Study on nonlocal morphological operators

This paper studies nonlocal morphological operators. Following the strategy proposed for the Nonlocal means filter, these operators are based on a local and adaptive definition of the structuring element which is specified by searching for patches in the image that are similar to the one surrounding the pixel being filtered. After presenting the basic nonlocal morphological operators using generic structuring elements, we study their robustness in the presence of noise. Then, we illustrate the interest of some nonlocal morphological operators using flat structuring elements for denoising