CROWn: A Unified Framework for Anti-Aliased Downsampling and Phase-Calibrated Fusion in 3D Medical Segmentation

Precise 3D medical image segmentation is a clinical cornerstone for diagnosis, therapy planning, and longitudinal monitoring. However, routine acquisition with anisotropic voxel spacing and heterogeneous reconstruction induces downsampling aliasing and cross-scale misalignment that blur boundaries, fragment topology, and undermine reliability. Existing U-shaped CNN or Transformer designs neither control alias injection at decimation nor explicitly align high-resolution evidence before decoder fusion, leading to unstable interfaces under device and protocol variability. We introduce the Coset-fibRated micrO-local co-attention Network (CROWn), a general segmentation framework that couples sampling theory with representation learning to jointly suppress aliasing and calibrate cross-scale fusion. CROWn comprises two complementary components. The Microlocal Polyphase Co-Attentive Decimator (\muPCAD) performs axis-aware polyphase analysis with pooled-subband co-attention and explicit anti-alias low-pass, routing boundary-relevant high-frequency evidence while attenuating spurious phase components during downsampling. The Octaphase Coset Fibration (OCF) anti-aliases high-resolution skips, restructures them via 3D space-to-depth into cosets, and applies phase attention with edge-gated modulation to deliver compact, phase-aligned, boundary-aware features to the decoder. Extensive evaluations across 15 publicly available datasets spanning CT, MRI, and OCT demonstrate CROWn's state-of-the-art performance against 17 recent leading methods, improves overlap and topological consistency, consistently reduces boundary errors, while maintaining controlled training and inference cost. The code is publicly available at https://github.com/IMOP-lab/CROWn.