Abstract
Tensor networks provide an efficient approximation of operations involving high dimensional tensors and have been extensively used in modelling quantum many-body systems. More recently, supervised learning has been attempted with tensor networks, primarily focused on tasks such as image classification. In this work, we propose a novel formulation of tensor networks for supervised image segmentation which allows them to operate on high resolution medical images. We use the matrix product state (MPS) tensor network on non-overlapping patches of a given input image to predict the segmentation mask by learning a pixel-wise linear classification rule in a high dimensional space. The proposed model is end-to-end trainable using backpropagation. It is implemented as a strided tensor network to reduce the parameter complexity. The performance of the proposed method is evaluated on two public medical imaging datasets and compared to relevant baselines. The evaluation shows that the strided tensor network yields competitive performance compared to CNN-based models while using fewer resources. Additionally, based on the experiments we discuss the feasibility of using fully linear models for segmentation tasks.(Source code: https://github.com/raghavian/strided-tenet)
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Notes
- 1.
First author of [22] noted their U-net work was cited more than once every hour in 2020. https://bit.ly/unet2020.
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Matrix product states are also known as Tensor Trains in literature.
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Tensor product is the generalisation of matrix outer product to higher order tensors.
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- 5.
Tensor indices are dropped for brevity in the remainder of the manuscript.
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- 8.
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Acknowledgements
Jens Petersen is partly funded by a research grants from the Danish Cancer Society (grant no. R231-A13976) and Varian Medical Systems.
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Selvan, R., Dam, E.B., Petersen, J. (2021). Segmenting Two-Dimensional Structures with Strided Tensor Networks. In: Feragen, A., Sommer, S., Schnabel, J., Nielsen, M. (eds) Information Processing in Medical Imaging. IPMI 2021. Lecture Notes in Computer Science(), vol 12729. Springer, Cham. https://doi.org/10.1007/978-3-030-78191-0_31
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