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SiNGR: Brain Tumor Segmentation via Signed Normalized Geodesic Transform Regression

Trung Dang, Huy Hoang Nguyen, Aleksei Tiulpin

TL;DR

This work tackles boundary uncertainty in brain tumor segmentation by replacing traditional voxel-wise classification with a voxel-wise regression that learns a soft certainty map. It introduces the Signed Normalized Geodesic Transform (SiNG) to generate signed soft labels that emphasize tumor borders and a Focal-L1 loss to weight hard voxels more heavily during training. Across BraTS 2020 and LGG FLAIR, SiNGR consistently improves Dice and HD95 across architectures (e.g., UNet3D, NestedFormer, Swin-UNETR), confirming its architecture-agnostic benefits. The method is simple to implement, end-to-end trainable, and accompanied by public code, making it practical for broader adoption in clinical brain tumor segmentation tasks.

Abstract

One of the primary challenges in brain tumor segmentation arises from the uncertainty of voxels close to tumor boundaries. However, the conventional process of generating ground truth segmentation masks fails to treat such uncertainties properly. Those "hard labels" with 0s and 1s conceptually influenced the majority of prior studies on brain image segmentation. As a result, tumor segmentation is often solved through voxel classification. In this work, we instead view this problem as a voxel-level regression, where the ground truth represents a certainty mapping from any pixel to the border of the tumor. We propose a novel ground truth label transformation, which is based on a signed geodesic transform, to capture the uncertainty in brain tumors' vicinity. We combine this idea with a Focal-like regression L1-loss that enables effective regression learning in high-dimensional output space by appropriately weighting voxels according to their difficulty. We thoroughly conduct an experimental evaluation to validate the components of our proposed method, compare it to a diverse array of state-of-the-art segmentation models, and show that it is architecture-agnostic. The code of our method is made publicly available (\url{https://github.com/Oulu-IMEDS/SiNGR/}).

SiNGR: Brain Tumor Segmentation via Signed Normalized Geodesic Transform Regression

TL;DR

This work tackles boundary uncertainty in brain tumor segmentation by replacing traditional voxel-wise classification with a voxel-wise regression that learns a soft certainty map. It introduces the Signed Normalized Geodesic Transform (SiNG) to generate signed soft labels that emphasize tumor borders and a Focal-L1 loss to weight hard voxels more heavily during training. Across BraTS 2020 and LGG FLAIR, SiNGR consistently improves Dice and HD95 across architectures (e.g., UNet3D, NestedFormer, Swin-UNETR), confirming its architecture-agnostic benefits. The method is simple to implement, end-to-end trainable, and accompanied by public code, making it practical for broader adoption in clinical brain tumor segmentation tasks.

Abstract

One of the primary challenges in brain tumor segmentation arises from the uncertainty of voxels close to tumor boundaries. However, the conventional process of generating ground truth segmentation masks fails to treat such uncertainties properly. Those "hard labels" with 0s and 1s conceptually influenced the majority of prior studies on brain image segmentation. As a result, tumor segmentation is often solved through voxel classification. In this work, we instead view this problem as a voxel-level regression, where the ground truth represents a certainty mapping from any pixel to the border of the tumor. We propose a novel ground truth label transformation, which is based on a signed geodesic transform, to capture the uncertainty in brain tumors' vicinity. We combine this idea with a Focal-like regression L1-loss that enables effective regression learning in high-dimensional output space by appropriately weighting voxels according to their difficulty. We thoroughly conduct an experimental evaluation to validate the components of our proposed method, compare it to a diverse array of state-of-the-art segmentation models, and show that it is architecture-agnostic. The code of our method is made publicly available (\url{https://github.com/Oulu-IMEDS/SiNGR/}).
Paper Structure (11 sections, 4 equations, 3 figures, 3 tables)

This paper contains 11 sections, 4 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Method
  3. Overview
  4. Signed Normalized Geodesic Transform
  5. Unsigned transform.
  6. Signed version.
  7. Focal-L1 Loss
  8. Experiments
  9. Setup
  10. Results
  11. Conclusion

Figures (3)

  • Figure 1: The overview of Signed Normalized Geodesic transform Regression (SiNGR).
  • Figure 2: Comparison between L1 and Focal-L1 losses: (a-b) 2D loss surfaces, and (c) a behavior of the proposed Focal-L1 loss. Colors in (a-b) represent loss magnitudes. In (c), we assume that $|\mathcal{S}_i| = 1$ or $|\mathcal{Z}_i|=1, \forall i \in \Omega$.
  • Figure 3: Pair-wise comparisons between baselines using hard labels (in blue) and our method (in orange) across different architectures and metrics. NF, SU, and TBTS mean NestedFormer, Swin-UNETR, and TransBTS respectively.