A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology

Abstract

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 three experiments. Firstly we create a synthetic task in which handwritten MNIST digits are de-noised, and show that using this kind of topological prior knowledge in the training of the network significantly improves the quality of the de-noised digits. Secondly we perform an experiment in which the task is segmenting the myocardium of the left ventricle from cardiac magnetic resonance images. We show that the incorporation of the prior knowledge of the topology of this anatomy improves the resulting segmentations in terms of both the topological accuracy and the Dice coefficient. Thirdly, we extend the method to 3D volumes and demonstrate its performance on the task of segmenting the placenta from ultrasound data, again showing that incorporating topological priors improves performance on this challenging task. 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.

arXiv commentIEEE Transactions on Pattern Analysis and Machine Intelligence, 2020

References in corpus (13)

• Very Deep Convolutional Networks for Large-Scale Image Recognition
• A Survey on Deep Learning in Medical Image Analysis
• Efficient Inference in Fully Connected CRFs with Gaussian Edge Potentials
• Generalised Dice overlap as a deep learning loss function for highly unbalanced segmentations
• Conditional Random Fields as Recurrent Neural Networks
• A roadmap for the computation of persistent homology
• Anatomically Constrained Neural Networks (ACNN): Application to Cardiac Image Enhancement and Segmentation
• Deep Residual Learning for Compressed Sensing CT Reconstruction via Persistent Homology Analysis
• Topology-Preserving Deep Image Segmentation
• Persistent Homology analysis of Phase Transitions
• Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology
• A Topology Layer for Machine Learning
• Connectivity-Optimized Representation Learning via Persistent Homology

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