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Register a new userA Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology
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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 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.
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We present a novel method to explicitly incorporate topological prior knowledge into deep learning based segmentation, which is, to our knowledge, the first work to do so. Our method uses the concept of persistent homology, a tool from topological data analysis, to capture high-level topological characteristics of segmentation results in a way which is differentiable with respect to the pixelwise probability of being assigned to a given class. The topological prior knowledge consists of the sequence of desired Betti numbers of the segmentation. As a proof-of-concept we demonstrate our approach by applying it to the problem of left-ventricle segmentation of cardiac MR images of 500 subjects from the UK Biobank dataset, where we show that it improves segmentation performance in terms of topological correctness without sacrificing pixelwise accuracy.
With respect to spatial overlap, CNN-based segmentation of short axis cardiovascular magnetic resonance (CMR) images has achieved a level of performance consistent with inter observer variation. However, conventional training procedures frequently depend on pixel-wise loss functions, limiting optimisation with respect to extended or global features. As a result, inferred segmentations can lack spatial coherence, including spurious connected components or holes. Such results are implausible, violating the anticipated topology of image segments, which is frequently known a priori. Addressing this challenge, published work has employed persistent homology, constructing topological loss functions for the evaluation of image segments against an explicit prior. Building a richer description of segmentation topology by considering all possible labels and label pairs, we extend these losses to the task of multi-class segmentation. These topological priors allow us to resolve all topological errors in a subset of 150 examples from the ACDC short axis CMR training data set, without sacrificing overlap performance.
Multi-class segmentation of cardiac magnetic resonance (CMR) images seeks a separation of data into anatomical components with known structure and configuration. The most popular CNN-based methods are optimised using pixel wise loss functions, ignorant of the spatially extended features that characterise anatomy. Therefore, whilst sharing a high spatial overlap with the ground truth, inferred CNN-based segmentations can lack coherence, including spurious connected components, holes and voids. Such results are implausible, violating anticipated anatomical topology. In response, (single-class) persistent homology-based loss functions have been proposed to capture global anatomical features. Our work extends these approaches to the task of multi-class segmentation. Building an enriched topological description of all class labels and class label pairs, our loss functions make predictable and statistically significant improvements in segmentation topology using a CNN-based post-processing framework. We also present (and make available) a highly efficient implementation based on cubical complexes and parallel execution, enabling practical application within high resolution 3D data for the first time. We demonstrate our approach on 2D short axis and 3D whole heart CMR segmentation, advancing a detailed and faithful analysis of performance on two publicly available datasets.
Multiple sclerosis (MS) lesions occupy a small fraction of the brain volume, and are heterogeneous with regards to shape, size and locations, which poses a great challenge for training deep learning based segmentation models. We proposed a new geometric loss formula to address the data imbalance and exploit the geometric property of MS lesions. We showed that traditional region-based and boundary-aware loss functions can be associated with the formula. We further develop and instantiate two loss functions containing first- and second-order geometric information of lesion regions to enforce regularization on optimizing deep segmentation models. Experimental results on two MS lesion datasets with different scales, acquisition protocols and resolutions demonstrated the superiority of our proposed methods compared to other state-of-the-art methods.
To ensure the privacy of sensitive data used in the training of deep learning models, a number of privacy-preserving methods have been designed by the research community. However, existing schemes are generally designed to work with textual data, or are not efficient when a large number of images is used for training. Hence, in this paper we propose a lightweight and efficient approach to preserve image privacy while maintaining the availability of the training set. Specifically, we design the pixel block mixing algorithm for image classification privacy preservation in deep learning. To evaluate its utility, we use the mixed training set to train the ResNet50, VGG16, InceptionV3 and DenseNet121 models on the WIKI dataset and the CNBC face dataset. Experimental findings on the testing set show that our scheme preserves image privacy while maintaining the availability of the training set in the deep learning models. Additionally, the experimental results demonstrate that we achieve good performance for the VGG16 model on the WIKI dataset and both ResNet50 and DenseNet121 on the CNBC dataset. The pixel block algorithm achieves fairly high efficiency in the mixing of the images, and it is computationally challenging for the attackers to restore the mixed training set to the original training set. Moreover, data augmentation can be applied to the mixed training set to improve the trainings effectiveness.
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