A deep-learning framework for brain tumor segmentation via three-dimensional mass-preserving geometric transformation

Tsung-Ming Huang; Kai-Qian Zheng; Wen-Wei Lin; Tiexiang Li; Shing-Tung Yau

doi:10.1186/s40708-026-00307-z

A deep-learning framework for brain tumor segmentation via three-dimensional mass-preserving geometric transformation

Brain Inform. 2026 May 5;13(1):14. doi: 10.1186/s40708-026-00307-z.

Authors

Tsung-Ming Huang¹, Kai-Qian Zheng², Wen-Wei Lin^{2

3}, Tiexiang Li^{3

4}, Shing-Tung Yau⁵

Affiliations

¹ Department of Mathematics, National Taiwan Normal University, Taipei, 116, Taiwan. min@ntnu.edu.tw.
² Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu, 300, Taiwan.
³ Shanghai Institute for Mathematics and Interdisciplinary Sciences, Shanghai, China.
⁴ School of Mathematics, Southeast University, Nanjing, China.
⁵ Yau Mathematical Sciences Center, Tsinghua University, Beijing, China.

Abstract

This article presents a robust and efficient framework for brain tumor segmentation based on deep learning. We introduce a novel three-dimensional (3D) mass-preserving geometric transformation (MPGT) that employs a homotopy method to transform irregular brain magnetic resonance (MR) images into standardized solid cubes. This transformation preserves local mass ratios while maintaining global structural integrity, providing a structured input for deep learning models. Furthermore, we propose a modified two-phase segmentation strategy to minimize inference time and a postprocessing technique to enhance lesion-wise performance. Extensive validation on the Brain Tumor Segmentation (BraTS) Challenge 2023 dataset demonstrates that our method, when integrated with nnU-Net, achieves competitive Dice scores of 0.9282 (Whole Tumor), 0.8812 (Tumor Core), and 0.8527 (Enhanced Tumor). These results are superior to or comparable with top-ranking competition entries.

Keywords: 3D medical imaging; Brain tumor segmentation; Geometric transformation; Homotopy method; Mass-preserving parameterization; Two-phase segmentation; nnU-Net.