# Fast Marching Energy CNN

arXiv: https://arxiv.org/abs/2306.16109 · HTML: https://mlsanity.com/paper/2306.16109/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 16 references that are in the map.
- First posted on arXiv 28 Jun 2023.

## Builds on (most cited first, 5 of 5)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [A review of deep learning in medical imaging: Imaging traits, technology trends, case studies with progress highlights, and future promises](https://mlsanity.com/paper/2008.09104/) (2020)
- [Riemannian Metric Learning via Optimal Transport](https://mlsanity.com/paper/2205.09244/) (2022)
- [Ground Metric Learning on Graphs](https://mlsanity.com/paper/1911.03117/) (2019)

## Built on by (most cited first, 1 of 1)

- [Metric Convolutions: A Unifying Theory to Adaptive Image Convolutions](https://mlsanity.com/paper/2406.05400/) (2024)

## Abstract (arXiv)

Leveraging geodesic distances and the geometrical information they convey is key for many data-oriented applications in imaging. Geodesic distance computation has been used for long for image segmentation using Image based metrics. We introduce a new method by generating isotropic Riemannian metrics adapted to a problem using CNN and give as illustrations an example of application. We then apply this idea to the segmentation of brain tumours as unit balls for the geodesic distance computed with the metric potential output by a CNN, thus imposing geometrical and topological constraints on the output mask. We show that geodesic distance modules work well in machine learning frameworks and can be used to achieve state-of-the-art performances while ensuring geometrical and/or topological properties.