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Graph neural networks (GNNs) have been proposed for medical image segmentation, by predicting anatomical structures represented by graphs of vertices and edges. One such type of graphs are predefined with fixed size and connectivity to represent a reference of anatomical regions of interest, thus known as templates. This work explores the potentials in these GNNs with common topology for establishing spatial correspondence, implicitly maintained during segmenting two or more images. With an example application of registering local vertebral sub-regions found in CT images, our experimental results showed that the GNN-based segmentation is capable of accurate and reliable localisation of the same interventionally interesting structures between images, not limited to the segmentation classes. The reported average target registration errors of 2.2$\pm$1.3 mm and 2.7$\pm$1.4 mm, for aligning holdout test images with a reference and for aligning two test images, respectively, were by a considerable margin lower than those from the tested non-learning and learning-based registration algorithms. Further ablation studies assess the contributions towards the registration performance, from individual components in the originally segmentation-purposed network and its training algorithm. The results highlight that the proposed segmentation-in-lieu-of-registration approach shares methodological similarity with existing registration methods, such as the use of displacement smoothness constraint and point distance minimisation albeit on non-grid graphs, which interestingly yielded benefits for both segmentation and registration. We therefore conclude that the template-based GNN segmentation can effectively establish spatial correspondence in our application, without any other dedicated registration algorithms.
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