# An End-to-End learnable Flow Regularized Model for Brain Tumor Segmentation

arXiv: https://arxiv.org/abs/2109.00622 · HTML: https://mlsanity.com/paper/2109.00622/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 1 Sep 2021.

## Builds on (most cited first, 6 of 6)

- [Efficient Multi-Scale 3D CNN with Fully Connected CRF for Accurate Brain Lesion Segmentation](https://mlsanity.com/paper/1603.05959/) (2016)
- [Improving Cytoarchitectonic Segmentation of Human Brain Areas with Self-supervised Siamese Networks](https://mlsanity.com/paper/1806.05104/) (2018)
- [MRI Tumor Segmentation with Densely Connected 3D CNN](https://mlsanity.com/paper/1802.02427/) (2018)
- [Autofocus Layer for Semantic Segmentation](https://mlsanity.com/paper/1805.08403/) (2018)
- [CompNet: Complementary Segmentation Network for Brain MRI Extraction](https://mlsanity.com/paper/1804.00521/) (2018)
- [Deep Recurrent Level Set for Segmenting Brain Tumors](https://mlsanity.com/paper/1810.04752/) (2018)

## Abstract (arXiv)

Many segmentation tasks for biomedical images can be modeled as the minimization of an energy function and solved by a class of max-flow and min-cut optimization algorithms. However, the segmentation accuracy is sensitive to the contrasting of semantic features of different segmenting objects, as the traditional energy function usually uses hand-crafted features in their energy functions. To address these limitations, we propose to incorporate end-to-end trainable neural network features into the energy functions. Our deep neural network features are extracted from the down-sampling and up-sampling layers with skip-connections of a U-net. In the inference stage, the learned features are fed into the energy functions. And the segmentations are solved in a primal-dual form by ADMM solvers. In the training stage, we train our neural networks by optimizing the energy function in the primal form with regularizations on the min-cut and flow-conservation functions, which are derived from the optimal conditions in the dual form. We evaluate our methods, both qualitatively and quantitatively, in a brain tumor segmentation task. As the energy minimization model achieves a balance on sensitivity and smooth boundaries, we would show how our segmentation contours evolve actively through iterations as ensemble references for doctor diagnosis.