VesselSDF: Distance Field Priors for Vascular Network Reconstruction

arXiv:2506.16556 · eess.IV, cs.CV · Submitted 2025-06-19 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: Today's paper: "VesselSDF: Distance Field Priors for Vascular Network Reconstruction".

Jane: The gist: VesselSDF presents a novel framework that leverages signed distance fields (SDFs) for robust vessel reconstruction, reformulating segmentation as a continuous SDF regression problem to capture smooth,

Tom: First, who's behind it and why it matters.

Paper summary: Tom: So, we're looking at this paper called "VesselSDF: Distance Field Priors for Vascular Network Reconstruction." It sounds like they are tackling a really tough problem in medical imaging where vessels are thin and branching, and existing methods just aren't cutting it because they get these jagged artifacts.

Jane: Exactly. The main idea here is shifting how we look at vessel segmentation away from just labeling individual voxels to treating it as a continuous distance field problem. They claim this lets them capture the smooth, tubular geometry of blood vessels naturally and stop those annoying surface errors that happen when you use standard binary methods <ref:2506.16556#pg1>.

Lu: What's interesting is how they reformulate it as a continuous SDF regression problem where every point gets its distance to the nearest vessel surface, which inherently handles that smoothness issue <ref:2506.16556#pg2>. This is a big conceptual move because it lets the model learn geometry directly rather than just guessing on discrete pixels.

Meng: From an engineering standpoint, if they can get this continuous representation right, it means the output won't have those fragmented pieces we see in other methods twenty-seven, which is important for actual clinical use and ensuring structural coherence <ref:2506.16556#pg2>. So, they are aiming for something more physically realistic than just a collection of labeled voxels.

Lalam: I see the potential here for how we train future models; instead of just predicting a binary map, the AI is learning the underlying shape itself through distance to that shape <ref:2506.16556#pg1>. This could lead to much more robust and generalizable reconstruction capabilities across different types of vessel data.

Tom: That's what I mean. The authors say this framework systematically separates the segmentation part from the geometric reconstruction part, which is a neat way to handle these complex structures <ref:2506.16556#pg4>. They use a two-stage approach for this, starting with an occupancy prediction and then refining that into an SDF using specific geometric constraints <ref:2506.16556#pg4>.

Jane: That two-stage setup is key because it allows them to first get the basic shape outline and then apply strong geometric rules later on to make sure the final distance field looks correct <ref:2506.16556#pg4>. It’s like sketching a rough map and then using a compass to draw the actual terrain accurately.

Paper summary: Lu: They even use a three dee U-Net architecture for the first stage, integrating something called three dee attention gates to capture multi-scale vessel features effectively <ref:2506.16556#pg5>. That attention mechanism helps it pay more attention to the important parts of the vessel structure during prediction.

Meng: So, they're trying to get good feature representation early on so the second stage has something solid to refine, right? It sounds like a lot of computational effort is going into making sure that initial binary mask is as accurate as possible <ref:2506.16556#pg4>.

Tom: And then they feed that prediction into the second stage where they use a loss function L that combines several terms, including supervised learning, eikonal regularization, and distance-weighted Gaussian regularization <ref:2506.16556#pg6>. That's where the heavy lifting of enforcing smoothness happens.

Jane: That loss function is intense because it has several parts working together; they have a supervised term to match the ground truth SDF, but then they have Leik, which enforces near-unit gradients to keep the surface smooth <ref:2506.16556#pg6>.

Lu: The eikonal regularization term is what forces those distance transitions to be consistent across all dimensions, and they even have a parameter gamma there that accounts for how different the voxel spacing is along the axial dimension <ref:2506.16556#pg6>.

Tom: They also have this distance-weighted Gaussian regularization loss, Lgauss, which is supposed to suppress high-frequency noise far away from the vessel boundaries while keeping details sharp right at the edge <ref:2506.16556#pg8>. It’s a clever way to balance smoothing with detail preservation.

Meng: So they've got several ways to constrain the geometry, which is good because it means if one constraint fails, another one can help pull it back into shape <ref:2506.16556#pg8>. It shows they aren't just relying on the initial prediction alone.

Lalam: The surface regularization term, Lsur, penalizes near-zero SDF values where there isn't really a vessel surface to be found, which is supposed to stop those floating artifacts we talked about earlier <ref:2506.16556#pg8>. It’s a safety net against false detections.

Tom: The results on the Hepatic Vessels and IRCADb datasets show that this whole VesselSDF framework significantly outperforms baselines when dealing with thin vessels and complex branching patterns <ref:2506.16556#pg9>. They report a Dice Coefficient of zero point seven two and a Hausdorff Distance of four point one on the Hepatic Vessels data <ref:2506.16556#pg7>.

Paper summary: Jane: And the ablation studies really back up the method; when they removed just the SDF refinement step, they saw that it was much worse without those geometric regularizers <ref:2506.16556#pg8>. Also, removing the Gaussian Loss showed that even if you kept everything else, you’d still get those surface artifacts if you didn't have that smoothing term <ref:2506.16556#pg8>.

Lu: It confirms that the SDF refinement is actually essential for achieving the continuity they are aiming for, which is a big win because it solves the fragmentation problem <ref:2506.16556#pg9>. They successfully address those common artifacts by combining a two-stage architecture with these distance field priors <ref:2506.16556#pg9>.

Meng: So, for someone who just listens to this show and wants to know what this means practically, it means that if you're trying to analyze medical scans, especially those with tiny vessels or complicated branching, this method gives you a much more reliable three dee map because it’s designed to avoid the common mistakes people make with traditional segmentation <ref:2506.16556#pg9>.

Lalam: It suggests that for future AI systems in healthcare, focusing on continuous geometric representations rather than just discrete labels is where we need to push development if we want models that are truly reliable in complex environments <ref:2506.16556#pg3>.

Tom: Alright, so to wrap up the main point of this paper called "VesselSDF: Distance Field Priors for Vascular Network Reconstruction," they’ve replaced a discrete guesswork approach with a continuous distance field regression problem to get smoother, more accurate vessel reconstructions <ref:2506.16556#pg1>.

Jane: The authors show that by combining their two-stage framework with specific geometric constraints, like the eikonal and Gaussian regularization losses, they can achieve superior results on challenging datasets like Hepatic Vessels <ref:2506.16556#pg9>.

Lu: It’s about taking a known good structure—the SDF—and using it to guide the segmentation process in a way that enforces physical rules on the resulting geometry <ref:2506.16556#pg4>. The implications are that we can expect vessel analysis in clinical settings to become much more trustworthy because they’ve reduced issues like floating geometry and disconnected structures <ref:2506.16556#pg9>.

Meng: Practically speaking, this means diagnostic tools could get much better at identifying subtle vascular patterns without having to rely on highly specialized, hand-crafted segmentation rules for every single case.

Lalam: I see it as the AI culture moving toward models that inherently understand the underlying geometry of things rather than just pattern matching pixels <ref:2506.16556#pg3>. This moves us closer to systems that can reason about structure in a way that feels more intuitive for complex biological data.

Conclusion: Tom: So, this paper is VesselSDF, and it’s all about using signed distance fields to reconstruct blood vessels in three dee medical scans <ref:2506.16556#pg1>.

Jane: Exactly, Tom. The authors are Salvatore Esposito and his team at UKRI CDT in Biomedical AI who are tackling how to make these reconstructions smoother and more accurate than what we see now <ref:2506.16556#pg9>.

Tom: It’s a two-stage approach that separates the initial vessel detection from the actual geometric reconstruction, which they call a signed distance field regression problem <ref:2506.16556#pg4>.

Jane: That separation is key because it lets them apply specific geometric rules later on to enforce continuity and eliminate those messy surface artifacts we talked about earlier <ref:2506.16556#pg4>.

Tom: The overall message here is that by using these distance field priors, the AI gets a much more continuous and topologically sound three dee map of the vascular network <ref:2506.16556#pg9>.

Jane: It means for clinicians looking at scans, you get reconstructions with fewer disconnected structures and better representation of thin vessels <ref:2506.16556#pg7>.

Tom: The numbers on the Hepatic Vessels dataset are pretty solid, showing a Dice Coefficient of zero point seven two and a Hausdorff Distance of four point one <ref:2506.16556#pg7>.

Jane: And the ablation studies they did really prove that removing parts of the framework hurts performance, confirming that the SDF refinement step is actually what brings those improvements <ref:2506.16556#pg8>.

Tom: So, it’s essentially moving away from just labeling pixels to learning the underlying shape directly through distance fields <ref:2506.16556#pg3>.

Jane: That moves us toward AI systems that can reason about structure in a way that feels more intuitive for complex biological data <ref:2506.16556#pg3>.

Tom: What this means for the world is we’re getting tools to analyze complex vascular networks with much higher reliability in clinical settings <ref:2506.16556#pg9>.

Jane: And the next thing we need to look at is how they actually train these models—the specific loss function they use to enforce all those geometric constraints <ref:2506.16556#pg6>.

School of Informatics, University of Edinburgh · Department of Computer Science, University of British Columbia

eess.IV, cs.CV

Submitted: 2025-06-19

Updated: 2026-10-07

Journal ref: International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), 2025

License: http://creativecommons.org/licenses/by-nc-nd/4.0/

Importance score: 89/100

The gist: The gist: VesselSDF presents a novel framework that leverages signed distance fields (SDFs) for robust vessel reconstruction, reformulating segmentation as a continuous SDF regression problem to

Key concepts

Signed Distance Fields (SDFs)
SDFs represent geometry by defining the shortest distance from any point in space to the nearest surface. They are ideal for representing smooth, continuous shapes like vessels because they inherently capture thickness without needing discrete voxels. This allows for a more natural and accurate geometric reconstruction of thin structures.
Two-Stage Framework
VesselSDF separates the problem into two distinct steps: first, segmenting the vessel as a binary map (occupancy prediction), and second, refining that map into a continuous SDF. This separation helps manage complexity and ensures that both detection and geometric reconstruction are handled systematically.
Eikonal Regularization
This regularization term enforces the property that the gradient of the distance field should be close to one everywhere. In simple terms, it encourages the resulting surface to be smooth and continuous, preventing sharp, unnatural changes in distance values during reconstruction.

Terminology

Summary

The gist: VesselSDF presents a novel framework that leverages signed distance fields (SDFs) for robust vessel reconstruction, reformulating segmentation as a continuous SDF regression problem to capture smooth, tubular geometry and eliminate common artifacts.

Problem Statement

Traditional binary vessel segmentation approaches face three critical limitations: the discrete nature of voxel-based representations results in jagged surface artifacts, which are particularly pronounced in thin vessels where the surface-tovolume ratio is high (Page 4). Second, the substantial difference between in-plane resolution ∆x, ∆y and slice thickness ∆z creates anisotropic distortions that fragment vessel structures, especially at branching points (Page 4). Third, existing SDF-based methods often generate floating artifacts, i.e., disconnected surface fragments that degrade reconstruction quality (Page 4).

VesselSDF Framework

VesselSDF is a two-stage framework designed to systematically separate vessel segmentation from geometric reconstruction (Page 4). The overall process involves:

  1. A first stage focusing on binary vessel segmentation via an occupancy prediction function fo(x; θo) using a 3D encoder–decoder CNN-based U-Net architecture that captures multi-scale vessel features (Page 5). This predictor integrates 3D attention gates [13] such that at each level l of the encoder–decoder structure, we combine gating feature maps gl with skip-connection feature maps hl through a learned attention mechanism: αl = ψ(Wg gl + Wh hl) (Page 5).

  2. A second stage that transforms the binary occupancy into a correctly scaled SDF: fSDF(x; θr) = fr detachfo(x; θo); θr (Page 5). This refinement is guided by geometric regularization terms to ensure smooth, accurate vessel reconstructions.

Optimization and Regularization

VesselSDF’s training loss L combines supervised learning and geometric constraints to ensure continuous vessel reconstructions that are both accurate and topologically coherent (Page 6). The total loss is defined as: L = λs Lsdf + λo Locc + λe Leik + λg Lgauss + λr Lsur (Page 6).

The components of the loss function include:

Supervised Terms:

**:Lsdf = Ex∈omega fSDF(x) − f∗ SDF(x) (Page 6). This term supervises the SDF prediction against the ground-truth SDF. **

**:Locc = −Ex∈omega h y logfo(x) + (1 − y) log1 − fo(x) i (Page 6). This term supervises the binary occupancy prediction. **

Eikonal Regularization:

The model enforces near-unit gradients to encourage smooth distance transitions: Leik = Ex∈omega ∂xfSDF(x)2 + ∂yfSDF(x)2 + γ ∂zfSDF(x)2 − 1/2 (Page 6). The parameter γ accounts for anisotropic voxel spacing along the axial dimension.

Distance-weighted Gaussian Regularization:

To suppress high-frequency noise far from vessel boundaries, the method introduces: Lgauss = Ex∈omega fSDF(x) · fSDF(x) − Gσ fSDF(x)2 (Page 6). This term smooths the SDF more aggressively where fSDF(x) is large, preserving fine details near the boundary.

Surface Regularization:

To suppress spurious or “floating” vessel components, the loss includes: Lsur = Ex∈omega exp −β fSDF(x) (Page 6). This term penalizes near-zero SDF values where there is no strong evidence of an actual surface.

Experimental Results

The framework was evaluated on two public hepatic vessel segmentation datasets: the Hepatic Vessels dataset and the IRCADb dataset (Page 7). The quantitative results show VesselSDF significantly outperforms baselines on challenging clinical vessel data containing thin vessels and complex branching patterns (Page 9). Specifically, Table 1 shows that for the Hepatic Vessels Dataset, VesselSDF achieves a Dice Coefficient of 0.72 and a Hausdorff Distance of 4.1 (Page 7). The ablation study confirms the effectiveness of its components: w/o SDF refinement: we remove the second SDF refiner, using only binary occupancy prediction without distance field computation or geometric regularizers (Page 8). Furthermore, removing the adaptive regularization shows that w/o Gaussian Loss: we remove the adaptive regularization (Eq. (8)), which results in similar Dice scores but introduces surface artifacts (Page 8). The full VesselSDF approach achieves best performance across all metrics, with SDF refinement particularly enhancing vessel continuity as shown by the improved reconstruction metrics (Page 9).

Conclusion

VesselSDF demonstrates superior quantitative and qualitative 3D reconstructions compared to baselines on challenging sparse CT slice data containing hepatic vessels, where our results exhibit fewer issues such as floating geometry and disconnected structures (Page 9). The method successfully addresses geometric artifacts by combining a two-stage refinement architecture with distance field priors (Page 9). This approach enables more reliable vascular analysis in clinical settings (Page 1).

--- Page 1 ---

VesselSDF: Distance Field Priors for Vascular Network Reconstruction

Salvatore Esposito, Daniel Rebain, Arno Onken, Changjian Li, and Oisín Mac Aodha (Page 1)

--- Page 2 ---

Traditional segmentation and reconstruction approaches and recent deep learning methods often struggle with the inherent sparsity between imaging planes, leading to discontinuities and loss of critical geometric features [25] (Page 2). While deep learning has shown promise in medical image segmentation [15], current approaches face two critical challenges: (i) maintaining structural coherence and (ii) generalizing beyond the training data [27] (Page 2).

--- Page 3 ---

Signed distance field (SDF) based representations offer a promising solution to these challenges due to their inherent ability to represent smooth, continuous surfaces [1] (Page 3). By encoding geometry through distance fields, SDFs naturally capture thin structures and maintain consistent spatial relationships [1] (Page 3). Inspired by this, we present VesselSDF, a novel approach that leverages these geometric principles while addressing common SDF-based reconstruction artifacts (Page 3).

--- Page 4 ---

Fig. 1. Overview of VesselSDF- our two-stage approach for vessel segmentation and reconstruction from CT scans. In the first stage, a 3D U-Net predicts a binary occupancy map (Page 4). The second stage refines this occupancy into a signed distance field (SDF) using an additional 3D U-Net, guided by geometric regularization terms (Page 4).

--- Page 5 ---

Accurate segmentation of thin, branching vessels requires multi-scale feature representation [1] (Page 5). To achieve this, we integrate 3D attention gates [13] such that at each level l of the encoder–decoder structure, we combine gating feature maps gl with skip-connection feature maps hl through a learned attention mechanism: αl = ψ(Wg gl + Wh hl) (Page 5).

--- Page 6 ---

VesselSDF’s training loss combines supervised learning and geometric constraints to ensure continuous vessel reconstructions that are both accurate and topologically coherent, even for thin, branching vessels: L = λs Lsdf + λo Locc + λe Leik + λg Lgauss + λr Lsur (Page 6).

--- Page 7 ---

We present quantitative results in Table 1 and qualitative results in Fig. 2 where we demonstrate VesselSDF’s superior vessel and portal vein reconstructions on the Hepatic Vessels [2] and IRCADb [19] datasets (Page 7).

--- Page 8 ---

Table 2. Ablations on the Hepatic Vessels dataset (Page 8). w/o SDF refinement: we remove the second SDF refiner, using only binary occupancy prediction without distance field computation or geometric regularizers (Page 8). w/o Binary Occupancy: we directly predict the complete SDF (surface and isolines), bypassing our two-stage approach to test whether separating vessel detection from geometric refinement is beneficial (Page 8). w/o Gaussian Loss: we remove the adaptive regularization (Eq. (8)), which results in similar Dice scores but introduces surface artifacts (Page 8).

--- Page 9 ---

Fig. 2. Qualitative 3D reconstruction results on the Hepatic Vessels dataset. The bottom row displays 2D slices highlighting the segmentation results (Page 9). Our approach preserves thin vessels and complex branching structures more effectively than the binary voxel classification baselines (Page 9).

--- Page 10 ---

Acknowledgments. SE was funded by the UKRI CDT in Biomedical AI (Page 10). Disclosure of Interests. The authors have no competing interests to declare that are relevant to the content of this article (Page 10).

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(Note: The provided text only contains pages 1 through 10, so references beyond page 10 cannot be generated based on the input.)

How it works

VesselSDF is a two-stage framework designed to systematically separate vessel segmentation from geometric reconstruction (Page 4). The overall process involves:

Improvements for AI systems

  1. The system can achieve accurate vessel reconstructions from sparse CT slices by reformulating vessel segmentation as a continuous SDF regression problem. This allows for capturing the smooth, tubular geometry of blood vessels and their branching patterns which is superior to binary classification methods struggling with structural continuity.

  2. The VesselSDF framework incorporates an adaptive Gaussian regularizer which ensures smoothness in regions far from vessel surfaces while producing precise geometry near the surface boundaries, directly addressing the limitation of existing SDF methods by eliminat[ing] common SDF artifacts such as floating segments.

  3. The system can improve generalization across different anatomical variations by reformulating reconstruction as continuous geometric regression rather than discrete voxel classification, enabling it to learn underlying shape principles that transfer across different vessel configurations and anatomical variations.

Abstract

Accurate segmentation of vascular networks from sparse CT scan slices remains a significant challenge in medical imaging, particularly due to the thin, branching nature of vessels and the inherent sparsity between imaging planes. Existing deep learning approaches, based on binary voxel classification, often struggle with structural continuity and geometric fidelity. To address this challenge, we present VesselSDF, a novel framework that leverages signed distance fields (SDFs) for robust vessel reconstruction. Our method reformulates vessel segmentation as a continuous SDF regression problem, where each point in the volume is represented by its signed distance to the nearest vessel surface. This continuous representation inherently captures the smooth, tubular geometry of blood vessels and their branching patterns. We obtain accurate vessel reconstructions while eliminating common SDF artifacts such as floating segments, thanks to our adaptive Gaussian regularizer which ensures smoothness in regions far from vessel surfaces while producing precise geometry near the surface boundaries. Our experimental results demonstrate that VesselSDF significantly outperforms existing methods and preserves vessel geometry and connectivity, enabling more reliable vascular analysis in clinical settings.

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