We propose a framework for rotation and translation covariant deep learning using SE(2) group convolutions. The group product of the special Euclidean motion group SE(2) describes how a concatenation of two roto-translations results in a net roto-translation. We encode this geometric structure into convolutional neural networks (CNNs) via SE(2) group convolutional layers, which fit into the standard 2D CNN framework, and which allow to generically deal with rotated input samples without the need for data augmentation. We introduce three layers: a lifting layer which lifts a 2D (vector valued) image to an SE(2)-image, i.e., 3D (vector valued) data whose domain is SE(2); a group convolution layer from and to an SE(2)-image; and a projection layer from an SE(2)-image to a 2D image. The lifting and group convolution layers are SE(2) covariant (the output roto-translates with the input). The final projection layer, a maximum intensity projection over rotations, makes the full CNN rotation invariant. We show with three different problems in histopathology, retinal imaging, and electron microscopy that with the proposed group CNNs, state-ofthe-art performance can be achieved, without the need for data augmentation by rotation and with increased performance compared to standard CNNs that do rely on augmentation.

DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

No abstract

Abstract. Convolutional neural networks (CNNs) have been applied to various automatic image segmentation tasks in medical image analysis, including brain MRI segmentation. Generative adversarial networks have recently gained popularity because of their power in generating images that are difficult to distinguish from real images. In this study we use an adversarial training approach to improve CNNbased brain MRI segmentation. To this end, we include an additional loss function that motivates the network to generate segmentations that are difficult to distinguish from manual segmentations. During training, this loss function is optimised together with the conventional average per-voxel cross entropy loss. The results show improved segmentation performance using this adversarial training procedure for segmentation of two different sets of images and using two different network architectures, both visually and in terms of Dice coefficients.

DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement: