Global Control for Local SO(3)-Equivariant Scale-Invariant Vessel Segmentation

TL;DR

The paper tackles the challenge of generating accurate, topologically correct 3D vascular models with user-controlled regions of interest. It introduces a global controller that leverages coarse segmentations to provide seed points $p_i$ and ROI boundaries $\Omega_i$, guiding a local, scale-invariant, rotation-equivariant vessel tracker which jointly segments vessels. Surface realism is achieved by fitting a neural field representing the signed distance function (SDF) to the contour outputs, producing watertight meshes at arbitrary resolution. The approach demonstrates competitive segmentation quality on AAA-related arteries (aorta, iliac, renal) with strong data efficiency and flexible ROI modification, enabling streamlined, patient-specific vascular modeling suitable for diagnostic and planning tasks.

Abstract

Personalized 3D vascular models can aid in a range of diagnostic, prognostic, and treatment-planning tasks relevant to cardiovascular disease management. Deep learning provides a means to obtain such models automatically from image data. Ideally, a user should have control over the included region in the vascular model. Additionally, the model should be watertight and highly accurate. To this end, we propose a combination of a global controller leveraging voxel mask segmentations to provide boundary conditions for vessels of interest to a local, iterative vessel segmentation model. We introduce the preservation of scale- and rotational symmetries in the local segmentation model, leading to generalisation to vessels of unseen sizes and orientations. Combined with the global controller, this enables flexible 3D vascular model building, without additional retraining. We demonstrate the potential of our method on a dataset containing abdominal aortic aneurysms (AAAs). Our method performs on par with a state-of-the-art segmentation model in the segmentation of AAAs, iliac arteries, and renal arteries, while providing a watertight, smooth surface representation. Moreover, we demonstrate that by adapting the global controller, we can easily extend vessel sections in the 3D model.

Figures (4)

• Figure 1: Proposed framework. A global segmentation or localization method is used to provide boundary conditions $[\Omega_i, p_i]$, such as points or regions-of-interest (ROIs) for the global control of local vessel segmentation. A local joint tracking and segmentation model accurately segments vessels in a rotation-equivariant, scale-invariant manner. Obtained contour sets are reconstructed into a watertight surface using neural fields and blended into a single vascular model alblas2022going.
• Figure 2: Overview of our iterative segmentation method, consisting of two steps. (1) At a point $x$, local vessel orientations are determined based on multi-scale spherical image features. (2) Based on the multi-scale responses, the optimal scale $\tilde{r}$ is selected, from which a scale-adaptive polar image normal to the local vessel orientation is constructed. CNN $h(\cdot; \theta_h)$ predicts lumen radii for each angle in $p^{\text{in}}_{\tilde{r}}$, forming a closed contour in Cartesian space.
• Figure 3: DSC scores of the contour regression modules on 2D contours in the test set for the data ablation experiments. Left: DSC for all contours for data ablation at patient level. Right: DSC per vessel for data ablation at the vessel level.
• Figure 4: Automatically acquired 3D vascular models using different $\Omega_{\text{aorta}}$.