  Over the last decade of machine learning, convolutional neural networks have
been the most striking successes for feature extraction of rich sensory and
high-dimensional data. While learning data representations via convolutions is
already well studied and efficiently implemented in various deep learning
libraries, one often faces limited memory capacity and insufficient number of
training data, especially for high-dimensional and large-scale tasks. To
overcome these limitations, we introduce a network architecture using a
self-adjusting and data dependent version of the Radon-transform (linear data
projection), also known as x-ray projection, to enable feature extraction via
convolutions in lower-dimensional space. The resulting framework, named PiNet,
can be trained end-to-end and shows promising performance on volumetric
segmentation tasks. We test proposed model on public datasets to show that our
approach achieves comparable results only using fractional amount of
parameters. Investigation of memory usage and processing time confirms PiNet's
superior efficiency compared to other segmentation models.
