An adaptive differential evolution algorithm to optimal multi-level thresholding for MRI brain image segmentation

Segmentation is an important method for MRI medical image analysis as it can provide the radiologists with noninvasive information about a patient that is crucial to the diagnostic process. The efficiency of such a computer-aided diagnosis system relies on the accuracy of an adopted image segmentation method. Multi-level thresholding is a segmentation method that has been widely adopted in medical image analysis in recent studies, where selecting the optimal thresholds has a pivotal role in determining the efficiency and the accuracy of the segmentation algorithm. While some well-known methods, such as Kapur’s and Otsu’s, are proven effective for bi-level thresholding, multi-level thresholding remains a challenge as it is computationally expensive. Evolutionary algorithms, such as Differential Evolution (DE), have the potential to address this problem, as they can find sufficiently good solutions with manageable computational effort. While a number of DE solutions have been proposed for multi-level thresholding, they are not stable, in that, when the number of thresholds increases, the algorithm efficiency decreases due to the imbalance between exploration and exploitation. In this paper, we propose a DE solution that achieves a good balance between exploration and exploitation through a new adaptive approach and new mutation strategies. The new adaptive approach can generate optimal solutions in assigning populations by measuring the quality of candidate solutions to evaluate the efficiency of different parts of the proposed DE algorithm. The new mutation methods harness Mantegna Lévy and Cauchy distributions, as well as Cotes’ Spiral to improve global search, and to further balance between exploitation and exploration. We further experimentally compare the proposed DE algorithm, referred to as Adaptive Differential Evolution with Lévy Distribution (ALDE), against three DE benchmark algorithms on T2 weighted MRI brain images. Our results show that ALDE can, not only obtain optimal thresholds at a reasonable computational cost, but more importantly, clearly outperforms the benchmark algorithms.