# Patch-based Medical Image Segmentation using Matrix Product State Tensor Networks

arXiv: https://arxiv.org/abs/2109.07138 · HTML: https://mlsanity.com/paper/2109.07138/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 60 references that are in the map.
- First posted on arXiv 15 Sep 2021.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [The Medical Segmentation Decathlon](https://mlsanity.com/paper/2106.05735/) (2021)
- [Identifying the Best Machine Learning Algorithms for Brain Tumor Segmentation, Progression Assessment, and Overall Survival Prediction in the BRATS Challenge](https://mlsanity.com/paper/1811.02629/) (2018)
- [Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers](https://mlsanity.com/paper/1811.04918/) (2018)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Carbontracker: Tracking and Predicting the Carbon Footprint of Training Deep Learning Models](https://mlsanity.com/paper/2007.03051/) (2020)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [The De-democratization of AI: Deep Learning and the Compute Divide in Artificial Intelligence Research](https://mlsanity.com/paper/2010.15581/) (2020)
- [TensorNetwork for Machine Learning](https://mlsanity.com/paper/1906.06329/) (2019)
- [One Network to Segment Them All: A General, Lightweight System for Accurate 3D Medical Image Segmentation](https://mlsanity.com/paper/1911.01764/) (2019)
- [Tensor Networks for Medical Image Classification](https://mlsanity.com/paper/2004.10076/) (2020)
- [Tensor-based algorithms for image classification](https://mlsanity.com/paper/1910.02150/) (2019)
- [Probabilistic Graphical Models and Tensor Networks: A Hybrid Framework](https://mlsanity.com/paper/2106.15666/) (2021)
- [Segmenting two-dimensional structures with strided tensor networks](https://mlsanity.com/paper/2102.06900/) (2021)
- [Locally orderless tensor networks for classifying two- and three-dimensional medical images](https://mlsanity.com/paper/2009.12280/) (2020)

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

- [Deep Tree Tensor Networks](https://mlsanity.com/paper/2502.09928/) (2025)
- [Positive unlabeled learning with tensor networks](https://mlsanity.com/paper/2211.14085/) (2022)

## Abstract (arXiv)

Tensor networks are efficient factorisations of high-dimensional tensors into a network of lower-order tensors. They have been most commonly used to model entanglement in quantum many-body systems and more recently are witnessing increased applications in supervised machine learning. In this work, we formulate image segmentation in a supervised setting with tensor networks. The key idea is to first lift the pixels in image patches to exponentially high-dimensional feature spaces and using a linear decision hyper-plane to classify the input pixels into foreground and background classes. The high-dimensional linear model itself is approximated using the matrix product state (MPS) tensor network. The MPS is weight-shared between the non-overlapping image patches resulting in our strided tensor network model. The performance of the proposed model is evaluated on three 2D- and one 3D- biomedical imaging datasets. The performance of the proposed tensor network segmentation model is compared with relevant baseline methods. In the 2D experiments, the tensor network model yields competitive performance compared to the baseline methods while being more resource efficient.