A Quantum Optimization Method for Geometric Constrained Image Segmentation

Abstract

Quantum image processing is a growing field attracting attention from both the quantum computing and image processing communities. We propose a novel method in combining a graph-theoretic approach for optimal surface segmentation and hybrid quantum-classical optimization of the problem-directed graph. The surface segmentation is modeled classically as a graph partitioning problem in which a smoothness constraint is imposed to control surface variation for realistic segmentation. Specifically, segmentation refers to a source set identified by a minimum s-t cut that divides graph nodes into the source (s) and sink (t) sets. The resulting surface consists of graph nodes located on the boundary between the source and the sink. Characteristics of the problem-specific graph, including its directed edges, connectivity, and edge capacities, are embedded in a quadratic objective function whose minimum value corresponds to the ground state energy of an equivalent Ising Hamiltonian. This work explores the use of quantum processors in image segmentation problems, which has important applications in medical image analysis. Here, we present a theoretical basis for the quantum implementation of LOGISMOS and the results of a simulation study on simple images. Quantum Approximate Optimization Algorithm (QAOA) approach was utilized to conduct two simulation studies whose objective was to determine the ground state energies and identify bitstring solutions that encode the optimal segmentation of objective functions. The objective function encodes tasks associated with surface segmentation in 2-D and 3-D images while incorporating a smoothness constraint. In this work, we demonstrate that the proposed approach can solve the geometric-constrained surface segmentation problem optimally with the capability of locating multiple minimum points corresponding to the globally minimal solution.