The Texture-Shape Dilemma: Boundary-Safe Synthetic Generation for 3D Medical Transformers

Vision Transformers (ViTs) have revolutionized medical image analysis, yet their data-hungry nature clashes with the scarcity and privacy constraints of clinical archives. Formula-Driven Supervised Learning (FDSL) has emerged as a promising solution to this bottleneck, synthesizing infinite annotated samples from mathematical formulas without utilizing real patient data. However, existing FDSL paradigms rely on simple geometric shapes with homogeneous intensities, creating a substantial gap by neglecting tissue textures and noise patterns inherent in modalities like CT and MRI. In this paper, we identify a critical optimization conflict termed boundary aliasing: when high-frequency synthetic textures are naively added, they corrupt the image gradient signals necessary for learning structural boundaries, causing the model to fail in delineating real anatomical margins. To bridge this gap, we propose a novel Physics-inspired Spatially-Decoupled Synthesis framework. Our approach orthogonalizes the synthesis process: it first constructs a gradient-shielded buffer zone based on boundary distance to ensure stable shape learning, and subsequently injects physics-driven spectral textures into the object core. This design effectively reconciles robust shape representation learning with invariance to acquisition noise. Extensive experiments on the BTCV and MSD datasets demonstrate that our method significantly outperforms previous FDSL, as well as SSL methods trained on real-world medical datasets, by 1.43% on BTCV and up to 1.51% on MSD task, offering a scalable, annotation-free foundation for medical ViTs. The code will be made publicly available upon acceptance.