0.16 Lab 10b - image processing (part 2)

Questions or comments concerning this laboratory should be directedto Prof. Charles A. Bouman, School of Electrical and Computer Engineering, Purdue University, West Lafayette IN 47907;(765) 494-0340; bouman@ecn.purdue.edu

Introduction

This is the second part of a two week experiment in image processing.In the first week, we covered the fundamentalsof digital monochrome images, intensity histograms, pointwise transformations, gamma correction, and image enhancement based on filtering.

During this week, we will cover some fundamental concepts of color images. This will include a brief description on how humans perceive color,followed by descriptions of two standard color spaces . We will also discuss an application known as halftoning , which is the process of converting a gray scale image into a binary image.

Color images

Background on color

Color is a perceptual phenomenon related to the human response to different wavelengths of light, mainly in the region of 400 to 700nanometers (nm). The perception of color arises from the sensitivities of three types ofneurochemical sensors in the retina, known as the long (L), medium (M), and short (S) cones . The response of these sensors to photonsis shown in [link] . Note that each sensor responds to a range of wavelengths.

Due to this property of the human visual system, all colors can be modeled as combinations of the three primary color components: red (R), green (G), and blue (B).For the purpose of standardization, the CIE (Commission International de l'Eclairage — the International Commission on Illumination)designated the following wavelength values for the three primary colors: blue = $435.8nm$ , green = $546.1nm$ , and red = $700nm$ .

The relative amounts of the three primary colors of light required to produce a colorof a given wavelength are called tristimulus values . [link] shows the plot of tristimulus values using the CIE primary colors.Notice that some of the tristimulus values are negative , which indicates that colors at thosewavelengths cannot be reproduced by the CIE primary colors.

Color spaces

A color space allows us to represent all the colors perceived by human beings.We previously noted that weighted combinations of stimuli at three wavelengths aresufficient to describe all the colors we perceive. These wavelengths form a naturalbasis, or coordinate system, from which the color measurement process can be described. In this lab, we will examine two common color spaces: $RGB$ and $Y{C}_b{C}_r$ . For more information, refer to [link] .

• RGB space is one of the most popular color spaces, and is based on the tristimulus theory of human vision, as described above.The RGB space is a hardware-oriented model, and is thus primarily used in computer monitors and other raster devices.Based upon this color space, each pixel of a digital color image has three components: red, green, and blue.
• $Y{C}_b{C}_r$ space is another important color space model. This is a gamma corrected space defined by the CCIR (InternationalRadio Consultative Committee), and is mainly used in the digital video paradigm.This space consists of luminance ( $Y$ ) and chrominance ( $C_b{C}_r$ ) components. The importance of the $Y{C}_b{C}_r$ space comes from the fact that the human visual system perceives a color stimulus in terms of luminance and chrominance attributes, rather thanin terms of $R,G$ , and $B$ values. The relation between $Y{C}_b{C}_r$ space and gamma corrected $RGB$ space is given by the following linear transformation.
  $$\begin{array}{ccc}Y\hfill & =\hfill & 0.299R+0.587G+0.114B\hfill \\ C_b\hfill & =\hfill & 0.564(B-Y)+128\hfill \\ C_r\hfill & =\hfill & 0.713(R-Y)+128\hfill \end{array}$$