On the Properties of Some Adaptive Morphological Filters for Salt and Pepper Noise Removal

Mathematical Morphology (MM) is a tool that can be applied to many digital image processing tasks that include the reduction of impulsive or salt and pepper noise in grayscale images. The morphological filters used for this task are filters resulting from two basic operators: erosion and dilation. However, when the level of contamination of the image is higher, these filters tend to distort the image. In this work we propose a pair of operators with properties, that better adapt to impulsive noise than other classical morphological filters, it is demonstrated to be increasing idempotent morphological filters. Furthermore, the proposed pair turns out to be a ∧-filter and a ∨-filter which allow to build morphological openings and closings. Finally, they are compared with other filters of the state-of-the-art such as: SMF, DBAIN, AMF and NAFSM, and have shown a better performance in time-quality ratio when the noise level is above 50%.