  We present a framework for edge-aware optimization that is an order of
magnitude faster than the state of the art while having comparable performance.
Our key insight is that the optimization can be formulated by leveraging
properties of the domain transform, a method for edge-aware filtering that
defines a distance-preserving 1D mapping of the input space. This enables our
method to improve performance for a variety of problems including stereo, depth
super-resolution, and render from defocus, while keeping the computational
complexity linear in the number of pixels. Our method is highly parallelizable
and adaptable, and it has demonstrable scalability with respect to image
resolution.
