A Comparison of Some Gradient Threshold Estimators for the Nonlinear Diffusion of Perona-Malik. A Novel Proposal to Improve Edges Detection in Mammography Images

In this work, based on the nonlinear Perona-Malik anisotropic diffusion (AD) model, we develop an efficient smoothing algorithm for mammography images that preserves edges and provides valuable information for any segmentation process. AD is believed to enhance image edges by a diffusion process with a variable diffusion coefficient including a gradient or contrast threshold parameter to which it is highly sensitive. This work proposes an algorithm, named AD-KMLS2, to estimate the gradient threshold of the diffusion coefficient in a way tailored for mammography images. AD-KMLS2 is compared with two other known methods for gradient threshold parameter estimation. When AD-KMLS2 is used, the results are better for \(45\%\) of the analyzed images in terms of two quality measures: Pratt’s figure of merit and the Root Mean Square Error. In the cases where AD-KMLS2 does not reach the best results, it is only \(5\times 10^{-5}\) away from these with respect to the metrics used. In this work the anisotropic diffusion smoothing process is performed by region using the superpixel segmentation technique called simple linear iterative clustering (SLIC).