The analysis and segmentation of articular cartilage magnetic resonance (MR) images belongs to one of the most commonly routine tasks in diagnostics of the musculoskeletal system of the knee area. Conventional regional segmentation methods, which are based either on the histogram partitioning (e.g., Otsu method) or clustering methods (e.g., K-means), have been frequently used for the task of regional segmentation. Such methods are well known as fast and well working in the environment, where cartilage image features are reliably recognizable. The well-known fact is that the performance of these methods is prone to the image noise and artefacts. In this context, regional segmentation strategies, driven by either genetic algorithms or selected evolutionary computing strategies, have the potential to overcome these traditional methods such as Otsu thresholding or K-means in the context of their performance. These optimization strategies consecutively generate a pyramid of a possible set of histogram thresholds, of which the quality is evaluated by using the fitness function based on Kapur's entropy maximization to find the most optimal combination of thresholds for articular cartilage segmentation. On the other hand, such optimization strategies are often computationally demanding, which is a limitation of using such methods for a stack of MR images. In this study, we publish a comprehensive analysis of the optimization methods based on fuzzy soft segmentation, driven by artificial bee colony (ABC), particle swarm optimization (PSO), Darwinian particle swarm optimization (DPSO), and a genetic algorithm for an optimal thresholding selection against the routine segmentations Otsu and K-means for analysis and the features extraction of articular cartilage from MR images. This study objectively analyzes the performance of the segmentation strategies upon variable noise with dynamic intensities to report a segmentation's robustness in various image conditions for a various number of segmentation classes (4, 7, and 10), cartilage features (area, perimeter, and skeleton) extraction preciseness against the routine segmentation strategies, and lastly the computing time, which represents an important factor of segmentation performance. We use the same settings on individual optimization strategies: 100 iterations and 50 population. This study suggests that the combination of fuzzy thresholding with an ABC algorithm gives the best performance in the comparison with other methods as from the view of the segmentation influence of additive dynamic noise influence, also for cartilage features extraction. On the other hand, using genetic algorithms for cartilage segmentation in some cases does not give a good performance. In most cases, the analyzed optimization strategies significantly overcome the routine segmentation methods except for the computing time, which is normally lower for the routine algorithms. We also publish statistical tests of significance, showing differences in the performance of individual optimization strategies against Otsu and K-means method. Lastly, as a part of this study, we publish a software environment, integrating all the methods from this study.

Department of Cybernetics and Biomedical Engineering VŠB Technical University of Ostrava 17 listopadu 2172 15 Poruba 708 00 Ostrava Czech Republic

Department of Security Services Faculty of Safety Engineering VŠB Technical University of Ostrava ul Lumirova 3 700 30 Ostrava Czech Republic

MEDIN a s Vlachovicka 619 592 31 Nove Mesto na Morave Czech Republic

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