Location Matters: Frequency-Spatial Dual-Space Adaptation for Cross-Domain Few-Shot Segmentation

Current cross-domain few-shot semantic segmentation (CD-FSS) methods tend to overlook a fundamental yet domain-agnostic prior: the spatial correspondence between support and query images driven by the task itself. Unlike semantic similarity, this spatial correlation arises from the consistent structural layout of foreground objects across domains. To exploit this structural prior, we propose a novel frequency-spatial dual space adaptation (FDSA) framework, to learn domain-invariant structures and task-specific priors by jointly suppressing domain-specific redundancy in frequency domain and reinforcing geometric priors in spatial domain. Specifically, FDSA consists of two sequential modules, i.e., the frequency structural adapter (FSA) and the spatial geometry adapter (SGA). FSA performs image modulation in the frequency domain by emphasizing low-frequency foreground semantics and attenuating high-frequency noise, thus maintaining structural integrity of these input images. By contrast, SGA leverages handcrafted local descriptors to extract keypoints from both support and query images, generating Gaussian-based geometric priors that highlight desirable aligned regions. Additionally, we introduce spatial-guided SAM refinement (SSR) to extend our spatial geometric prior into the Segment Anything Model (SAM). SSR generates a soft Gaussian point prompt centered on the coarse mask, enabling SAM to refine segmentation masks without manual intervention. This integration effectively bridges task-specific localization with high-quality segmentation. Extensive experiments on four standard CD-FSS benchmarks demonstrate that our method achieves new state-of-the-art performance. Code is available at https://github.com/CVL-hub/FDSA.git.