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

TL;DR

FDIF introduces a formula-driven, implicit-function-based pre-training framework for 3D medical image segmentation that eliminates the need for real data and annotations, achieving competitive results.

Contribution

The paper presents FDIF, a novel implicit-function-based framework enabling scalable, data-free pre-training for 3D medical image segmentation and classification tasks.

Findings

FDIF improves segmentation performance across multiple benchmarks and architectures.

FDIF achieves results comparable to large-scale self-supervised pre-training.

FDIF benefits 3D classification tasks, demonstrating its versatility.

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.