LatticeRank: Spacing-Ranked Consistency for Native-Grid 3D Medical Image Segmentation

Volumetric medical image segmentation is essential for both preoperative diagnosis and intraoperative guidance. While recent years have witnessed rapid progress in segmentation architectures, comparatively little attention is paid to the physical voxel spacing of anatomical data. Indeed, volumetric image resampling is a ubiquitous preprocessing step before segmentation, yet its interaction with downstream segmentation has not been systematically exploited. In this work, we study the correlation between image resampling and segmentation, and propose Consispace, a semantic-aware resampling framework that achieves consistent voxel spacing in the axial direction while preserving anatomical and semantic consistency. Consispace introduces an ODE-based anatomical constraint to model inter-slice dynamics with a continuous interpolator, enabling faithful reconstruction under complex anatomical transitions beyond discrete interpolation. To further couple resampling with segmentation objectives, we leverage dense features from a pretrained vision model to build intra-slice semantic correlation maps and inject class-wise semantic consistency via feature reweighting during resampling. Both intra-slice and inter-slice constraints are integrated into an implicit neural network, supporting arbitrary-scale resampling. Extensive experiments on multiple datasets demonstrate that Consispace achieves superior reconstruction quality and perceptual fidelity, produces smoother inter-slice anatomy, and improves downstream segmentation performance when used as a preprocessing step.

Three-dimensional (3D) medical image enhancement, including denoising and super-resolution, is critical for clinical diagnosis in CT, PET, and MRI. Although diffusion models have shown remarkable success in 2D medical imaging, scaling them to high-resolution 3D volumes remains computationally prohibitive due to lengthy diffusion trajectories over high-dimensional volumetric data. We observe that in conditional enhancement, strong anatomical priors in the degraded input render dense noise schedules largely redundant. Leveraging this insight, we propose a sparse voxel-space diffusion framework that trains and samples on a compact set of uniformly subsampled timesteps. The network predicts clean data directly on the data manifold, supervised in velocity space for stable gradient scaling. A lightweight Structure-aware Trajectory Modulation (STM) module recalibrates time embeddings at each network block based on local anatomical content, enabling structure-adaptive denoising over the shared sparse schedule. Operating directly in voxel space, our framework preserves fine anatomical detail without lossy compression while achieving up to $10\times$ training acceleration. Experiments on four datasets spanning CT, PET, and MRI demonstrate state-of-the-art performance on both denoising and super-resolution tasks. Our code is publicly available at: https://github.com/mirthAI/sparse-3d-diffusion.

The growing number of medical vision foundation models highlights the need for effective model selection. However, mainstream selection methods rely on exhaustive fine-tuning, which is computationally expensive. Most of the existing Transferability Estimation (TE) metrics are primarily designed for image-level classification. They fail to preserve spatial relationships and fine-grained boundary details, which are crucial for the segmentation task. Additionally, while image-level tasks typically process a single feature vector per input, dense prediction tasks in 3D medical imaging require voxel-wise evaluation against dense annotations. To bridge these gaps, we propose a non-parametric, topology-driven framework that estimates transferability directly from the alignment between the sparse 1-skeleton graph of dense features and semantic labels via Minimum Spanning Trees (MST). We decouple the alignment into two complementary geometric scales: Local Boundary-Aware Topological Consistency (LBTC) to assess boundary separability, where we prove that the MST leakage rate serves as a finite-sample lower bound on the Bayes error; and Global Representation Topology Divergence (GRTD) to evaluate the overall anatomical layout. Crucially, we formally justify a counterintuitive mechanism: Although without fine-tuning, the randomly initialized segmentation decoder acts as a topology-preserving spatial projector, reducing the variance of pairwise distance estimates and stabilizing global alignment evaluation. Fused via a task-adaptive gating mechanism, these dual metrics adapt to diverse clinical complexities. Evaluated on a large-scale benchmark of 114,000 3D medical volumes across diverse anatomical tasks, our topological framework achieves state-of-the-art transferability estimation with an average weighted Kendall (outperforming by 0.36) while accelerating evaluation by 56 times.