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A computational anatomy atlas is a set of internal organ geometries. It is based on data of real patients and complemented with virtual cases by using a some numerical approach. Atlases are in demand in computational physiology, especially in cardiological and neurophysiological applications. Usually, atlas generation uses explicit object representation, such as voxel models or surface meshes. In this paper, we propose a method of atlas generation using an implicit representation of 3D objects. Our approach has two key stages. The first stage converts voxel models of segmented organs to implicit form using the usual multilayer perceptron. This stage smooths the model and reduces memory consumption. The second stage uses a multilayer perceptron with Lipschitz regularization. This neural network provides a smooth transition between implicitly defined 3D geometries. Our work shows examples of models of the left and right human ventricles. All code and data for this work are open.

Computational anatomy atlas using multilayer perceptron with Lipschitz regularization