The Domain Transform Solver

We present a novel framework for edge-aware optimization that is an order of magnitude faster than the state of the art while maintaining comparable results. 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 wide variety of problems including stereo, depth super-resolution, render from defocus, colorization, and especially high-resolution depth filtering, while keeping the computational complexity linear in the number of pixels. Our method is highly parallelizable and adaptable, and it has demonstrable linear scalability with respect to image resolutions. We provide a comprehensive evaluation of our method w.r.t speed and accuracy for a variety of tasks.