On Image Filtering, Noise and Morphological Size Intensity Diagrams

In the absence of a pure noise-free image it is hard to define what noise is, in any original noisy image, and as a consequence also where it is, and in what amount. In fact, the definition of noise depends largely on our own aim in the whole image analysis process, and (perhaps more important) in our self-perception of noise. For instance, when we perceive noise as disconnected and small it is normal to use MMAF filters to treat it. There is two evidences of this. First, in many instances there is no ideal and pure noise-free image to compare our filtering process (nothing but our self-perception of its pure image); second, and related with this first point, MM transformations that we chose are only based on our self and perhaps fuzzy notion. This also yields a third point: that once the appropriate filter is found, it is no longer applicable for a new noisy image, with a different kind of noise intensity, distribution and size. In other words, the design of MM filtering algorithms for one particular noise-removal problem and by using our perception is only extended for similar images. Algorithm robustness and adaptation is no longer possible. However, in the absence of that ideal pure noisefree image and by using the strategy of comparing two simultaneous filtering process on the same original noisy image, it is possible to find some relations that can help us, one step more through the direction of automatically chose the right filtering process. The present proposal combines the results of two MM filtering transformations (FT1, FT2) and makes use of some measures and quantitative relations on their Size/Intensity Diagrams to find the most appropriate noise removal process. Results can also be used for finding the most appropriate stop criteria, and the right sequence of MM operators combination on Alternating Sequential Filters (ASF), if these measures are applied, for instance, on a Genetic Algorithm’s target function.