A study on particle swarm optimization and artificial bee colony algorithms for multilevel thresholding

Segmentation is a critical task in image processing. Bi-level segmentation involves dividing the whole image into partitions based on a threshold value, whereas multilevel segmentation involves multiple threshold values. A successful segmentation assigns proper threshold values to optimise a criterion such as entropy or between-class variance. High computational cost and inefficiency of an exhaustive search for the optimal thresholds leads to the use of global search heuristics to set the optimal thresholds. An emerging area in global heuristics is swarm-intelligence, which models the collective behaviour of the organisms. In this paper, two successful swarm-intelligence-based global optimisation algorithms, particle swarm optimisation (PSO) and artificial bee colony (ABC), have been employed to find the optimal multilevel thresholds. Kapur's entropy, one of the maximum entropy techniques, and between-class variance have been investigated as fitness functions. Experiments have been performed on test images using various numbers of thresholds. The results were assessed using statistical tools and suggest that Otsu's technique, PSO and ABC show equal performance when the number of thresholds is two, while the ABC algorithm performs better than PSO and Otsu's technique when the number of thresholds is greater than two. Experiments based on Kapur's entropy indicate that the ABC algorithm can be efficiently used in multilevel thresholding. Moreover, segmentation methods are required to have a minimum running time in addition to high performance. Therefore, the CPU times of ABC and PSO have been investigated to check their validity in real-time. The CPU time results show that the algorithms are scalable and that the running times of the algorithms seem to grow at a linear rate as the problem size increases.

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► PSO and ABC algorithms have been used as unsupervised-nonparametric-global-multilevel thresholding methods.
► ABC algorithm is more efficient and more robust than PSO in multilevel thresholding.
► The fitness functions based on Kapur's entropy and the between-class variance have been compared to each other.
► The algorithms based on Kapur's entropy seem to produce higher fidelity than those using between-class variance.