  Patterns, which are collections of elements arranged in regular or
near-regular arrangements, are an important graphic art form and widely used
due to their elegant simplicity and aesthetic appeal. When a pattern is encoded
as a flat image without the underlying structure, manually editing the pattern
is tedious and challenging as one has to both preserve the individual element
shapes and their original relative arrangements. State-of-the-art deep learning
frameworks that operate at the pixel level are unsuitable for manipulating such
patterns. Specifically, these methods can easily disturb the shapes of the
individual elements or their arrangement, and thus fail to preserve the latent
structures of the input patterns. We present a novel differentiable compositing
operator using pattern elements and use it to discover structures, in the form
of a layered representation of graphical objects, directly from raw pattern
images. This operator allows us to adapt current deep learning based image
methods to effectively handle patterns. We evaluate our method on a range of
patterns and demonstrate superiority in the context of pattern manipulations
when compared against state-of-the-art
