A Hybrid Quantum-Classical Algorithm for Robust Fitting
This addresses the need for reliable robust fitting in computer vision systems, offering a concrete quantum computing application, though it is incremental as it does not overcome fundamental intractability.
The paper tackles the problem of robust fitting in computer vision, which is intractable with outliers, by proposing a hybrid quantum-classical algorithm that provides global solutions or error bounds, achieving practical improvements over heuristics with results from a D-Wave Advantage quantum computer and simulations.
Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is therefore critical to develop novel approaches that can bridge the gap between exact solutions that are costly, and fast heuristics that offer no quality assurances. In this paper, we propose a hybrid quantum-classical algorithm for robust fitting. Our core contribution is a novel robust fitting formulation that solves a sequence of integer programs and terminates with a global solution or an error bound. The combinatorial subproblems are amenable to a quantum annealer, which helps to tighten the bound efficiently. While our usage of quantum computing does not surmount the fundamental intractability of robust fitting, by providing error bounds our algorithm is a practical improvement over randomised heuristics. Moreover, our work represents a concrete application of quantum computing in computer vision. We present results obtained using an actual quantum computer (D-Wave Advantage) and via simulation. Source code: https://github.com/dadung/HQC-robust-fitting