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Statistical shape analysis is a very useful tool in a wide range of medical and biological applications. However, it typically relies on the ability to produce a relatively small number of features that can capture the relevant variability in a population. State-of-the-art methods for obtaining such anatomical features rely on either extensive preprocessing or segmentation and/or significant tuning and post-processing. These shortcomings limit the widespread use of shape statistics. We propose that effective shape representations should provide sufficient information to align/register images. Using this assumption we propose a self-supervised, neural network approach for automatically positioning and detecting landmarks in images that can be used for subsequent analysis. The network discovers the landmarks corresponding to anatomical shape features that promote good image registration in the context of a particular class of transformations. In addition, we also propose a regularization for the proposed network which allows for a uniform distribution of these discovered landmarks. In this paper, we present a complete framework, which only takes a set of input images and produces landmarks that are immediately usable for statistical shape analysis. We evaluate the performance on a phantom dataset as well as 2D and 3D images.