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Tensor networks provide an efficient approximation of operations involvinghigh dimensional tensors and have been extensively used in modelling quantummany-body systems. More recently, supervised learning has been attempted withtensor networks, primarily focused on tasks such as image classification. Inthis work, we propose a novel formulation of tensor networks for supervisedimage segmentation which allows them to operate on high resolution medicalimages. We use the matrix product state (MPS) tensor network on non-overlappingpatches of a given input image to predict the segmentation mask by learning apixel-wise linear classification rule in a high dimensional space. The proposedmodel is end-to-end trainable using backpropagation. It is implemented as aStrided Tensor Network to reduce the parameter complexity. The performance ofthe proposed method is evaluated on two public medical imaging datasets andcompared to relevant baselines. The evaluation shows that the strided tensornetwork yields competitive performance compared to CNN-based models while usingfewer resources. Additionally, based on the experiments we discuss thefeasibility of using fully linear models for segmentation tasks.

Segmenting two-dimensional structures with strided tensor networks