A Quantum Computational Approach to Correspondence Problems on Point Sets
This work addresses a specific computer vision problem for researchers in quantum computing and vision, but it is incremental as it builds on existing quantum methods with limited prior applications in this domain.
The authors tackled the problem of solving correspondence problems on point sets by developing a new algorithm for adiabatic quantum computers, achieving subquadratic computational complexity in state preparation and demonstrating successful transformation estimation and point set alignment in simulations.
Modern adiabatic quantum computers (AQC) are already used to solve difficult combinatorial optimisation problems in various domains of science. Currently, only a few applications of AQC in computer vision have been demonstrated. We review AQC and derive a new algorithm for correspondence problems on point sets suitable for execution on AQC. Our algorithm has a subquadratic computational complexity of the state preparation. Examples of successful transformation estimation and point set alignment by simulated sampling are shown in the systematic experimental evaluation. Finally, we analyse the differences in the solutions and the corresponding energy values.