GeoSFLoRA: Geometry-Conditioned Spectral Flow Low-Rank Adaptation for 2D-to-3D Transfer in Medical Image Segmentation

Abstract

Accurate volumetric medical image segmentation is critical for clinical diagnosis, yet adapting two-dimensional vision foundation models (VFMs) to three-dimensional medical imaging remains challenging. While parameter-efficient fine-tuning (PEFT) methods such as LoRA and adapter-based schemes provide efficient alternatives to full fine-tuning, their geometry-agnostic parameter-space adaptations are insufficient to reconcile discrepancies induced by anisotropic voxel spacing and inter-slice discontinuities. We propose GeoSFLoRA, a geometry-constrained spectral-flow low-rank adaptation framework for efficient 2D-to-3D transfer learning. GeoSFLoRA adapts frozen 2D pretrained vision backbones by operating within a fixed low-rank spectral subspace induced by pretrained linear projections. For each adapted layer, a truncated singular value decomposition is computed once and kept frozen, preserving the original pretrained bases. A lightweight Geometry-Conditioned Encoder (GCE) extracts local volumetric descriptors, which are mapped to token-conditional residuals in the singular-value space, enabling bounded and geometry-aware spectral modulation. GeoSFLoRA consistently improves Dice and HD95 on BraTS20, MSD-Prostate, and MSD-Lung, approaching full fine-tuning performance and demonstrating an effective paradigm for 2D-to-3D medical image segmentation. The code is publicly available at https://github.com/chenbn266/GeoSFLoRA.