo
1	2.91	2.70	4.18	2.08	1.98	3.14	9.29	9.15	12.33
2	6.24	5.79	7.46	5.37	4.82	6.65	12.66	12.25	13.57
3	4.41	4.29	6.39	3.08	3.09	5.02	13.33	13.04	16.27
4	3.34	3.17	4.99	2.41	2.34	4.22	8.91	8.92	11.61
5	2.92	2.48	5.02	2.45	2.08	4.72	7.88	6.62	9.77
All	4.30	4.01	5.84	3.20	2.97	4.88	13.33	13.04	16.27

Table 5 presents a comparison between estimating scale factors along all three axes (x, y, z) and estimating scale solely along the z-axis. The results show that introducing scale estimation for all axes degrades pose estimation accuracy. This decline occurs because, during bronchoscopic forward motion, scale variation is primarily along the depth (z) direction, while changes along the x and y axes are minimal. Enforcing scale regression on the x and y axes therefore introduces ill-constrained degrees of freedom, increases prediction noise, and destabilizes the pose optimization process. The ablation of the PC Loss is shown in the last row of Table 3. Incorporating the PC Loss leads to a 0.41% decrease in rotation error and a 1.42% decrease in translation error , indicating a marginal improvement, since the PC Loss serves as an auxiliary temporal regularization.

Table 5.

6-DOF pose estimation error for ablation studies (mean ± standard deviation). (z) denotes that the scale module predicts only the scale factor along the z-axis, whereas (xyz) indicates that the module estimates scale factors along the x, y, and z axes. Bold font denotes the best performance.

(z)	(xyz)	/mm↓	/mm↓	/mm↓	/mm↓	↓	↓	↓	↓
\checkmark		0.54 ± 0.67	0.45 ± 0.46	2.70 ± 2.72	1.23 ± 1.07	3.05 ± 4.91	3.04 ± 3.32	1.40 ± 1.69	2.50 ± 2.26
	\checkmark	0.56 ± 0.68	0.48 ± 0.45	2.97 ± 2.91	1.34 ± 1.12	3.09 ± 4.89	3.06 ± 3.29	1.44 ± 1.68	2.53 ± 2.22

Experiment on virtual bronchus dataset

The pose estimation comparison experiments are conducted on the Virtual Bronchus Dataset, with results summarized in Table 6. Compared to Monodepth2²², DaAPNet achieves improved performance in this simulated environment, reducing the translation error by 35.99%, particularly along the z-axis, and the rotation error by 4.26%. By leveraging the synergistic effects of the Depth-aware Attention module and the Scale Prediction module, DaAPNet better captures spatial structures and motion dynamics, leading to more accurate pose estimations within the Virtual Dataset. Fig. 7 illustrates the trajectory results of DaAPNet along the bronchial lumen, showing that the optimized pose P'' is closer to the GT pose P than the initial pose P'.

Table 6.

6-DOF pose estimation error for input (mean ± standard deviation). Bold font denotes the best performance, while underlining indicates the second-best result.

Methods	/mm↓	/mm↓	/mm↓	/mm↓	↓	↓	↓	↓	fps↑
monodepth2-Res18	0.54 ± 0.67	0.45 ± 0.46	4.77 ± 3.19	1.92 ± 1.25	3.11 ± 4.93	3.24 ± 3.35	1.48 ± 1.69	2.61 ± 2.27	50
monodepth2-Res50	0.54 ± 0.67	0.45 ± 0.46	4.78 ± 3.19	1.92 ± 1.25	3.10 ± 4.93	3.00 ± 3.25	1.43 ± 1.67	2.51 ± 2.25	51
ESM	0.54 ± 0.68	0.46 ± 0.46	4.81 ± 3.19	1.94 ± 1.25	4.46 ± 5.37	3.54 ± 3.42	1.56 ± 1.58	3.19 ± 2.22	34
EDM	0.54 ± 0.67	0.46 ± 0.45	4.79 ± 3.26	1.93 ± 1.26	8.85 ± 11.44	5.08 ± 6.23	7.39 ± 10.06	7.10 ± 6.92	1
AF-SfMLearner	0.54 ± 0.67	0.45 ± 0.46	4.80 ± 3.19	1.93 ± 1.25	2.98 ± 4.90	3.57 ± 3.59	1.45 ± 1.70	2.67 ± 2.29	120
LiteMono	0.54 ± 0.67	0.45 ± 0.46	4.78 ± 3.19	1.92 ± 1.25	3.09 ± 4.90	3.27 ± 3.38	1.51 ± 1.67	2.62 ± 2.25	76
LiteMono-8m	0.54 ± 0.67	0.45 ± 0.46	4.78 ± 3.19	1.92 ± 1.25	3.13 ± 4.86	3.21 ± 3.21	1.49 ± 1.65	2.61 ± 2.20	62
EndoDAC	0.54 ± 0.67	0.45 ± 0.46	4.80 ± 3.19	1.93 ± 1.25	3.01 ± 4.91	3.54 ± 3.58	1.40 ± 1.72	2.65 ± 2.30	96
SPIdepth	0.54 ± 0.67	0.45 ± 0.46	4.68 ± 3.18	1.89 ± 1.24	3.12 ± 4.93	3.12 ± 3.38	1.43 ± 1.71	2.55 ± 2.30	121
DaAPNet-Res18	0.54 ± 0.67	0.45 ± 0.46	2.70 ± 2.72	1.23 ± 1.07	3.05 ± 4.91	3.04 ± 3.32	1.40 ± 1.69	2.50 ± 2.26	36
DaAPNet-Res50	0.54 ± 0.67	0.45 ± 0.46	2.85 ± 2.70	1.28 ± 1.06	3.12 ± 4.94	2.94 ± 3.20	1.43 ± 1.69	2.49 ± 2.23	27

Fig. 7.

Optimized trajectories of – inputs from the Virtual Bronchus Dataset along the main bronchus, right upper lobe, and left lower lobe. Markers show the positions where images (orange), (red), and optimized (green) were captured.

A visual comparison of the optimized images is provided in Fig. 8. Each virtual image is rendered at the corresponding optimized pose P'' estimated by different methods. DaAPNet demonstrates improved performance, producing optimized images that more closely resemble the real images in visual appearance compared to other methods.

Fig. 8.

Visual comparison of optimized images . The input image pairs and are from the Virtual Bronchus Dataset.

Table 7 presents the translational error for each method on 5 trajectories. Among these methods, DaAPNet achieves the lowest translation error, demonstrating its accuracy in position estimation across varying trajectories. Fig. 9 compares the curves of SPIdepth⁴⁴ and DaAPNet-Res18 across all trajectories. The error curve of DaAPNet-Res18 lies below that of SPIdepth across most trajectories, demonstrating better positional accuracy.

Table 7.

Absolute Trajectory Error (ATE) evaluation on 5 trajectories (mean ± standard deviation). Bold font denotes the best performance, while underlining indicates the second-best result.

Trajectory Num	mono depth2 -Res18	ESM	EDM	AF- SfM Learner	Lite Mono	Lite Mono −8m	Endo DAC	SPI depth	DaAPNet -Res18
1	3.13 ± 2.77	3.17 ± 2.77	3.08 ± 2.77	3.16 ± 2.77	3.14 ± 2.77	3.14 ± 2.77	3.16 ± 2.77	3.02 ± 2.76	1.98 ± 1.84
2	6.64 ± 3.39	6.70 ± 3.39	6.85 ± 3.46	6.66 ± 3.39	6.65 ± 3.38	6.65 ± 3.38	6.66 ± 3.39	6.60 ± 3.37	4.82 ± 3.21
3	5.02 ± 3.94	5.06 ± 3.94	4.98 ± 3.96	5.05 ± 3.94	5.03 ± 3.94	5.03 ± 3.94	5.05 ± 3.94	4.92 ± 3.92	3.09 ± 2.96
4	4.21 ± 2.66	4.25 ± 2.66	4.17 ± 2.68	4.24 ± 2.67	4.22 ± 2.67	4.22 ± 2.66	4.24 ± 2.67	4.11 ± 2.66	2.34 ± 2.14
5	4.72 ± 1.70	4.75 ± 1.71	4.71 ± 1.75	4.74 ± 1.70	4.73 ± 1.70	4.72 ± 1.70	4.74 ± 1.70	4.62 ± 1.70	2.08 ± 1.35
All	4.88 ± 3.21	4.91 ± 3.22	4.90 ± 3.28	4.90 ± 3.21	4.88 ± 3.21	4.88 ± 3.21	4.90 ± 3.21	4.79 ± 3.21	2.97 ± 2.69

Fig. 9.

Comparison of translational error curves of SPIdepth and DaAPNet-Res18 across trajectories.

Experiment on phantom bronchus dataset

The Phantom Bronchus Dataset does not provide GT virtual camera poses in the CT-rendered environment. However, there is a large modality gap between and images than that in the Virtual Bronchus Dataset. Therefore, it remains valuable for evaluating DaAPNet’s generalization ability and can be used to qualitatively assess pose and depth estimation across diverse image samples. A visual comparison of the optimized images is provided in Fig. 10. Compared with other methods, DaAPNet demonstrates improved performance, producing optimized images that more closely resemble the real images in visual appearance. This evaluation highlights DaAPNet’s potential for robust performance in phantom scenarios with varied image modalities.

Fig. 10.

Visual comparison of optimized images . The input image pairs and are from the the Phantom Bronchus Dataset.

A visual comparison of depth estimation results on the Phantom Bronchus Dataset is presented in Fig. 11. The white and green boxes indicate close-range and far-range regions, respectively. The ESM⁴² generates overly smooth depth maps that fail to accurately estimate close-range and far-range regions, and cannot reliably depict bronchial bifurcations. This reduces spatial awareness and limits its utility for pose estimation. SPIdepth⁴⁴ can estimate accurate depth maps; however, its performance degrades under low illumination. When the input image is captured under low illumination, it is difficult to extract reliable depth information. This leads to inaccurate spatial relationships between the and images. In contrast, DaAPNet predicts depth maps that are structurally coherent and preserve hierarchical depth features. It effectively distinguishes close-range and far-range regions, better capturing the intrinsic spatial relationships of bronchial structures and thereby enhancing pose estimation accuracy.

Fig. 11.

Depth estimation visualization of - inputs from Phantom Bronchus Dataset. The white and green boxes highlight regions where our DaAPNet performs well close-range and far-range regions, respectively.

Generalization on clinical images

To evaluate the generalization ability of DaAPNet in real clinical scenarios, we further test the trained model on publicly available bronchoscopic images from Ref⁴⁰, which contain no GT poses or CT models. Therefore, only qualitative depth evaluation is conducted. Fig. 12 visualizes the predicted depth maps on clinical images. Despite severe specular highlights, DaAPNet produces structurally consistent depth distributions and preserves bifurcation-aware geometry, indicating robustness to real-world domain shifts. Additionally, we observe that LiteMono achieves superior depth sharpness. Although Lite-Mono achieves superior performance in monocular depth estimation, this is mainly due to its architecture being explicitly optimized for depth reconstruction. Lite-Mono adopts a hybrid CNN–Transformer design that effectively captures both local details and long-range global context, enabling sharper and more accurate depth recovery. Our method, in contrast, does not aim to optimize depth sharpness alone, but focuses on producing geometrically reliable depth cues for pose estimation in bronchial lumen environments.

Fig. 12.

Depth estimation visualization of clinical images.

Discussion

Pose optimization is essential for aligning real bronchoscopic views with virtual camera views, thereby assisting physicians in identifying the correct navigation path. DaAPNet is a self-supervised pose estimation method designed to address the modality gap between virtual (CT-rendered) and real bronchoscopic images, which introduces appearance and scale ambiguities that hinder robust pose estimation. Experiments on virtual and phantom datasets are conducted to analyze the performance of DaAPNet. The results demonstrate that all modules collectively improve pose estimation accuracy. The DaA module effectively learns robust structural cues from cross-modality depth maps, enabling the method to selectively focus on reliable bifurcation regions and thereby reduce the adverse effects of cross-modality appearance ambiguity. The scale prediction module, which estimates , plays a critical role in addressing forward-motion scale ambiguity inherent to bronchoscopy. Results show that compensating only the z-axis scale yields more stable performance, compared to imposing scale regressions on the x and y axes, which introduces unconstrained degrees of freedom.

Quantitative results on the Virtual Bronchus Dataset show that DaAPNet achieves improved pose estimation accuracy compared with Monodepth2, reducing translation error by 35.99% and rotation error by 4.26%. Paired t-tests were conducted to assess the statistical significance of the improvements between Monodepth2 and DaAPNet. The reduction in translation error is statistically significant (p<0.05), whereas the decrease in rotation error is not (p>0.05). The significant improvement in translation accuracy can be attributed to the effectiveness of the scale prediction and DaA modules. In contrast, the limited improvement in rotation estimation may be attributed to the lumen cross-section at the bifurcation, which is approximately circular. Rotations around the viewing axis produce nearly identical projected contours in the image, providing the method with minimal cues to accurately learn rotational transformations. Future work will focus on enhancing rotation estimation by incorporating additional geometric constraints to improve the robustness of pose prediction in low-variation bronchial scenarios. Qualitative results on the Phantom Bronchus Dataset show that the depth maps estimated by DaAPNet better preserve close–far regions compared with those estimated by other methods. Accurate depth maps are crucial for maintaining stable spatial awareness and thus support accurate pose estimation across cross-modality scenarios.

However, a key limitation of this study is that the pose estimation evaluation of DaAPNet has been largely limited to virtual and phantom datasets, and its performance on real bronchoscopic clinical data remains to be assessed. Evaluation in real bronchoscopic procedures is challenging due to constraints related to medical ethics, patient safety in clinical scenarios. In addition, respiratory motion can significantly impact pose estimation accuracy. Nevertheless, virtual and phantom datasets are widely adopted in early-stage navigation research, as they allow controlled evaluation in a risk-free manner and provide reliable reference poses for assessing the feasibility of the method. We further analyze the parameter size of each module to evaluate the feasibility of deployment in clinical scenarios. The results show that the parameter sizes of DepthNet and PoseNet are 59.61 MB and 49.64 MB, respectively, while the introduced DaA and Relative Scale Prediction modules add only 50.32 KB and 4.57 KB of parameters, imposing a negligible overhead. Under the inference setting with a batch size of 1, the peak GPU memory consumption during end-to-end inference is 422.20 MB. In terms of inference efficiency, the current implementation achieves near real-time performance at 36 fps, suggesting that the proposed method has practical potential for deployment on standard GPU platforms. In future work, we plan to develop motion-aware pose optimization strategies that explicitly account for respiratory-induced deformations, while reducing virtual rendering overhead through selective rendering and event-triggered pose refinement around anatomically informative regions such as airway bifurcations.

Conclusion

In this paper, we propose a novel self-supervised pose estimation method, DaAPNet, for hybrid bronchoscopic navigation. DaAPNet addresses two challenges in cross-modality scenarios: appearance ambiguity and scale ambiguity. The Depth-aware Attention module emphasizes geometrically reliable regions, mitigating the impact of appearance ambiguity. The scale prediction module estimates the relative scale factor between virtual (CT-rendered) and real depth maps, enabling the method to reduce the effects of cross-modality scale ambiguity. Experiments on virtual and phantom bronchus datasets demonstrate the effectiveness of DaAPNet in improving pose estimation accuracy, supporting its feasibility in simulated scenarios. Future work will focus on enhancing its robustness on real clinical bronchoscopic data, addressing challenges such as respiratory-induced deformations and inaccuracies in rotation estimation.

Author contributions

X.L. and X.D. conceptualized the DaAPNet framework, designed the experiments, and implemented the model. T.X., T.G., and C.Z. supervised the research, analyzed the data, and validated the results. P.W., H.Z., and X.Y. handled project administration and analyzed the results. All authors contributed to manuscript writing, reviewed the final draft, and approved the submission.

Funding

This research was supported by the Cross-disciplinary Collaboration Original Project Cultivation Funding Program of Department of General Surgery Sir Run-Run Shaw Hospital School of Medicine, and Department of Biomedical Engineering, Zhejiang University (Grant Nos. 114105-I22402), the Key Research and Development Plan of Zhejiang Province (Grant No. 2023C03094,2024C03008).

Data availability

Data underlying the results presented in this paper are available in Ref³⁸. (It is publicly available at: https://zenodo.org/records/10077275), Ref³⁹.(It is publicly available at: https://drive.google.com/drive/folders/1-VhVHH1hfjf6TE_1ByHPaPkggUEpf3N4) and and Ref⁴⁰. (It is publicly available at: https://www.kaggle.com/datasets/timesxy/bronchoscopic-dataset-bi2k-3-classification).

Declarations

Competing interests

The authors declare no competing interests.