Multivariate mathematical morphology based on fuzzy extremum estimation

The existing lexicographical ordering approaches respect the total ordering properties, thus making this approach a very robust solution for multivariate ordering. However, different marginal components derived from various representations of a colour image will lead to different results of multivariate ordering. Moreover, the output of lexicographical ordering only depends on the first component leading to the followed components taking no effect. To address these issues, three new marginal components are obtained by means of quaternion decomposition, and they are employed by fuzzy lexicographical ordering, and thus a new fuzzy extremum estimation algorithm (FEEA) based on quaternion decomposition is proposed in this study. The novel multivariate mathematical morphological operators are also defined according to FEEA. Comparing with the existing solutions, experimental results show that the proposed FEEA performs better results on multivariate extremum estimation, and the presented multivariate mathematical operators can be easily handled and can provide better results on multivariate image filtering.