  We present a bottom-up differentiable relaxation of the process of drawing
points, lines and curves into a pixel raster. Our approach arises from the
observation that rasterising a pixel in an image given parameters of a
primitive can be reformulated in terms of the primitive's distance transform,
and then relaxed to allow the primitive's parameters to be learned. This
relaxation allows end-to-end differentiable programs and deep networks to be
learned and optimised and provides several building blocks that allow control
over how a compositional drawing process is modelled. We emphasise the
bottom-up nature of our proposed approach, which allows for drawing operations
to be composed in ways that can mimic the physical reality of drawing rather
than being tied to, for example, approaches in modern computer graphics. With
the proposed approach we demonstrate how sketches can be generated by directly
optimising against photographs and how auto-encoders can be built to transform
rasterised handwritten digits into vectors without supervision. Extensive
experimental results highlight the power of this approach under different
modelling assumptions for drawing tasks.
