Multidimensional Signal and Color Image Processing Using Lattices

1Introduction

This book presents the theory of multidimensional (multiD) signals and systems, primarily in the context of image and video processing. MultiD signals are considered to be functions defined on some domain of dimension two or higher with values belonging to a set , the range. These values may represent the brightness or color of an image or some other type of measurement at each point in the domain. With this interpretation, a multiD signal is represented as

(1.1)

i.e. each element of the domain is mapped to the value belonging to the range . In conventional continuous‐time one‐dimensional (1D) signals and systems theory [Oppenheim and Willsky (1997)], and are both the set ...