Can AI depth estimation from endoscopy measure airway cross-sectional area?

What the 5.3% error actually measures

The headline number compares two areas, not two images. For each of 18 patient-specific 3D airway models, the authors knew the true nasopharyngeal cross-sectional area (CSA) from the geometry itself. They then ran the AI-generated depth map through a reconstruction pipeline and computed an area from it. The median percent error of 5.3% is the median of |A_3D − A_depth map| / A_3D across those 18 models, so it is a relative error against a geometric ground truth, not against a clinical measurement.

The same test was run twice: once with the perfect, ground-truth depth maps and once with the AI-predicted ones. Ground-truth depth maps gave a median absolute error of 0.01 cm² and a median percent error of 0.6%; the AI-generated maps gave 0.06 cm² and 5.3%. The gap between those two rows isolates how much error the neural network adds on top of the point-cloud and perimeter-fitting method, which by itself was already accurate.

The 18 models had a mean nasopharyngeal CSA of 1.36 ± 0.71 cm², ranging from 0.38 to 2.40 cm². Because the errors are relative, a 5.3% median on an area near 1 cm² corresponds to roughly a few hundredths of a square centimeter — the same order as the reported 0.06 cm² median absolute error.

Why synthetic depth maps solve the labeling problem

Endoscopes do not carry depth sensors, so a real endoscopic video has no accompanying map of distances in meters. Training a network to output depth in physical units therefore needs ground-truth depth that is hard to obtain in patients. The paper's answer is to build the ground truth instead of measuring it: 3D airway models reconstructed from CT scans were rendered in Blender, an open-source 3D modeling tool, producing virtual endoscopy images paired with exact depth maps.

In those pairs, each pixel's grayscale value is the distance from the virtual camera to the nasal wall. That is what makes the task metric rather than scale-ambiguous: the network is not merely learning relative surface shape, it is regressing distances in physical units. The dataset contained 60,000 such pairs, split patient-wise into 48 nasal cavities with 48,000 training pairs and 12 nasal cavities with 12,000 validation pairs, so no patient appeared in both sets.

The cost of this choice is that everything the network learns comes from rendered geometry. The paper is explicit that this is a pilot using synthetic data, and the accuracy figures below inherit that boundary.

A plain U-Net was enough for depth

The architecture is a U-Net convolutional network with a symmetric encoder–decoder and skip connections. The encoder applies convolutional blocks and max pooling, doubling feature channels at each stage down to a bottleneck; the decoder mirrors this with transposed convolutions for upsampling and skip connections back to encoder outputs. The output is a single-channel 720 × 720 depth map, matching the input resolution pixel for pixel.

Training used mean squared error, which the authors chose because input and output pixels are strictly aligned — each image pixel corresponds directly to its depth value — making the regression problem easier to learn. They trained for 80 epochs with the Adam optimizer at a learning rate of 1×10⁻⁴. Validation MSE fell to about 0.02 within the first 15 epochs, and the best model, selected at epoch 24, reached 0.014. The small gap between training and validation MSE is the paper's evidence for minimal overfitting to unseen synthetic scenes.

The authors note they deliberately chose this straightforward architecture over more elaborate dual-branch or attention-based designs reported elsewhere in endoscopic depth estimation, citing computational efficiency and modest GPU requirements on consumer hardware. That is a design claim about their own results, not a head-to-head comparison.

From a depth map to an area in square centimeters

A depth map alone does not give an area. The pipeline first converts each pixel to a 3D point. Pixel coordinates become polar coordinates in the image, and the Equisolid fisheye lens model converts radius into a zenith angle using θ = 2 arcsin(c·r / 2f), with focal length f = 2.5 mm and a unit conversion c = 3.6 mm / 720 pixels = 0.005 mm/pixel, reflecting the 3.6-mm square sensor behind the 720-pixel image. Depth, zenith angle, and polar angle then give Cartesian X, Y, Z.

The resulting point cloud is the airway surface in three dimensions. A user places a plane at a chosen distance from the camera and rotates it until it is perpendicular to the point cloud at the target site; the airway perimeter is the intersection of that plane with the point cloud. Ordering the perimeter points sequentially lets the area be computed as a contour integral, A = |Σ vᵢ Δuᵢ|.

This differs from the team's earlier approach, which counted pixels inside the perimeter and multiplied by a distance-dependent conversion factor. That older method measured area perpendicular to the camera, so the camera had to be aligned with the airway axis. Reconstructing a point cloud removes that alignment requirement, which matters because the plane can now be set perpendicular to the airway rather than to the scope.

Where the AI depth maps failed

Of 30 patient-specific models, 7 had an idealized nasopharynx generated from CT scans that did not capture the region, so they were excluded from accuracy analysis as anatomically inaccurate. Of the remaining 23, four lacked an extension tube and the AI performed poorly: light reflections on the non-anatomical distal wall, corresponding to the distal boundary of the CT segmentation, degraded the predicted depth maps enough that the airway perimeter could not be delineated at the measurement site. The authors attribute this to training data containing few examples where the distal wall was visible.

One further model with an extension tube was excluded because a prominent soft-palate hump partially obstructed the measurement site, preventing a complete perimeter. That left 18 models for the accuracy analysis.

These exclusions are not incidental bookkeeping. They mark the conditions under which the method worked: an extension tube present, an unobstructed measurement site, and no strong reflection artifact at the distal wall. The 5.3% median describes performance inside that envelope.

Correlation without systematic bias

Beyond the median error, the paper reports agreement statistics. Areas from depth maps were not statistically different from the known 3D values, with p = 0.96 for ground-truth depth maps and p = 0.99 for AI-generated ones. Pearson correlation was r = 0.998 (p < 0.0001) for ground-truth maps and r = 0.987 (p < 0.0001) for AI-generated maps.

The Bland–Altman analysis showed negligible bias and no systematic error, with agreement holding across both small and large measurements. That last point matters more than the correlation coefficient: a high r can coexist with a consistent offset, whereas the absence of systematic bias means the method was not simply over- or under-estimating by a fixed amount across the 0.38–2.40 cm² range.

The distribution of errors is also worth reading alongside the median. With ground-truth depth maps, percent error was below 2% in 16 of 18 models. With AI-generated maps, error was ≤ 22% in all cases and below 10% in 13 of 18. The median of 5.3% therefore sits inside a tail that reaches 22% in the worst model.

What this proof of concept does not show

Every image in training, validation, and testing came from rendered 3D models built from CT scans. The test set was separate from the 60,000 training pairs and drawn patient-wise, which supports generalization to unseen synthetic scenes, but it does not test real endoscopic video with its tissue deformation, mucus, specular reflections, and motion. The paper calls the work a pilot using synthetic data and frames the result as feasibility evidence.

The measurement target was also narrow. Accuracy was assessed at one landmark, the distal end of the nasopharynx, chosen because it was readily identifiable in the 3D models and, for most patients, corresponded to the minimum nasopharyngeal CSA due to the curvature of the soft palate. The paper does not report accuracy at other airway levels or across the full nasal cavity.

Finally, the pipeline is not fully automatic. A user positions and rotates the cutting plane until it is perpendicular to the point cloud at the target location, so the reported accuracy includes that human step.

Why the internal comparison matters most

The paper positions its contribution against prior endoscopic depth work that produced metric depth maps but stopped before estimating airway cross-sectional area. Its own claim to novelty is that AI-generated depth maps can yield accurate airway CSA measurements, and the evidence for that claim is the internal comparison between the ground-truth-depth row and the AI-depth row.

Read that way, the 0.6% versus 5.3% median percent error is the paper's most informative pair of numbers. It says the geometric machinery — fisheye point-cloud reconstruction, plane intersection, contour integration — was nearly exact on perfect depth input, and that the learned depth prediction is where essentially all the remaining error enters. For anyone extending this work, that locates the bottleneck in the network's depth maps rather than in the area computation.

The practical priority that follows is specific: the next evidence needed is performance on real endoscopic images of the same nasopharyngeal landmark, and on the cases this study had to exclude — models without an extension tube, where distal-wall reflections broke the depth prediction. Until then, the 5.3% median is a synthetic-data benchmark, and the 22% worst-case error in the 18 tested models is the more conservative figure to carry forward.

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