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.
The recent work of @cite_2 introduced a topological regulariser for classification problems by considering the stability of connected components of the classification boundary and can be extended to higher-order topological features. It also provided a differentiable loss function which can be incorporated in the training of a neural network. This approach differs from ours in that firstly, it imposes topological constraints on the shape of the classification boundary in the feature space of inputs to the network, rather than topological constraints in the space of the pixels in the image, and secondly it aims only to reduce overall topological complexity. Our approach aims to fit the desired absence or presence of certain features and so complex features can be penalised or rewarded, as is appropriate for the task at hand.
@cite_2
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Regularization plays a crucial role in supervised learning. A successfully regularized model strikes a balance between a perfect description of the training data and the ability to generalize to unseen data. Most existing methods enforce a global regularization in a structure agnostic manner. In this paper, we initiate a new direction and propose to enforce the structural simplicity of the classification boundary by regularizing over its topological complexity. In particular, our measurement of topological complexity incorporates the importance of topological features (e.g., connected components, handles, and so on) in a meaningful manner, and provides a direct control over spurious topological structures. We incorporate the new measurement as a topological loss in training classifiers. We also propose an efficient algorithm to compute the gradient. Our method provides a novel way to topologically simplify the global structure of the model, without having to sacrifice too much of the flexibility of the model. We demonstrate the effectiveness of our new topological regularizer on a range of synthetic and real-world datasets. The recent success of deep learning techniques in classification and object detection tasks has been leveraged for segmentation tasks. However, a weakness of these deep segmentation models is their limited ability to encode high level shape priors, such as smoothness and preservation of complex interactions between object regions, which can result in implausible segmentations. In this work, by formulating and optimizing a new loss, we introduce the first deep network trained to encode geometric and topological priors of containment and detachment. Our results on the segmentation of histology glands from a dataset of 165 images demonstrate the advantage of our novel loss terms and show how our topology aware architecture outperforms competing methods by up to 10 in both pixel-level accuracy and object-level Dice. This paper introduces a methodology for neural network global optimization. The aim is the simultaneous optimization of multilayer perceptron (MLP) network weights and architectures, in order to generate topologies with few connections and high classification performance for any data sets. The approach combines the advantages of simulated annealing, tabu search and the backpropagation training algorithm in order to generate an automatic process for producing networks with high classification performance and low complexity. Experimental results obtained with four classification problems and one prediction problem has shown to be better than those obtained by the most commonly used optimization techniques Complex networks have been employed to model many real systems and as a modeling tool in a myriad of applications. In this paper, we use the framework of complex networks to the problem of supervised classification in the word disambiguation task, which consists in deriving a function from the supervised (or labeled) training data of ambiguous words. Traditional supervised data classification takes into account only topological or physical features of the input data. On the other hand, the human (animal) brain performs both low- and high-level orders of learning and it has facility to identify patterns according to the semantic meaning of the input data. In this paper, we apply a hybrid technique which encompasses both types of learning in the field of word sense disambiguation and show that the high-level order of learning can really improve the accuracy rate of the model. This evidence serves to demonstrate that the internal structures formed by the words do present patterns that, generally, cannot be correctly unveiled by only traditional techniques. Finally, we exhibit the behavior of the model for different weights of the low- and high-level classifiers by plotting decision boundaries. This study helps one to better understand the effectiveness of the model.