A key step in medical image-based diagnosis is image segmentation. A common use case for medical image segmentation is the identification of single structures of an elliptical shape. Most organs like the heart and kidneys fall into this category, as well as skin lesions, polyps, and other types of abnormalities. Neural networks have dramatically improved medical image segmentation results, but still require large amounts of training data and long training times to converge. In this paper, we propose a general way to improve neural network segmentation performance and data efficiency on medical imaging segmentation tasks where the goal is to segment a single roughly elliptically distributed object. We propose training a neural network on polar transformations of the original dataset, such that the polar origin for the transformation is the center point of the object. This results in a reduction of dimensionality as well as a separation of segmentation and localization tasks, allowing the network to more easily converge. Additionally, we propose two different approaches to obtaining an optimal polar origin: (1) estimation via a segmentation trained on non-polar images and (2) estimation via a model trained to predict the optimal origin. We evaluate our method on the tasks of liver, polyp, skin lesion, and epicardial adipose tissue segmentation. We show that our method produces state-of-the-art results for lesion, liver, and polyp segmentation and performs better than most common neural network architectures for biomedical image segmentation. Additionally, when used as a pre-processing step, our method generally improves data efficiency across datasets and neural network architectures.