Context:

Interior operators have interesting properties that can be used in detecting relevant features in digital images. In this respect, it is pertinent to study the behaviour of the opening and erosion operators from the perspective of fuzzy morphological mathematics.

Method:

Bearing in mind the reticular properties inherent to the mathematical anaysis of an image by fuzzy morphological mathematics we seek to find restrictions on the structural element intended to filter the image so as to obtain characterizations of the opening and erosion operators.

Results:

We prove that if the structural relationship is reflexive or *-antitransitive the opening operator is interior. On the other hand, we found that if the relationship meets both erosion is a interior operator.

Conclusions:

The fuzzy morphological operators can give us more information than the classical methods when we filter an image, especially if we implement the opening operator with a right structural element.

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