Fuzzy transformation and its applications
Yuge Nie, Kenneth E. Barner · 2004
In this paper, we introduce the basic concepts of the fuzzy transformation (FZT) theory and their applications in image denoising. FZT is a data-adaptive nonlinear transformation, where the transformation matrix is a dynamic real-valued spatial-rank (SR) matrix (i.e., fuzzy SR matrix) generated by using an order invariant membership function. The clustering property is the essential property of FZT, and is exploited (through the re suiting fuzzy samples and fuzzy ranks) in two image denoising applications, namely, DCT coded image deblocking and impulsive noise elimination. Our proposed methods demonstrate superior performance than the conventional methods in all the simulations, showing that FZT is a powerful tool for image processing.