# Nonlinear Markov Random Fields Learned via Backpropagation

arXiv: https://arxiv.org/abs/1902.10747 · HTML: https://mlsanity.com/paper/1902.10747/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2019.

## Built on by (most cited first, 2 of 2)

- [An MRF-UNet Product of Experts for Image Segmentation](https://mlsanity.com/paper/2104.05495/) (2021)
- [Factorisation-based Image Labelling](https://mlsanity.com/paper/2111.10326/) (2021)

## Abstract (arXiv)

Although convolutional neural networks (CNNs) currently dominate competitions on image segmentation, for neuroimaging analysis tasks, more classical generative approaches based on mixture models are still used in practice to parcellate brains. To bridge the gap between the two, in this paper we propose a marriage between a probabilistic generative model, which has been shown to be robust to variability among magnetic resonance (MR) images acquired via different imaging protocols, and a CNN. The link is in the prior distribution over the unknown tissue classes, which are classically modelled using a Markov random field. In this work we model the interactions among neighbouring pixels by a type of recurrent CNN, which can encode more complex spatial interactions. We validate our proposed model on publicly available MR data, from different centres, and show that it generalises across imaging protocols. This result demonstrates a successful and principled inclusion of a CNN in a generative model, which in turn could be adapted by any probabilistic generative approach for image segmentation.