FDIF: Formula-Driven supervised Learning with Implicit Functions for 3D Medical Image Segmentation

2026-03-24

AI Summary

This work addresses the challenge of scarce and expert-dependent annotations in 3D medical image segmentation by proposing a synthetic data-free, formula-driven pretraining framework. It introduces the signed distance function (SDF) into implicit representations for the first time, enabling mathematically controlled synthesis of 3D training samples that exhibit both complex geometric structures and realistic intensity textures. Evaluated with mainstream architectures such as SwinUNETR and nnUNet across three major benchmarks—AMOS, ACDC, and KiTS—the method significantly outperforms existing formula-driven approaches and achieves performance on par with large-scale real-data-based self-supervised pretraining. Furthermore, the learned representations successfully transfer to 3D classification tasks, overcoming the limited expressiveness inherent in conventional voxel-based methods.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Representation Learning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Semantics and Knowledge: Representation, semantic annotation, enhancement, enrichments, access and/or integration of a variety of data on the Web
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

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.

Problem

• 3D medical image segmentation
• labeled data scarcity
• expert annotation cost
• privacy constraints
• data-free representation learning

Innovation

• Implicit Functions
• Signed Distance Functions
• Formula-Driven Supervised Learning
• Data-Free Pretraining
• 3D Medical Image Segmentation