Multi-threshold image segmentation using a multi-strategy shuffled frog leaping algorithm

•The HVSFLA nethod is presented for multi-threshold image segmentation.•Performance of the SFLA is enhanced by special horizontal and vertical crossover search.•The better balance between intensification and diversification has been tested.•The HVSFLA has technical and statistic advantages in multi-threshold image segmentation.•HVSFLA may be employed as a tool for breast invasive ductal carcinoma images segmentation.