Deep Distance Transform for Tubular Structure Segmentation in CT Scans

1. Introduction

• Tubular segmentation can support disease characterization; pancreatic duct dilatation or abrupt caliber change signifies high PDAC risk.Obstructed vessels are also linked to coronary heart disease.Source: §1 · p. 1
• Geometry-based methods exploit tubular shape, while voxel-classification networks can ignore voxel arrangement and fail to ensure a proper shape.Geometry-based methods also struggle with poor contrast, noise, and complicated backgrounds.Source: §1 · p. 1
• DDT predicts a segmentation mask and a voxelwise distance map, whose ridge encodes skeleton and cross-sectional scales, enabling shape-prior refinement without skeleton ground truth.The distance values are defined throughout the structure, avoiding the skeleton-versus-neighbor labeling discontinuity; a distance loss further trains precise distance prediction.Source: §1 · p. 2
• DDT's cross-sectional scales provide a geometric measurement that may support further study, including clinical diagnosis and virtual endoscopy.The method combines distance-transform intuitions for skeletonization with deep segmentation networks.Source: §1 · p. 2
• Over 13% improvement in Dice-Sørensen coefficient (DSC) was reported for pancreatic duct segmentation on 3D-Unet.The introduction reports this result among DDT's evaluations on five segmentation datasets and one clinical-diagnosis dataset.Source: §1 · p. 2

2.1.1 Geometry-based Methods

• Geometry-based methods include contour fitting, minimal paths, model tracking, and centerline detection; DDT instead learns skeleton and radius implicitly with distance transforms and reconstructs the mask from shape priors.The overview describes these earlier methods as exploiting geometric characteristics in different ways.Source: §2.1.1 · pp. 2–3

2.1.2 Learning-based Method

• Deep segmentation networks have been applied across organs and vessels, but how to integrate geometric information with deep networks for tubular shapes remained unstudied.The related-work overview includes multi-organ segmentation, retinal vessels, kidney vessels, and pancreatic tissues among prior learning-based approaches.Source: §2.1.2 · p. 3

2.2. Learning-based Skeleton Extraction

• Learned skeleton methods can jointly predict skeleton labels and scales, but their direct application to tubular segmentation is hindered by difficult-to-obtain 3D skeleton ground truth.Prior skeleton-learning work reported that multi-task skeleton classification and scale regression helped scale accuracy and skeleton-based object segmentation.Source: §2.2 · p. 3

3. Methodology

• DDT predicts a binary label for each CT voxel, with the network trained to target both the segmentation map and a quantized distance-derived scale map.The scale map is based on distance to the tubular structure surface; quantization frames scale prediction as classification rather than direct regression.Source: §3 · p. 4, §3.2 · p. 4, §3.1 · p. 4

3.1. Distance Transform for Tubular Structure

• Each foreground voxel receives its nearest distance to the tubular surface; distances are quantized into scale classes because direct regression is described as unstable under annotation outliers.The paper uses Euclidean distance, noting that skeletons from Euclidean distance maps are robust to rotations.Source: §3.1 · p. 4

3.2. Network Training for Deep Distance Transform

• Two network heads learn voxel segmentation and tubular-voxel scale classes, combining weighted cross-entropy classification with a distance loss that penalizes scale-class differences.The total training loss is the sum of the classification and distance losses.Source: §3.2 · p. 4

3.3. Geometry-aware Refinement

• Refinement thresholds the segmentation probabilities into a pseudo-skeleton, reconstructs a softened shape from predicted scales, and uses that shape to refine the segmentation map.The reconstruction softens balls centered at skeleton points with a Gaussian kernel because quantized scales otherwise produce a non-smooth surface; predicted scales also provide a geometrical measurement for clinical diagnosis.Source: §3.3 · p. 5

4.1.1 Implementation Details and Evaluation Metric

• Experiments span five segmentation datasets and one clinical-diagnosis dataset; the PDAC benchmark has 239 pathologically proven cases.Training uses augmented patches, and testing uses sliding windows.Source: §4 · p. 5, §4.1.2 · p. 5, §4.1.1 · p. 5

4.1.2 The PDAC Segmentation Dataset [46]

• DDT outperforms the pancreatic-duct SegBaseline and, with 3D-UNet, the multi-phase HPN by more than 13% in DSC.SegBaseline and DDT use venous-phase scans, whereas multi-phase HPN combines arterial and venous scans.Source: §4.1.2 · p. 6, Table 1 · p. 6
• In geometry-aware refinement, varying one parameter at a time while fixing the other at its default (T p = 0.98, T r = 0.5), larger T p improved performance, while performance was insensitive to T r from 0.1 to 1.Ablations were conducted on PDAC segmentation using ResDSN, including variants without distance loss and with or without geometry-aware refinement.Source: §4.1.2 · p. 6

4.1.3 Tubular Structure Datasets

• Across three tubular-structure datasets and three backbones, DDT exceeds SegBaseline; the reported 3D-HED gain is 8%.The comparison reports DSC and mean surface distance; qualitative examples indicate better robustness to noise and complicated backgrounds.Source: §4.1.3 · p. 6, Table 3 · p. 7

4.1.4 Hepatic Vessels Dataset in MSD Challenge

• The hepatic-vessel experiment trains DDT on 303 cases and compares its vessel predictions with leading challenge submissions.The text says the comparison shows DDT's effectiveness but gives no specific leaderboard values.Source: §4.1.4 · p. 7, Table 4 · p. 7

4.2. Finding PDAC Tumor by Dilated Duct

• On cases missed by, the dilated-duct workflow found all tumor regions in abnormal cases and discarded non-tumor candidates in normal cases.The test covered 8 abnormal and 197 normal cases; 18 candidate regions were generated.Source: §4.2 · p. 8

• DDT combines classical distance-transform intuitions for skeletonization with deep segmentation to guide tubular-structure segmentation.Source: §5 · p. 8
• Geometry-aware segmentation also provides cross-sectional scales as a measure of tubular thickness.Source: §5 · p. 8
• Evaluation on six datasets spanning pancreatic duct, aorta, veins, and vessels showed superiority for segmentation and clinical application.Source: §5 · p. 8