Vector mathematical morphological operators based on fuzzy extremum estimation

Two fundamental problems in vector extremum estimation based on lexicographical ordering are investigated in this paper. The first problem is the choice of the optimal marginal components applying to lexicographical ordering. And the second is that the lexicographical ordering only depends on the first component which leads to the followed components taking no effect. To solve the two problems, three novel marginal components are presented by means of the quaternion description of a color image. Moreover, a new fuzzy extremum estimation algorithm (FEEA) is also proposed and applied to vector ordering. Comparing with the existing solutions, experimental results show that the proposed FEEA has better effect on vector extremum estimation, and the presented frame of vector mathematical morphology can be used to process color image and provide better result.