Multi-level thresholding using quantum inspired meta-heuristics

Image thresholding is well accepted and one of the most imperative practices to accomplish image segmentation. This has been widely studied over the past few decades. However, as the multi-level thresholding computationally takes more time when level increases, hence, in this article, quantum mechanism is used to propose six different quantum inspired meta-heuristic methods for performing multi-level thresholding faster. The proposed methods are Quantum Inspired Genetic Algorithm, Quantum Inspired Particle Swarm Optimization, Quantum Inspired Differential Evolution, Quantum Inspired Ant Colony Optimization, Quantum Inspired Simulated Annealing and Quantum Inspired Tabu Search. As a sequel to the proposed methods, we have also conducted experiments with the two-Stage multithreshold Otsu method, maximum tsallis entropy thresholding, the modified bacterial foraging algorithm, the classical particle swarm optimization and the classical genetic algorithm. The effectiveness of the proposed methods is demonstrated on fifteen images at the different level of thresholds quantitatively and visually. Thereafter, the results of six quantum meta-heuristic methods are considered to create consensus results. Finally, statistical test, called Friedman test, is conducted to judge the superiority of a method among them. Quantum Inspired Particle Swarm Optimization is found to be superior among the proposed six quantum meta-heuristic methods and the other five methods are used for comparison. A Friedman test again conducted between the Quantum Inspired Particle Swarm Optimization and all the other methods to justify the statistical superiority. Finally, the computational complexities of the proposed methods have been elucidated for the sake of finding out the time efficiency of the proposed methods.