The Domain Transform Solver

TL;DR

This paper introduces a fast, edge-aware optimization framework using the domain transform, significantly improving speed while maintaining performance across various vision tasks.

Contribution

It leverages the domain transform for efficient, linear-complexity edge-aware optimization applicable to multiple computer vision problems.

Findings

Achieves an order of magnitude speedup over state-of-the-art methods.

Maintains comparable performance to existing techniques.

Scales effectively with image resolution.

Abstract

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.