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 yeilds competitive performance compared to the baseline methods while being more resource efficient.