ABSTRACT
CONTENTS 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.2 Affine Filter Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.3 Fuzzy Ordering and Fuzzy Median Filter Applications . . . . . . . . . . . . 91 3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
This chapter builds on the theory of fuzzy methods in nonlinear signal processing developed in Part I of this two-chapter set. The theory developed in Part I shows that for the heavy-tailed Laplacian distribution, the maximum likelihood estimation criteria yield the well-known median and weighted median filters. Moreover, this development shows the importance of spatial order and rank order in estimator, or filter, development. This importance leads to the formalization of spatial and rank (SR) order theory and the more general fuzzy SR order theory. The fuzzy generalization is particularly important in that it enables sample spread, or affinity, to be included in the SR information.
