Is there a perceptual color space?

BOOK REVIEWS

Billmeyer and Saltzman’s Principles of Color Technol-ogy, 3rd Edition, by Roy S. Berns, John Wiley & Sons,New York, 2000. 272 pp, $99.95.

The third edition ofBillmeyer and Saltzman’s Principlesof Color Technologyis an excellent resource for chemistsand technicians new to the areas of color and appearance.Laboratory managers and colors specialists will find thistext equally useful as a refresher. The new edition illus-trates colorimetry methods and examples in the textiles,plastics, and coatings fields, as well as the newer colorimaging industries like desktop publishing and digitalphotography. Readers familiar with the previous addi-tions will also find a new appendix devoted to the math-ematics of color technology.

The first chapter defines the relationships among lightsources, objects, and observers. Light sources are definedwith spectral power distributions. Light interaction withmaterials is discussed in detail covering topics such asabsorption, scattering, and transmission. The surface andmaterial effects of the object are discussed in their relationto color perception. Readers new to colorimetry can easilyfollow along as the book expands upon the light, object, andobserver interaction into color-order systems and color-difference calculations.

Chapter two introduces the reader to visual color-ordersystems like Munsell and the Natural Color System (NCS).The limitations of visual spacing systems are discussed andthe development of standard observers is introduced indetail. Using easy-to-follow graphs and illustrations as wellas straight-forward text, the reader is shown how a lightsource, object, and observer can be mathematically de-scribed as tristimulus values. The discussion naturally leadsinto color-space equations beginning with the chromaticitydiagram and progressing into more uniform color spaceslike CIELAB.

Chapter three discusses color measurement includingboth instrumental measurement and visual assessments.Controlling the viewing conditions and limit standards arejust a few of the topics discussed to increase the accuracyand precision of a visual measurement system. Correlationof instrumental measurement to visual observations is alsodiscussed. Color measurement and appearance devices suchas spectrophotometers, colorimeters, and gloss meters arecompared and contrasted. This chapter provides the readerwith a good explanation of the difference between a color-imeter and a spectrophotometer, but it does not discussspecific instrument models or manufacturers. However thischapter provides readers new to color measurement withvaluable information on the basic instrument types andgeometries available for color measurement.

Chapter four deals with measuring color quality. The idea

of acceptability vs. perceptibility is discussed to help read-ers make decisions on how to develop standards and spec-ifications for colored products. A brief historical look at theadvancement from color-order systems like Munsell tomore uniform color-difference equations like CMC is pre-sented. Numerical examples showing how to set color tol-erances using both instrumental and visual data are providedto assist readers in ensuring that their applied tolerances incolor space equations correlate to visual assessments. Colorconstancy is discussed, and the reader is introduced tometamerism indices. Readers new to colorimetry will findthe real world examples relevant to common problems andconcerns expressed in quality-control labs and productionsettings.

Colorants are classified and discussed in Chapter five.Tips for selecting colorants are presented along with colorgamuts to help readers understand when it is practical to usea colorant to reach a desired target. Readers will also findhints on where to find additional information to help themselect colorants that would suit their needs. Readers willfind this information useful for general colorant questions,but this chapter is not a list of manufactures and theirrespective colorants.

The final chapter in this text covers producing colors andcomputer color matching. Color-mixing laws are discussed,contrasting additive and subtractive mixing laws. Readersare introduced to Beer’s law and the Kubelka–Munk equa-tion using easy-to-follow text and relevant numerical exam-ples. The complex topic of computer color matching isplainly described, covering topics such as colorant databasedevelopment, colorant identification, and batch correction.By emphasizing the basics and providing relevant numericexamples, this text provides an excellent standalone re-source for anyone interested in colorimetry and color ap-pearance. I would highly recommend this book to anyoneinvolved in the production of colored materials.

LUKE MAUK

Billmeyer and Saltzman’s Principles of Color Technol-ogy, 3rd Edition, by Roy S. Berns, John Wiley & Sons,New York, 2000. 272 pp, $99.95

This is a new edition of a venerable guide and textbook forwhich many of us in color technology have longed. The waitis over and I, for one, do not believe that anyone can bedisappointed.

Like the new author, my exposure to the book dates backto the years when I was a graduate student in the RensselaerColor Measurement Laboratory. Roy Berns writes in thepreface to the Third Edition how that the second edition of

322 COLOR research and application

the book was published just in time for his first course incolor science. Being there, a few years before ProfessorBerns, I watched the second edition being drafted. I ob-served the compromises and struggles between Fred Bill-meyer, Jr. and Max Saltzman and also between them and thepublisher as they sought to create a book that was aspractical as it was technically correct. I can state withouthesitation that Roy Berns has stepped in and accepted theirbaton without missing a step.

The book has seven chapters and an Appendix. Chapter 1,Defining Color, describes what the book is about and givesthe traditional introduction of light source, object, observertriplet. It introduces topics like light sources and illumi-nants, perceiving colors, describing color—the desert islandexperiment and metamerism. Chapter 2, Describing Color,continues on the theme introduced in Chapter 1, bringing inthe ideas of color order systems. It separates them intosystems based on color mixing, systems based on colorperception, and systems based on color matching such as theCIE system. Chapter 3, Measuring Color, brings in both thevisual and instrumental quantification of both object andself-luminous color. For the first time, spectroradiometers,photometers, and source colorimeters are described on anequal basis with spectrophotometers, spectrocolorimeters,and filter colorimeters. The chapter concludes with a dis-cussion of precision and accuracy in color measurement.Chapter 4, Measuring Color Quality, introduces the readerto the perceptibility and acceptability issues in visual eval-uation of product. The area of color-difference equationsand color-tolerance equations is presented along with anexample of how to set up a production color tolerance.Finally, the chapter briefly looks at what the book callsone-dimensional scales of color, which includes the white-ness index, yellowness index, and metameric indices. Chap-ter 5, Colorants, covers issues such as terminology andwhen is a colorant a dye and when is it a pigment, how toselect colorants for use, and treating color as an engineeringmaterial. Chapter 6, Producing Colors, describes the variousmodels and algorithms for colorant mixing and color match-ing, both visual-based and instrument-based approaches andfinishes with a discussion of color matching of images andgraphics. Chapter 7, Back to Principles, is a two-page sum-mary of the content of the book. The Appendix covers theMathematics of Color Technology and highlights such top-ics as matrix algebra, the integral equations used in color-imetry, transformation of primaries, TV and CRT displaycolorimetry, the equations used in computer color-matchingsystems, indices of metamerism and of color constancy, andfinally the newest area of color engineering, color-manage-ment systems. There is no longer an annotated Bibliogra-phy, but there is a comprehensive bibliography of the liter-ature cited in the chapters. Each chapter ends with aSummary section that pulls together the various topics cov-ered in the chapter. This is a necessary requirement, becausethe chapter topics are so broad that they allow rather diversetopics to be raised within the chapter boundaries.

Using the resources available to him at the RochesterInstitute of Technology, Chester F. Carlson Center for Im-

aging Science, Professor Berns has added many features tothe book for which Fred and Max often longed. All theillustrations are now in color—many with accurate, fullcolor images. While the many figures in the book, bothcharts and graphs, are greatly enhanced by the addition ofcolor, the lack of figure numbers can often make it difficultto find the text that refers to the illustration or, worse yet, thefigure that is described by the text. Still, the full-colorimages greatly enhance the section on color-order systems.

Additions to the book include sections on color manage-ment and on the development of what the book calls“weighted color-difference equations,” but which are reallycolor-tolerance systems in which the standard is given aspecial status within the metric of CIELAB space. Minorsemantic differences aside, the historical review and discus-sion of the development of the equations is very wellwritten. In the second edition, Fred was able to add somesections on color matching. In the third edition, Roy hasexpanded that greatly, providing a discussion of severaldifferent applications of color matching. This will be bothuseful and disappointing to the modern color technologist.Useful, because computer-assisted color matching and colo-rant formulation is so common in most color-related indus-tries. Disappointing, because it describes technologies thatare at least a decade old. Modern, multi-flux (as opposed tothe many-flux technology that was pioneered when WillardRichards worked at Cabot Corp. and was an adjunct pro-fessor in the Rensselaer Color Measurement Laboratory)technology more accurately describes the interaction oflight and matter in nonopaque films and polymers. The thirdedition further extends the section on how to set productiontolerances, including a worked example of fitting the cumu-lative pass/fail decisions of a production shader to a com-puted CIE94 color-tolerance number. The example is mucheasier to follow and to implement than the example given inother recent textbooks on industrial color control.

With all the praise that I have been heaping upon thebook, one might get the idea that the book has no short-comings. Unfortunately, that conclusion is not supported bythis reviewer’s experience. Very early in the first chapter,the book introduces the concepts of standard sources andilluminants, and states emphatically that they are normal-ized at 560 nm. Two pages later are two sets of figures, oneshows a rather smoothed version of D65 compared to afluorescent lamp and a continuous xenon arc lamp. All threecurves have been normalized at 560 nm as indicated in thetext. In the other figure on the page are shown CIE standardilluminant F2, F6, F7, and F11 with none of them beingnormalized at 560 nm with no mention of why this might be.In addition, no explanation of why F2 and F11 should beplotted together is given. This is a minor oversight in termsof the total text, but an eventual source of confusion in theapplication of this information. Also in Chapter 2 on color-order systems, the Colorcurve® system is classified as asystem based on visual perception instead of on colormatching. The system was derived using CIELAB spacingand Maxwell disk technology, not visual judgments.

Expanding the section on visual color measurement was

Volume 26, Number 4, August 2001 323

an excellent decision, because it clearly identifies many ofthe reasons why casual evaluations of the color of materialsoften have large disagreements with instrumental methods.I particularly liked Section D of Chapter 3 on instrumentcolor measurement. It did a fine job of covering the varioustopics and ended with an excellent discussion of what toconsider when selecting a color-measuring instrument. Asin earlier editions of the book, the emphasis is placed onusefulness rather than on cost or size. More importantly, astrong emphasis is placed on testing instrument perfor-mance with product or production specimens rather thanwith standard reference materials. The selection of a short-hand terminology for instrumental geometry was unfortu-nate, especially in view of the book’s citation of ISO 5 andASTM E 1767, which describe international standard nota-tions. The section on precision and bias tries to carry for-ward the theme from Section D, but quickly loses its focus.Supplying definitions for calibration that are today calledstandardization and erroneously indicating that an equationgiven on page 96 is equally applicable to instruments stan-dardized with black traps or black tiles is clearly not thecase, except in certain very limited situations, not describedin the text, and such conditions are clearly identified in CIEPublication 130, a cited but obviously unread reference.

Finally, pages 137–138 of the text discuss the measure-ment of fluorescent colors and fluorescent whitening agents(FWA) as if they were equivalent problems when they arenot. The two classes of materials, UV-activated luminescentmaterials and visible-activated luminescent materialspresent significantly different measurement and analysisproblems. On page 137, the various methods for separatingthe reflected and fluoresced radiance factor of a visible-activated fluorescent material is presented sequentially withthe Griesser method source adjustment to obtain a fit to D65in the UV spectral region for UV-activated FWAs. Theformer method derives an approximation to the two radi-ance factor components, while the latter creates an accurateapproximate to one part of D65 that results in a predictableexcitation and emission spectrum. From the cited referenceCIE Publication 76, it is shown that reproducibility betweenresearch instruments with “good” quality daylight simula-tion is about 103 worse than for nonfluorescent specimenson the same instruments. With the Griesser adjustmentmethod, it is possible to characterize the “color” of FWAswith approximately the same level of uncertainty as that ofnonfluorescent white reference materials. This subtle dis-tinction is one of the most serious pitfalls in setting colortolerances in the graphic arts today.

Overall, there are many, many more positive things thatcan be written about the book than negative ones. In thislimited space, it is possible only to highlight the overallpositive nature of the book and to document some of thepotential stumbling blocks. Still, this book will sit promi-nently on my desk and never be far out of reach whensomeone comes to visit with a question on color technology.

DANNY C. RICH

Fundamentals of Sensation and Perception, 3rd Ed., byLevine, Oxford University Press, 2000. 28.99 pounds,604 pp. soft cover

The timing was perfect: I was in the midst of preparationsfor my “Perception for Visualization: From Design to Eval-uation” tutorial at SIBGRAPI 2000 (the Brazilian computergraphics conference that took place in Gramado, RS, Brazil,October 17–20) when this book arrived. I had taught vari-ations of this one-day tutorial several times before, so itwasn’t a question of “knowing” the material, but I amalways looking for better ways to explain phenomena, andfor examples. I found this book invaluable for these twogoals.

You might want to own a copy of this book even if youare an expert in the field; it would serve you as a good“shelf” reference for those moments when you need toconsult such a reference because you don’t quite remembersome obscure detail. Or, it would be a good textbook for acourse you are going to teach on the subject. In either case,this book would deliver the “merchandise.” If you are astudent taking a course on the subject or a researcher tryingto get up to speed on perception, this is one to own.

If you are only interested in color perception (as, I havebeen advised, manyColor Research and Applicationread-ers are), you might find this book somewhat wanting: it isdefinitely not a color perception book. However, I (whohave spend a significant part of my career doing color-related research) found the book useful.

While I cannot say that I read the book cover to cover,those parts that I did read, I found written very well, withclear, reasonably concise, and accurate discussions. If youare in a hurry to get the quick fact on some topic or other,consulting one of the “boxes” can usually get you what youneed in no time. Indeed, for examples and quick explana-tions for my tutorial, I mostly scanned those boxes and thefigures. Boxes are focused at the more advanced reader.Quoting from the Preface: “in some cases a few equationscould help to make a point but would only confuse anyreader who is not familiar with mathematics. In manyplaces, demonstrations make the material clearer.” I fullyagree. Reading through a box or going through a demon-stration gave me very quickly the facts and details I needed,without having to go through lengthy text. However, whenI did go through the full text, I found the explanations clear.The boxes are referred to from the main text using “hyper-links”; those point you at the appropriate box and alsoremind you where you left off. Nice.

There are plenty of figures, and many of them (in partic-ular those in Chapters 9–14) demonstrate a perceptual effector illusion in a “self contained” manner. At times, a quickglance will demonstrate the phenomenon, at others, a bitmore effort is required to get it.

In this third edition, for the first time, a CD-ROM isincluded with the book. What you get on the CD-ROM is aprogram, SensPerc, that provides “live” demonstrations ofmany of the phenomena discussed in the book. Most ofthem are quite interactive, allowing you to try it out. You’ll


be surprised how some of the illusions really “work”: evenif you know exactly what the “correct” answer should be,you’ll find yourself fooled by most illusions most of thetime. I found this program extremely useful to demonstratevarious phenomena during my tutorial. It broke the routinefor the students, they participated in some of the experi-ments, and even were able to get surprisingly good results.You should, however, download the patch after you haveinstalled the program from the CD. While I have not en-countered the effect of the reported bug in the originalversion, the author recommends the patch (http://www.oup.co.uk/best.textbooks/psychology/levine/errata/ sensperc.exe).

The “glossdex” — a combination glossary and index —is a nice touch; instead of having to look up a word in theglossary and then in the index, you get the pointer rightthere and then.

Another “first” for this edition: Jeremy Shefner’s interestshave changed, and he is no longer a coauthor.

All in all, I recommend this as both a reference and atextbook for any general perception professional or student.

HAIM LEVKOWITZ

Printing Materials: Science and Technology by BobThompson, PIRA, 1998. $90, 590 pp.

People interested in printing would presumably benefit fromat least a passing acquaintance with the underlying scientificstructure of the craft — the physics of light and optics, thechemistry of organic compounds, and the theory of quantumenergy. A diligent student with this book could learn morethan enough about these subjects to reinvent most of theprinting technology and paper making in use today.PrintingMaterials: Science and Technologyreviews fundamentalprinciples of printing materials and technologies, and theeconomic and ecological constraints that have enabledthem. In short, it is a fully authoritative reference work. Inthis field, however, reference works of this depth may rarelybe needed. To be sure, the book is not labeled a referencework. It is intended as a textbook for students of printingtechnology. As such a textbook, it could work well, but onlywith a good teacher who could help students distinguish thesignificant details from the inessential. The tone is set withthe book’s first words: “Whether the chicken came first orthe egg, one thing of which we can be certain is that theatom was there before either of them.” At a micro level, itis highly readable, from paragraph to paragraph. The au-thor’s language, for all its density, is straightforward and tothe point. The illustrations are placed nicely, clearly labeled,and support the text well. The chapters are organized so thatit is easy to find information. The book is well organized asa whole.

The book starts by reviewing basic applications of scien-tific concepts to printing, including in its scope topics suchas atoms, molecules, organic chemistry, and optics. It thencovers in more detail the substrates of printing — paper

manufacturing, processing of fibers, paper properties andstrengths, adhesion, printing problems, among other things.Basics of inks and coatings are also well covered, includingthe chemistry and physics of color, as are imaging systems.In short, it is a thorough primer of printing materials,complete with a periodic table of elements.

Unfortunately, some of the critical sections of the bookseem outdated. For example, in talking about digital pho-tography, the author states that digital cameras are priced atabout 20,000 pounds sterling. Furthermore, sometimes theauthor’s knowledge may get in the way of explaining con-cepts clearly. When talking about waveforms, the authormakes a diversion to talk about the media through whichsound waves travel. Why is this necessary in a book inwhich light is of fundamental interest? Furthermore, despiteall its depth about physics and chemistry, there is very littleattention paid to perception — the process that defines theeffectiveness of printed media. There is no mention ofpsychophysics, vision, or perception, in the index. There isabout a page on color perception. That page talks about thechemical and molecular mechanics of photoreceptors, andleaves it at that. As with much of the rest of the book, thereader is required to put the information in a larger context.A significant proportion of the book is devoted to colorconsiderations in printing. Topics include organic printingtechnology, measurement of chemistry and physics of color,as well as the measurement of color inks and film.

This would be an excellent book for students or begin-ning professionals joining the printing or publishing indus-try, who also want a primer on basic scientific concepts. Inparticular, for someone who never had to take a sciencecourse but needed knowledge on the scientific underpin-nings, particularly from the point of view of physics orchemistry, this would be the book to buy. It would providerefresher knowledge for those who have been in the industrysome time, as well as introduce some new technologies forthose who would like to keep current with how the newadvances are implemented. However, the desire of the au-thor to communicate the scientific principles leads him toinclude sections on physics that most people in the fieldwould already know.

FAITH FLORER

Is There a Perceptual Color Space?

Geometric Representations of Perceptual Phenomena.R. D. Luce, M. D’Zmura, D. Hoffman, G. J. Iverson,A. K. Romney, editors. Earlbaum 1995. 356 pp, $79.95.

“ . . . a law of inherent opposites,Of essential unity, is as pleasant as port,. . . We cannot go back to that.The squirming facts exceed the squamous mind,“

Wallace Stevens,Connoisseur of Chaos1


The possible geometric representations of perceived colorsand perceived space were the issues that most engagedTarow Indow , whose 70th birthday was celebrated by thebook under review. Modern science evolved from a scho-lastic tradition that tried to understand the world in terms ofuniversal harmonies and Pythagorean geometries. Colorscience too has long attempted to encapsulate the relationsbetween color percepts in low-dimensional geometricalspaces.2 However, the first color space based on empiricalmeasurements was presented by Maxwell.3 As is wellknown, the measurement procedure was color matching inaperture mode, which reduced the infinite-dimensionalwavelength space of visible lights to a three-dimensionalspace of metamers. Maxwellian spaces and their lineartransformations have proven invaluable in psychophysicaland neurophysiological studies of color vision. However,these spaces predict only which physically distinct mixturesof lights will appear the same when presented in aperturemode, and do not attempt to represent the relations betweencolor percepts.

A landmark relational theory was put forward by Hering,4

and Schrodinger cast it geometrically into a transformationof metamer space.5 Hering, as is well known, conceived ofthree perceptual axes anchored by pairs of opponent-colors:red/green, yellow/blue, and white/black. The genesis ofideas is almost impossible to reconstruct after a century haspassed, but I have sometimes wondered whether Hering wasusing an analogy to the geometry of space. A pair ofoppositions, North/South and East/West, work well for de-scribing all directions on maps; and two axes, up/down andright/left, suffice for describing all orientations in the frontalplane. As Runge responded to Goethe: “If we were to thinkof a bluish orange, a reddish green or a yellowish violet, wewould have the same feeling as in the case of a southwest-erly northwind.”

Since, in some quarters, there still exists a vestigial notionthat cortical neurophysiology should correspond to Hering’sscheme, orientation in space is an analogy worth pursuing alittle further. Despite the sufficiency of one pair of orthog-onal axes for representing orientation in the frontal plane,the orientation tuning of neurons in primary visual cortexprovides a finer grained sampling of orientations. The pre-ferred orientations of successive neurons in a cortical col-umn can differ by less than 10°, and during visual activitythe difference may be further refined by renormalizationbetween adjacent neurons.6 This diversity of mechanismspresumably underlies the fast and reliable computation oforiented energy over the visual field that is required for anumber of visual tasks, for example, the perception of 3Dshape from texture cues.7 In a similar fashion, psychophys-ical and physiological studies have converged on a pictureof the visual cortex as containing a large variety of color-sensitive neurons, each neuron tuned to a different directionin color space. This picture is supported by evidence from alarge number of psychophysical tasks including adaptationto prolonged temporal modulation,8,9 induced color appear-ance,10 color search,11 discrimination of color changes,12

separation of plaid motion into component motions,13 and

texture segmentation.14 In addition, there is evidence forrectified color mechanisms subserving detection15 and in-duction.16,17Electrophysiological evidence supports the ex-istence of two tightly clustered classes of Parvo-neurons inthe Lateral Geniculate Nucleus.18 The preferred color direc-tions of these classes, however, correspond to the cardinaldirections15 and not to Hering’s pure hues. The same elec-trophysiological methods applied to areas V1, V2, and V3of visual cortex revealed a much larger number of types ofcells, each type preferentially tuned to a different colordirection.19–21 Given the above evidence, if there is a low-dimensional perceptual color space, it is unlikely to bebased on a low-dimensional neurophysiological rationale.

The construction of a perceptual color space requires theconceptual leap that, not only can all visible lights bespecified as points in a 3-D space, but that this is also truefor all colors (seeIndow’s article). This assumption isalmost certainly untrue for the complete gamut of colorsthat we perceive in the world. Wittgenstein22 provided someof the clearest examples that the straightforward rules thatseem to apply when names are assigned to isolated colors,break down when colors have to be described in spatio-temporal configurations of lights or surfaces, particularlythose configurations that evoke percepts of metals, trans-parency, or luminosity. There are no metamers betweencolors perceived (or conceived) as belonging to differentclasses of physical entities such as substances, surfaces,illuminants, and transparent objects. Without a satisfactoryoperation of sameness across classes of perceived entities,there is no possibility of embedding all perceived colors intoone space, geometric or linguistic.

Indow’s article presents a thoughtful summary of his andother’s attempts to construct uniform color spaces for lightsseen mostly in aperture mode but sometimes with simplesurrounds. (Indow explicitly excludes only colors attributedto the gloss of the surface.) These attempts have used (i)psychophysics, which does not involve scaling, e.g., justnoticeable differences, and points of subjective equality;and (ii) direct scaling measurements that represent someaspect of perception caused by the stimuli. Maxwellianspaces are converted to uniform color spaces on the basis ofeither (i) a global criterion: whether the space represents theMunsell system without distortion; or (ii) a local criterion:whether JNDs are represented by segments of equal lengthin all directions and at all points.Indow’s steadfast andcareful work illuminates many complexities in using mul-tidimensional scaling (MDS) methods and should be re-quired reading for researchers investigating similar proce-dures. It does seem to me that this enterprise needs to besupplemented by investigations of processes and tasks. Itseems entirely circular to try to infer from MDS results whatobservers were doing when they provided the scaling dataor perceptual differences, therefore, independent experi-mental manipulations of strategy may be of use in makingsuch inferences. In addition, scaling tasks usually involvepairs of steady stimuli presented for prolonged periods onuniform backgrounds. It is unlikely that the results would besimilar in more spatio-temporally complex situations. For


example, discrimination ellipses measured under steady ad-aptation do not predict ellipses measured in conditions thatinclude transitions23,24 as would be the case in most natu-ralistic conditions. In addition, in bothIndow and Izmail-ov’s articles, MDS methods have been restricted to embed-ding perceived colors in low-dimension Euclidean spaces.This is a strong and probably untenable assumption.

The geometric properties of the neural representation ofcolor should be an issue of general interest, because manyquestions of complex color perception can be formallytranslated into geometric terms.Drosler’s article providesone such direction by considering Helmholtz’s line elementas a generalization of Weber’s Law. The line element isactually one example of what are called Minkowski Geom-etries.25 As discussed below, the larger class of such geom-etries is worth exploring for perceptual color spaces.

In one of the very few direct explorations of geometricoperations in color space, Wyszecki and Fielder26 being theother, Maloney, Wuerger, and Krauskopf used originaland clever combinations of proximity measurements to testthe Euclidean assumptions underlying MDS. Their resultsrejected these assumptions, and it would be interesting tosupplement their geometrical operations to test whether anyMinkowski geometry would be an adequate space for per-ceived colors. In such geometries, space does not have to beuniform and isotropic. From outside it appears that the unitfor measuring length is different in different directions,hence circles and spheres are not round objects but someother convex shape. From inside, distance measurementswould adjust to rotation, making it harder to judge theanisotropy. However, some interval measurements canshow that the space is non-Enclidean. For example, the ratioof circumference to radius of a circle varies with the planein the space, and is generally not 2p. A fundamental con-cordance with color percepts is the lack of a satisfactoryconcept of “orthogonal.” There are shortest distances froma point to a line or plane, but the orthogonal relationship isnot symmetric. Therefore, Pythagoras’ Theorem does noteven exist. Minkowski geometries, like metamer spaces, are“affine” in the sense that their properties are independent ofthe choice of basis vectors, which is equivalent to beinginvariant under invertible linear transformations.

The article byIverson andD’Zmura is a readable sum-mary of their extensive work on recovery of spectral prop-erties of light and surfaces, given different numbers ofphotopigments, lights and surfaces. Those readers inspiredby this article to read the more detailed original articles, willbe rewarded not only by more mathematically completeresults, but also by sophisticated examples of matrix ma-nipulations applied to the color domain. Spectral recoverymethods are possibly of greatest utility in machine-visionapplications requiring analyses of remote materials. Anybiological system that extracted infinite-dimensional oreven 31-dimensional spectra in the cortex, would eitherhave to be adept at reasoning in high-dimension spaces, orwould have to make a neural scheme that converts thisinformation back into a manageable few dimensions.

The article byD’Zmura , Iverson, andSinger, similar to

Brainard and Freeman,27 reformulates the spectral recoveryproblem in terms of Bayesian decision theory. This ap-proach is akin to bringing into the problem, accumulatedknowledge in the guise of prior probabilities of occurrenceof lights and surfaces. As is generally true of Bayesianprocedures, success depends on appropriateness of priorsand of independence assumptions. The article is open tocriticisms on both these grounds. Besides collection of moreextensive marginal frequency of occurrence data, it wouldbe worth collecting data on joint occurrences of surfacesand illuminants, and applying Lindley’s28 concept of coher-ence to obtain useful prior conditional probability distribu-tions.

I have tried to point out some of the “squirming facts”that complicate the search for a unified perceptual colorspace with a small number of opponent axes as basis vec-tors. For the readers ofColor Research and Application, thisreview has been limited to the six articles that discusscolor-related issues. If reviews of individual articles appearcontentious, it is only because these articles are engagingand thought provoking. I have enjoyed and profited fromreading this book, and so will any student of color percep-tion who works through the articles.

1. Stevens W. Parts of a world. New York: Knopf; 1942.2. Harris M. The natural system of colors. Leicester–Fields: Laidler;

1766.3. Maxwell JC. On the theory of compound colours and the relations of

the colours of the spectrum. Phil Trans; 1860;150:57–84. Reprinted in:Color Res Appl 1993;18:270–272.

4. Hering E. Zur Lehre Vom Lichtsinne. Wien: Carl Gerold’s Sohn;1878.

5. Schrodinger E. Grundlinien einer Theorie der Farbenmetrik im Tages-sehen. Ann. Physik; 1925;63:397–447, 481–520. Translation in: ColorRes Appl 1994;19:37–40.

6. Ringach DL, Hawken MJ, Shapley R. Dynamics of orientation tuningin macaque primary visual cortex. Nature 1997;387:281–284.

7. Li A, Zaidi Q. Perception of three-dimensional shape from texture isbased on patterns of oriented energy. Vision Res 2000;40:217–242.

8. Krauskopf J, Williams DR, Mandler MB, Brown AM. High-ordercolor mechanisms. Vision Res 1986;26:23–32.

9. Webster MA, Mollon JD. Changes in colour appearance followingpost-receptoral adaptation. Nature 1991;349:235–238.

10. Krauskopf J, Zaidi Q, Mandler MB. Mechanisms of simultaneouscolor induction. J Opt Soc Am A 1986;10:1752–1757.

11. D’Zmura M. Color in visual search. Vision Res 1991;31:951–966.12. Zaidi Q, Halevy D. Visual mechanisms that signal the direction of

color changes. Vision Res 1993;8:1037–1051.13. Krauskopf J, Wu HJ, Farrell B. Coherence, cardinal direction and

higher-order mechanisms. Vision Res 1996;36:1235–1245.14. Li A, Lennie P. Mechanisms underlying segmentation of colored

textures. Vision Res 1997;1:83–97.15. Krauskopf J, Williams DR, Heeley DW. Cardinal directions of color

space. Vision Res 1982;22:1123–1131.16. Krauskopf J, Zaidi Q. Induced desensitization. Vision Res 1986;26:

759–762.17. Smith VC, Pokorny J. Color contrast under controlled chromatic

adaptation reveals opponent rectification. Vision Res 1996;36:3087–3105.

18. Derrington AM, Krauskopf J, Lennie P. Chromatic mechanisms inlateral geniculate nucleus of macaque. J Physiol 1984;357:241–265.

19. Lennie P, Krauskopf J, Sclar G. Chromatic mechanisms in striatecortex of macaque. J Neurosci 1990;2:649–669.

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QASIM ZAIDI

Comment on Review of Colorand Its ReproductionThe review by Dr. Chris Hawkyard of my bookColor andIts Reproduction,published in the October 2000 issue,contains some obvious errors and some rather ill-informedcomments.

The reviewer incorrectly claims that I do not mention theuse of diffraction gratings within spectrophotometers (I do,on p. 97) and that I make no mention of the Pantone colorspecification system (in fact, most of p. 110 covers this andsimilar systems).

The reviewer finds it a “surprising omission” that I do notillustrate a cross-screen grid (a crossline screen) or theprocess by which halftone images are produced from con-tinuous tone negatives. He is apparently unaware that theindustry ceased using crossline screens in the 1960s and didnot make significant use of continuous tone negatives afterthe 1970s. Grid-based laser screening from digital databecame the preferred method of halftoning during the mid1970s. This method, which is described on pp. 305–311 ofthe text, has long been the exclusive method for graphic artscolor halftoning.

The reviewer cites two “errors” in the text:

a. No signal from the red sensitive cones (p. 52). The colorsensation chosen to explain the color vision mechanismis cyan, which, theoretically, does not reflect any redlight to activate the red sensitive cone. The diagram isillustrative of a simplified ideal system and, as such, isnot in error.

b. CIE chromaticity chart used to represent ink set gamutwith white at the center (p. 135 and cover). In using thediagram in this way, I am simply following the long-established lead of such authorities as David Mac-Adam.1 In fact, my diagram is a modified version ofone that MacAdam (and Eastman Kodak) used for

many years. There is nothing wrong with using thisdiagram to display the gamut of subtractive colors.

My final remarks concern the reviewer’s bizzare compar-ison of my book with Dr. R. W. G. Hunt’sThe Reproduc-tion of Colour.Most reviewers who were familiar with thecolor reproduction literature would know that if a compar-ison of my book with another text were to be made, it wouldbe made relative to Dr. J. A. C. Yule’sPrinciples of ColorReproduction.Dr. Yule’s classic 1967 text, which has re-cently been republished in an updated reprint edition, fo-cuses exclusively upon the graphic arts and related indus-tries.

The astonishing point about the reviewer’s comparison ofmy book with Dr. Hunt’s text is that he readily acknowl-edges that I clearly define the fundamentally different scopeand audience forColor and Its Reproductionin my preface.This fails to stop him from making a detailed comparison ofthe differences between the two texts. Perhaps this irrele-vant comparison would have been avoided if I had titled mybook Color and Its Reproduction for the Graphic Arts,butthe fact that the book is published by the Graphic ArtsTechnical Foundation (GATF) should provide a clear clueabout the book’s emphasis. The first edition of the book waspublished in 1988 and has been one of GATF’s best sellers.I am not aware of anybody being deceived by the titleduring these past twelve years.

The reviewers insistence on comparing Dr. Hunt’s book(written mainly for color scientists and engineers) with mine(written mainly for graphic arts practioners) traps him intothe further “surprising” observation that the main text doesnot contain a single mathematical equation. In fact, there arenumerous equations throughout the text, but the real pointhere is that the reviewer’s surprise seems to stem from abelief that the printing industry’s scanners and presses arebeing operated by scientists and engineers who would makeuse of a greater emphasis on mathematics. In practice, theindustry’s scanners and presses are being operated by de-signers and craftsmen who would find the equations I haveplaced in the Appendix to be quite irrelevant to the kind ofunderstanding of the subject that they are seeking from thebook.

The reviewer closes his review by candidly admitting hislack of knowledge of the book’s graphics content. It is a pitythat he did not learn more about this most important branchof color reproduction before making such confident judg-ments about the subject.

1. MacAdam, David L. Color difference evaluation. In: Industrial colortechnology, Gould RF, Editor. Washington, D.C.: American ChemicalSociety; 1972, p 69–86. (See, in particular, the diagram on p. 71, andthe color illustration on the dust jacket—my cover and p. 135 diagramsare adapted from this.)

GARY G. FIELD


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