Multidimensional Signal and Color Image Processing Using Lattices

8Processing of Color Signals

8.1 Introduction

This chapter presents the theory of the representation and processing of color signals, namely still and time‐varying color images. A color image is a function of two (spatial) or three (spatiotemporal) independent variables with values in a color space. We introduce the ideas of signals, linear shift‐invariant systems and Fourier transforms, in the continuous domain and in the sampled domain. This chapter extends the material in Chapters 2–6 from scalar valued signals to vector valued signals. It can also be viewed as a revision and extension of Chapter 6 of Dubois ( 2010).

8.2 Continuous‐Domain Systems for Color Images

8.2.1 Continuous‐Domain Color Signals

A continuous‐space color image is a function that assigns an element of a given color space to each spatial coordinate within a given image window. This image will be denoted . A time‐varying color image would be of the form . As before, we use a vector notation for the independent variables, and write for either still or time‐varying images, where denotes either or according ...