A polynomial model for the adaptive computation of threshold of gradient modulus in 2D anisotropic diffusion filter

Anisotropic Diffusion (AD) filter is a non-linear spatial filter, widely used for denoising Magnetic Resonance (MR) images. But, the degree of smoothening and the quality of the morphological edges in the restored image are greatly influenced by the selection of the optimum value Threshold of Gradient Modulus (TGM), which is one of the important operational parameters of AD filter. The method for tuning TGM to its optimum value through trial and error is subjective, cumbersome and time consuming. As a solution to this, a polynomial model to compute the optimum value of TGM from the Standard Deviation (SD) of the noise is proposed in this article. The optimum values of TGM for MR images with completely different information content and noise statistics have been identified objectively with the help of a novel edge preservation metric termed as 'Edge Content Ratio (ECR), with the support of subjective assessment of the quality of the restored images. The coefficient of prediction, r2 equal to 0.7431 is observed for the proposed polynomial model, formulated between the values of optimum TGM and SD of the noise, computed from the test MR images.