Computational Color Technology

Excerpt

Recent developments in color imaging have evolved from the classical broadband description to a spectral representation. Color reproductions were attempted with spectral matching, and image capture via digital camera has extended to multispectral recording. These topics have appeared in a couple of books and scattered across several digital imaging journals. However, there is no integrated view or consistent representation of spectral color imaging. This book is intended to fill that void and bridge the gap between color science and computational color technology, putting color adaptation, color constancy, color transforms, color display, and color rendition in the domain of vector-matrix representations and theories. The aim of this book is to deal with color digital images in the spectral level using vector-matrix representations so that one can process digital color images by employing linear algebra and matrix theory.

This is the onset of a new era of color reproduction. Spectral reconstruction provides the means for the highest level of color matching. As pointed out by Dr. R. W. G. Hunt, spectral color matching gives color fidelity under any viewing conditions. However, current color technology and mathematical tools are still insufficient for giving accurate spectral reconstructions (and may never be sufficient because of device variations and color measurement uncertainties). Nevertheless, this book provides the fundamental color principles and mathematical tools to prepare one for this new era and for subsequent applications in multispectral imaging, medical imaging, remote sensing, and machine vision. The intent is to bridge color science, mathematical formulations, psychophysical phenomena, physical models, and practical implementations all in one work.

The contents of this book are primarily aimed at digital color imaging professionals for research and development purposes. This book can also be used as a textbook for undergraduate and graduate students in digital imaging, printing, and graphic arts. The book is organized into five parts. The first part, Chapters 1–7, is devoted to the fundamentals of color science such as the CIE tristimulus specifications, principles of color matching, metamerism, chromatic adaptation, and color spaces. These topics are presented in vector-matrix forms, giving a new flavor to old material and, in many cases, revealing new perspectives and insights. This is because the representation of the spectral sensitivity of human vision and related visual phenomena in vector-matrix form provide the foundation for computational color technology. The vector-space representation makes possible the use of the well-developed fields of linear algebra and matrix theory.

Chapter 1 gives the definitions of CIE tristimulus values. Each component, such as color matching function, illuminant, and object spectrum, is given in vector-matrix notation under several different vector associations of components. This sets the stage for subsequent computations. Chapter 2 presents the fundamental principles governing color matching such as the identity, proportionality, and additivity laws. Based on these laws, the conversion of primaries is simply a linear transform. Chapter 3 discusses the metameric matching from the perspective of the vector-matrix representation, which allows the derivation of matrix R, the orthogonal projection of the tristimulus color space. The properties of matrix R are discussed in detail. Several levels of the metameric matching are discussed and metameric corrections are provided. Chapter 4 presents various models of the chromatic adaptation from the fundamental von Kries hypothesis to complex retinex theory. Chapter 5 presents CIE color spaces and their relationships. Color gamut boundaries for CIELAB are derived, and a spatial extension of CIELAB is given. The most recent color appearance model, CIE CAM2000, is also included. Chapter 6 gives a comprehensive collection of RGB primaries and encoding standards and derives the conversion formula between RGB primaries. These standards are compared and their advantages and disadvantages are discussed. Chapter 7 presents the device-dependent color spaces based on the ideal block dye model. The methods of obtaining the color gamut boundary of imaging devices and color gamut mapping are provided. They are the essential parts of color rendering at the system level.

The second part of the book, Chapters 8–11, provides tools for color transformation and spectrum reconstruction. These empirical methods are developed purely on mathematical grounds and are formulated in the vector-matrix forms to enable matrix computations. In Chapter 8, the least-square minimization regression technique is given, and the vector-matrix formulation of the forward and inverse color transformations are derived and extended to the spectral domain. To test the quality of the regression technique, real-world color conversion data are used. Chapter 9 focuses on lookup-table techniques, and the structure of the 3D lookup table and geometric interpolations are discussed in detail. Several extensions and improvements are also provided, and real data are used to test the value of the 3D-LUT technique. Chapter 10 shows the simplest spectrum reconstruction method by using the metameric decomposition of the matrix R theory. Two methods are developed for spectrum reconstruction; one using the sum of metameric black and fundamental spectra, and the other using tristimulus values without spectral information. The methods are tested by using CIE illuminants and spectra of the “Color Rendering Index” (CRI). Chapter 11 provides several sophisticated methods of the spectrum reconstruction, including the general inverse methods such as the smoothing inverse and Wiener inverse and the principal component analysis. Again, these methods are tested by using CRI spectra because spectrum reconstruction is the foundation for color spectral imaging, utilizing the vector-matrix representations.

The third part, Chapters 12–14, shows applications of spectral reconstruction to color science and technology, such as color constancy, white-point conversion, and multispectral imaging. This part deals with the psychophysical aspect of the surface reflection, considering signals reflected into the human visual pathway from the object surface under certain kinds of illumination. We discuss the topics of surface illumination and reflection, including metameric black, color constancy, the finite-dimensional linear model, white-point conversion (illuminant mapping), and multispectral image processing. These methods can be used to estimate (or recover) surface and illuminant spectra, and can be applied to remote sensing and machine vision. Chapter 12 discusses computational color constancy, which estimates the surface spectrum and illumination simultaneously. The image irradiance model and finite-dimensional linear models for approximating the color constancy phenomenon are presented, and various constraints are imposed in order to solve the finite-dimensional linear equations. Chapter 13 describes the application of fundamental color principles to white-point conversion. Several methods are developed and the conversion accuracy is compared. Chapter 14 discusses the applications of spectrum reconstruction for multispectral imaging. Multispectral images are acquired by digital cameras, and the camera characteristics with respect to color image quality are discussed. For device compatibility and cross-media rendering, a proposed multispectral image representation is given. Finally, the multispectral image quality is discussed.

The fourth part, Chapters 15–18, deals with the physical model accounting for the intrinsic physical and chemical interactions occurring in the colorants and substrates. This is mainly applied to the printing process, halftone printing in particular. In this section, physical models of the Neugebauer equations, the Murray-Davies equation, the Yule-Nielsen model, the Clapper-Yule model, the Beer-Lambert-Bouguer law, the density-masking equation, and the Kubelka-Munk theory are discussed. These equations are then reformulated in the vector-matrix notation and expanded in both spectral and spatial domains with the help of the vector-matrix theory in order to derive new insights and develop new ways of employing these equations. It is shown that this spectral extension has applications in the spectral color reproduction that greatly improve the color image quality. Chapter 15 describes densitometry beginning with the Beer-Lambert-Bouguer law and its proportionality and additivity failures. Empirical corrections for proportionality and additivity failures are then developed. The density-masking equation is then presented and extended to the device-masking equation, which can be applied to gray balancing, gray component replacement, and maximum ink loading. Chapter 16 reformulates the Kubelka-Munk theory in the vector-matrix form. A general Kubelka-Munk model is presented using four fluxes that can be reduced to other halftone printing models. Chapter 17 presents the Neugebauer equations, extending them to spectral domain by using the vector-matrix notation. This notation provides the means to finding the inverse Neugebauer equations and to obtaining the amounts of primary inks. Finally, Chapter 18 contains various halftone printing models such as the Murray-Davies equation, the Yule-Nielsen model, and the Clapper-Yule model. Chapter 18 also discusses dot gain and describes a physical model that takes the optical and spatial components into account.

The last part, Chapter 19, expresses my view of the salient issues in digital color imaging. Digital color imaging is an extremely complex phenomenon, involving the human visual model, the color appearance model, image quality, imaging technology, device characterization and calibration, color space transformation, color gamut mapping, and color measurement. The complexity can be reduced and image quality improved by a proper color architecture design. A simple transformation between sRGB and Internet FAX is used to illustrate this point.

Henry R. Kang

March 2006