Topological correctness, i.e., the preservation of structural integrity and specific characteristics of shape, is a fundamental requirement for medical imaging tasks, such as neuron or vessel segmentation. Despite the recent surge in topology-aware methods addressing this challenge, their real-world applicability is hindered by flawed benchmarking practices. In this paper, we identify critical pitfalls in model evaluation that include inadequate connectivity choices, overlooked topological artifacts in ground truth annotations, and inappropriate use of evaluation metrics. Through detailed empirical analysis, we uncover these issues' profound impact on the evaluation and ranking of segmentation methods. Drawing from our findings, we propose a set of actionable recommendations to establish fair and robust evaluation standards for topology-aware medical image segmentation methods.

Data-driven deformable image registration methods predominantly rely on operations that process grid-like inputs. However, applying deformable transformations to an image results in a warped space that deviates from a rigid grid structure. Consequently, data-driven approaches with sequential deformations have to apply grid resampling operations between each deformation step. While artifacts caused by resampling are negligible in high-resolution images, the resampling of sparse, high-dimensional feature grids introduces errors that affect the deformation modeling process. Taking inspiration from Lagrangian reference frames of deformation fields, our work introduces a novel paradigm for data-driven deformable image registration that utilizes geometric deep-learning principles to model deformations without grid requirements. Specifically, we model image features as a set of nodes that freely move in Euclidean space, update their coordinates under graph operations, and dynamically readjust their local neighborhoods. We employ this formulation to construct a multi-resolution deformable registration model, where deformation layers iteratively refine the overall transformation at each resolution without intermediate resampling operations on the feature grids. We investigate our method's ability to fully deformably capture large deformations across a number of medical imaging registration tasks. In particular, we apply our approach (GeoReg) to the registration of inter-subject brain MR images and inhale-exhale lung CT images, showing on par performance with the current state-of-the-art methods. We believe our contribution open up avenues of research to reduce the black-box nature of current learned registration paradigms by explicitly modeling the transformation within the architecture.

Anatomical atlases are widely used for population analysis. Conditional atlases target a particular sub-population defined via certain conditions (e.g. demographics or pathologies) and allow for the investigation of fine-grained anatomical differences - such as morphological changes correlated with age. Existing approaches use either registration-based methods that are unable to handle large anatomical variations or generative models, which can suffer from training instabilities and hallucinations. To overcome these limitations, we use latent diffusion models to generate deformation fields, which transform a general population atlas into one representing a specific sub-population. By generating a deformation field and registering the conditional atlas to a neighbourhood of images, we ensure structural plausibility and avoid hallucinations, which can occur during direct image synthesis. We compare our method to several state-of-the-art atlas generation methods in experiments using 5000 brain as well as whole-body MR images from UK Biobank. Our method generates highly realistic atlases with smooth transformations and high anatomical fidelity, outperforming the baselines.

The Circle of Willis (CoW) is an important network of arteries connecting major circulations of the brain. Its vascular architecture is believed to affect the risk, severity, and clinical outcome of serious neuro-vascular diseases. However, characterizing the highly variable CoW anatomy is still a manual and time-consuming expert task. The CoW is usually imaged by two angiographic imaging modalities, magnetic resonance angiography (MRA) and computed tomography angiography (CTA), but there exist limited public datasets with annotations on CoW anatomy, especially for CTA. Therefore we organized the TopCoW Challenge in 2023 with the release of an annotated CoW dataset. The TopCoW dataset was the first public dataset with voxel-level annotations for thirteen possible CoW vessel components, enabled by virtual-reality (VR) technology. It was also the first large dataset with paired MRA and CTA from the same patients. TopCoW challenge formalized the CoW characterization problem as a multiclass anatomical segmentation task with an emphasis on topological metrics. We invited submissions worldwide for the CoW segmentation task, which attracted over 140 registered participants from four continents. The top performing teams managed to segment many CoW components to Dice scores around 90%, but with lower scores for communicating arteries and rare variants. There were also topological mistakes for predictions with high Dice scores. Additional topological analysis revealed further areas for improvement in detecting certain CoW components and matching CoW variant topology accurately. TopCoW represented a first attempt at benchmarking the CoW anatomical segmentation task for MRA and CTA, both morphologically and topologically.