Fake It Right: Injecting Anatomical Logic into Synthetic Supervised Pre-training for Medical Segmentation

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.

Deep learning-based 3D medical image segmentation methods relies on large-scale labeled datasets, yet acquiring such data is difficult due to privacy constraints and the high cost of expert annotation. Formula-Driven Supervised Learning (FDSL) offers an appealing alternative by generating training data and labels directly from mathematical formulas. However, existing voxel-based approaches are limited in geometric expressiveness and cannot synthesize realistic textures. We introduce Formula-Driven supervised learning with Implicit Functions (FDIF), a framework that enables scalable pre-training without using any real data and medical expert annotations. FDIF introduces an implicit-function representation based on signed distance functions (SDFs), enabling compact modeling of complex geometries while exploiting the surface representation of SDFs to support controllable synthesis of both geometric and intensity textures. Across three medical image segmentation benchmarks (AMOS, ACDC, and KiTS) and three architectures (SwinUNETR, nnUNet ResEnc-L, and nnUNet Primus-M), FDIF consistently improves over a formula-driven method, and achieves performance comparable to self-supervised approaches pre-trained on large-scale real datasets. We further show that FDIF pre-training also benefits 3D classification tasks, highlighting implicit-function-based formula supervision as a promising paradigm for data-free representation learning. Code is available at https://github.com/yamanoko/FDIF.

Deep learning and generative models are advancing rapidly, with synthetic data increasingly being integrated into training pipelines for downstream analysis tasks. However, in medical imaging, their adoption remains constrained by the scarcity of reliable annotated datasets. To address this limitation, we propose 3D-LLDM, a label-guided 3D latent diffusion model that generates high-quality synthetic magnetic resonance (MR) volumes with corresponding anatomical segmentation masks. Our approach uses hepatobiliary phase MR images enhanced with the Gd-EOB-DTPA contrast agent to derive structural masks for the liver, portal vein, hepatic vein, and hepatocellular carcinoma, which then guide volumetric synthesis through a ControlNet-based architecture. Trained on 720 real clinical hepatobiliary phase MR scans from Samsung Medical Center, 3D-LLDM achieves a Fréchet Inception Distance (FID) of 28.31, improving over GANs by 70.9% and over state-of-the-art diffusion baselines by 26.7%. When used for data augmentation, the synthetic volumes improve hepatocellular carcinoma segmentation by up to 11.153% Dice score across five CNN architectures.