  Many computer vision applications need to recover structure from imperfect
measurements of the real world. The task is often solved by robustly fitting a
geometric model onto noisy and outlier-contaminated data. However, recent
theoretical analyses indicate that many commonly used formulations of robust
fitting in computer vision are not amenable to tractable solution and
approximation. In this paper, we explore the usage of quantum computers for
robust fitting. To do so, we examine and establish the practical usefulness of
a robust fitting formulation inspired by Fourier analysis of Boolean functions.
We then investigate a quantum algorithm to solve the formulation and analyse
the computational speed-up possible over the classical algorithm. Our work thus
proposes one of the first quantum treatments of robust fitting for computer
vision.
