Solving Combinatorial Optimization Problems in Computer Vision via Quantum Annealing

Since the ability of quantum computing to speed up certain, specific computations has a solid theoretical underpinning, it is a natural question to ask if problems in computer vision also benefit from it. This doctoral thesis is in particular concerned with the question if the recently emerging optimization method of quantum annealing is useful for solving combinatorial optimization problems that arise in computer vision. The computer vision problem that is mainly investigated here is the problem of shape matching. The task of shape matching is to obtain the correspondences of two objects in a scene that are described with point clouds. Most often, one is concerned with finding the correspondences for a person who is recorded in 3D two times but with a different pose. The reason why this computer vision problem was picked as an interesting candidate for an application of quantum annealing is because it can be formulated as a difficult combinatorial optimization problem with a quadratic objective. This is close to the type of optimization problem that recent quantum annealing devices try to solve. The biggest difference is that in quantum annealing one a priori has unconstrained problems so that one cannot include equality constraints in the optimization. In the first work of this thesis, multiple methods are presented to overcome this difference and for really small shape matching problems experiments with simulated quantum annealing and with quantum annealing on D-Wave quantum computers were presented. In the second work of this thesis an iterative method was developed so that it was even possible to solve shape matching problems with over 500 vertices. Finally, a third publication looked at problems where one needs to find the correspondences between multiple shapes.
Besides applications of quantum annealing for shape matching, this thesis also contains work on solving the motion segmentation problem with quantum annealing and work about integrating a quantum annealer in a neural network to solve computer vision problems. The integration of the quantum annealer in a neural network can also be viewed as the task to learn an appropriate formulation of a computer vision problem in a way that is solvable with a current quantum annealer. Finally, we also present work about an iterative method for compensating limited connectivity in quantum annealing devices. This work has no particular computer vision application in mind, but investigates the performance of the different approaches on Max-Cut problems.
The thesis is structured in a cumulative way, so that the individual publications are presented separately. On a broader picture, the works are motivated by the following questions: What could be the impact of quantum annealing on computer vision and how could computer vision algorithms that use quantum annealing look like? And from another perspective: How would the field of computer vision be changed if there were massive advances in building quadratic, unconstrained, binary optimization problem solvers with or even without utilizing quantum computing?