Adaptive granulation Renyi rough entropy image thresholding method with nested optimization

The rough entropy based image thresholding algorithm can effectively deal with the uncertainty information in an image. Nevertheless, the existing rough entropy based thresholding methods have two limitations. One is that there is no generalized rough entropy definition. The other is that the granule size cannot be selected automatically in combination with the image information in the granulation process. In order to address these two problems, an adaptive granulation Renyi rough entropy image thresholding method with nested optimization is proposed in this paper. First, a definition of generalized rough entropy with parameter based on Renyi entropy form is proposed to describe the uncertainty information of complex images. Second, in order to select the granule size in combination with the specific image information, a granule size selection method is proposed by maximizing the uniformity of the segmented image regions. Finally, a nested optimization adaptive granulation Renyi rough entropy thresholding segmentation algorithm is proposed. In the experiments, the Renyi rough entropy is compared with the existing four rough entropy in image thresholding. The new parametric rough entropy can obtain better segmentation results than the other existing rough entropy. The novel adaptive granulation Renyi rough entropy thresholding segmentation algorithm is compared with the state-of-the-art image segmentation methods on several different image data sets, which verifies the effectiveness of the novel algorithm. • Define a Renyi rough entropy measure. • Propose the minimized Renyi rough entropy thresholding (RRET) method. • Propose an adaptive granule size selection method. • Propose an adaptive granulation RRET algorithm with nested optimization.