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We introduce a method for training neural networks to perform image or volume segmentation in which prior knowledge about the topology of the segmented object can be explicitly provided and then incorporated into the training process. By using the differentiable properties of persistent homology, a concept used in topological data analysis, we can specify the desired topology of segmented objects in terms of their Betti numbers and then drive the proposed segmentations to contain the specified topological features. Importantly this process does not require any ground-truth labels, just prior knowledge of the topology of the structure being segmented. We demonstrate our approach in four experiments: one on MNIST image denoising and digit recognition, one on left ventricular myocardium segmentation from magnetic resonance imaging data from the UK Biobank, one on the ACDC public challenge dataset and one on placenta segmentation from 3-D ultrasound. We find that embedding explicit prior knowledge in neural network segmentation tasks is most beneficial when the segmentation task is especially challenging and that it can be used in either a semi-supervised or post-processing context to extract a useful training gradient from images without pixelwise labels. [ABSTRACT FROM AUTHOR]

Manifold alignment (MA) is a technique to map many high-dimensional datasets to one shared low-dimensional space. Here we develop a pipeline for using MA to reconstruct high-resolution medical images. We present two key contributions. First, we develop a novel MA scheme in which each high-dimensional dataset can be differently weighted preventing noisier or less informative data from corrupting the aligned embedding. We find that this generalisation improves performance in our experiments in both supervised and unsupervised MA problems. Second, we use the wave kernel signature as a graph descriptor for the unsupervised MA case finding that it significantly outperforms the current state-of-the-art methods and provides higher quality reconstructed magnetic resonance volumes than existing methods. [ABSTRACT FROM AUTHOR]