  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.

Computer Vision and Pattern Recognition