Convolutional neural networks have been applied to a wide variety of computer vision tasks. Recent advances in semantic segmentation have enabled their application to medical image segmentation. While most CNNs use two-dimensional kernels, recent CNN-based publications on medical image segmentation featured three-dimensional kernels, allowing full access to the three-dimensional structure of medical images. Though closely related to semantic segmentation, medical image segmentation includes specific challenges that need to be addressed, such as the scarcity of labelled data, the high class imbalance found in the ground truth and the high memory demand of three-dimensional images. In this work, a CNN-based method with three-dimensional filters is demonstrated and applied to hand and brain MRI. Two modifications to an existing CNN architecture are discussed, along with methods on addressing the aforementioned challenges. While most of the existing literature on medical image segmentation focuses on soft tissue and the major organs, this work is validated on data both from the central nervous system as well as the bones of the hand.

We propose to learn a stochastic recurrent model to solve the problem of simultaneous localisation and mapping (SLAM). Our model is a deep variational Bayes filter augmented with a latent global variable---similar to an external memory component---representing the spatially structured environment. Reasoning about the pose of an agent and the map of the environment is then naturally expressed as posterior inference in the resulting generative model. We evaluate the method on a set of randomly generated mazes which are traversed by an agent equipped with laser range finders. Path integration based on an accurate motion model is consistently outperformed, and most importantly, drift practically eliminated. Our approach inherits favourable properties from neural networks, such as differentiability, flexibility and the ability to train components either in isolation or end-to-end.

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Amortised inference enables scalable learning of sequential latent-variable models (LVMs) with the evidence lower bound (ELBO). In this setting, variational posteriors are often only partially conditioned. While the true posteriors depend, e.g., on the entire sequence of observations, approximate posteriors are only informed by past observations. This mimics the Bayesian filter-a mixture of smoothing posteriors. Yet, we show that the ELBO objective forces partially-conditioned amortised posteriors to approximate products of smoothing posteriors instead. Consequently, the learned generative model is compromised. We demonstrate these theoretical findings in three scenarios: traffic flow, handwritten digits, and aerial vehicle dynamics. Using fully-conditioned approximate posteriors, performance improves in terms of generative modelling and multi-step prediction.

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