Computational Model of Color Perception and Color Naming

Embodiment is the notioncategories, in a referential type semantics is in part determined by the physiology of the universality of basic color category foci can be explained in terms of

A Computational Model

of Color Perception

and Color Naming

by Johan Maurice Gisele Lammens

c Copyright by

Johan Maurice Gisele Lammens

1994

Voor mijn ouders.

This work was supported in part by Equipment Grant No EDUD-US-932022 from SUNMicrosystems Computer Corporation, and in part by NASA under contract NAS 9-19004,which is gratefully acknowledged

I would like to thank the members of my committee for their guidance, support, andvalued comments My advisor, Dr Stuart C Shapiro, has always given me plenty of leeway

to explore new concepts (and occasionally make a fool of myself), yet he has provideddirection and advice when necessary His experience, insight, and open-mindedness areadmirable Dr K Nicholas Leibovic introduced me to biophysics and the interdisciplinarystudy of vision, and has served as my personal model of what a true scientist should be.His attention and encouragement have been a great support Dr William J Rapaporthas certainly broadened my philosophical and general intellectual horizon, and has alwaysbeen helpful and supportive Dr Deborah K Walters, nally, has inspired me to searchfor meaningful computational models with roots in biology and neurophysiology, and hasoften provided excellent feedback My outside reader, Dr Christopher M Brown, has onmany occasions provided illuminating comments and feedback on color-related issues andbeyond I have always found it challenging, stimulating, and fun to carry on a conversationwith him, either in person or electronically

I would also like to thank the Computer Science department for continuing to support

me nancially and otherwise for almost six years, in my various guises as teaching, ratory, and research assistant Ellie Benzel, Sally Elder, Gloria Koontz, and all the othersecretaries deserve special mention as collective substitute-mothers for especially the for-eign graduate students They are truly the pillars upon which the department is built Myfellow graduate students in the SNePS research group and the department at large havebeen good colleagues, and in many instances great friends as well I have greatly enjoyedmeeting and working with people from all parts of the world Many thanks also to KenSmith, Devon Bowen, Davin Milun, Harry Delano, and the graduate \labbies" for providingtechnical support, allowing me to bumble in systems management, and being a great gang

labo-of people I will fondly remember my days as a labbie, and I am probably as proud labo-of

my super-user status as of my new title My only regret is that I cannot take my \sudoprivs" with me Harry has not only been the best possible boss but also a valued friend

Thanks to Joe Piazza also, for helping me out with color printing, and to Niloufer Mackey,for advice on matters of linear algebra, and for being a good friend One fellow graduatestudent deserves special mention: Henry Hexmoor, who has been my friend, house mate,and co-author of many a paper He not only introduced me to some southern cooking, but

Thanks also to my friends Kulbir Arora, Paula \Peej" Freedman, Terry Wilmarth, andthe occasional other members of our little Art Movie/dinner/general fun club It providedthe necessary entertainment and relaxation in times of need or despair Bualo is fortunate

to have the beautiful North Park theater that shows excellent movies, even subtitled foreignones (not to mention the cappuccino and chocolate chunk cookies)!

Many net.people have been very helpful in the course of my work I have often beensurprised by the kindness and helpfulness of people to whom I was just an unknown grad-uate student Long live the Internet! Many thanks, therefore, to Richard Aslin, JohnBradley, George Broadwell, Rene Collier, Reiner Eschbach, Brian Funt, Larry Hardin, Ste-van Harnad, Roland Hausser, Keith Karns, Paul Kay, Judith Klavans, Peter Lennie, HaimLevkowitz, John Limber, Richard Lively, Luisa Ma, Gerald Maguire, Walter Makous,David Mark, Ethan Montag, Carol Novak, Stephen Palmer, Steven Shafer, Kathy Straub,Kees Teunissen, Tom Wickham-Jones, David Zubin, and to those whose names I may haveomitted unintentionally

Many thanks also to my dear friends in Belgium and Holland and to my parents andfamily, for their support and encouragement, and for putting up with my long absence.And, last but certainly not least, my heartfelt thanks to my s.o Annalisa, without whosecontinuing love, support, encouragement, and patience I could not have nished the presentwork I will forever fondly remember that particular class in Knowledge Representationwhere we met!

JL

4.4.4 Computer graphics and computer vision color models : : : : : : : : 61

7.4 Semantics, Grounding, and Truth : : : : : : : : : : : : : : : : : : : : : : : : 151

8 An Application and Some Empirical Results 155

List of Figures

4.7 Relative spectral sensitivity of the three types of cones in the human retina 58

5.9 Linear tting of Y300 toY150 : : : : : : : : : : : : : : : : : : : : : : : : : : : 87

5.17 Some examples of the two kinds of spectra needed to generate Optimal Color

5.20 The Optimal Color Stimuli surface in the NPP color space, using the SL

5.21 The Optimal Color Stimuli surface in the NPP color space, using the SLN

5.26 Comparison of the shape of the Munsell color solid with the shape of the

5.30 Typical feed-forward network topology used with the error backpropagation

5.35 The gray axis in NPP space and as computed via the XYZ to NPP transform119

5.36 The OCS surface as computed via the 4-layer network XYZ to NPP transform120

6.3 The extent and focus for each of the eleven basic color categories of

6.6 The boundaries and foci of the Basic Color categories for (American) English 129

A.6 Overview of a complete setup using MRL : : : : : : : : : : : : : : : : : : : 210

List of Tables

5.2 Linear coecients and RMS error for linearly tting 300 spikes/sec functions

1.1 Background

anthropol-ogy, and philosophy has shown that in many cases, categories cannot be properly terized by a set of necessary and sucient conditions; i.e category membership is usuallynot an all-or-nothing phenomenon but rather a matter of degree, and people can judge the

charac-\typicality" and/or degree of membership of potential category members in a consistentway (see e.g [Wittgenstein 1953, Berlin & Kay 1969, Rosch 1978, Lako 1987]) Thisapplies not only to so-called natural categories, which correspond roughly to nouns in nat-ural languages, but also to many categories used in science, e.g biology [Lako 1987].Perhaps the only exceptions are mathematical categories which are explicitly de ned bynecessary and sucient conditions However, even the latter might be seen as abstractions

of real-world categories that would not necessarily be de nable in the same way, or as beingconstructed on the basis of such abstractions, cf [Aleksandrov 1956] Some of the ideasabout graded category membership have been formalized as fuzzy set theory [Zadeh 1971],which has found applications in various areas of control theory and AI, for instance [Kosko1992]

The concepts of embodiment [Lako 1987], symbol grounding [Harnad 1990], and situated

1 Mostly, categorization with respect to \natural categories", as in an ontology of what is \out there".

cognition[Suchman 1988] are related to issues in categorization Embodiment is the notion

categories, in a referential type semantics) is in part determined by the physiology of the

universality of basic color category foci can be explained in terms of the underlying physiological mechanism of color perception, which are the same for all people, regardless

neuro-of language [Berlin & Kay 1969]

catego-rization and perception of the environment the organism operates in Harnad's fundamentalclaim is that the symbols of \traditional" symbolic AI systems are only meaningful to a hu-

the fact that the symbols are systematically interpretable and have a meaning assigned tothem via an external semantic mapping or model Such a semantic model is an explanatorydevice, but it does not play any role in the system's internal functioning In contrast, Har-nad claims that symbols representing categories to people (like nouns in natural languages)are meaningful because they are connected to the world in a causal and non-arbitrary way,

are not.6

I essentially agree with Harnad's analysis Since categories are an essential part of ral language semantics, the analysis implies that models of natural language semantics musttake physiology and perception, or in general, the nature of the cognitive mechanism under-lying categorization, into account This in turn implies that a traditional model-theoreticapproach to natural language semantics is inadequate Model theory, as used in logic ormodern linguistics, starts with the assumption of a (real or possible) domain consisting of

natu-2 I am using the term extension here in the traditional model-theoretic sense of the set of objects in the model's domain that corresponds to a constant symbol Although part of the argument developed in this dissertation goes against traditional model theory, I will continue to use the term in this way, for convenience.

3 In particular, the physiology of perception, but perhaps also the physiology of motor control and even the physiology of emotion; cf [Lako 1987].

4 This is essentially the point that Searle tried to prove in his famous Chinese Room argument [Searle 1980]

5 This is true for directly grounded symbols corresponding to categories of perception only The hypothesis

is that other symbols are indirectly grounded by being constructed out of directly grounded ones Harnad is not very speci c on this point.

6 The intersection of the set of people using the term\symbol grounding" with the set of people using the term \embodiment" seems to be empty, but I will not let that disturb me.

discreteindividuals, properties, and relations, corresponding via a static semantic mappingwith constant and relation symbols in the language of interest These models have nothing

to say about how such a relation might be established or maintained in the rst place In

semantics to be part of the domain of the general study of intelligence, we may contrastthe symbol grounding or embodiment view with the \traditional" symbolic AI view thatintelligence (or \mental functions") can be studied in the abstract, without reference to theorganism displaying it, or the mechanism implementing it (e.g [Newell 1979])

process that happens to go on in real-world settings, but a real-world activity in which

we make use of language to delineate the collective relevance of a shared environment"[Suchman 1988, p 180] Again, the environment or the \real world" is seen as the groundingfor language, which implicitly requires perception to be taken into account

One particular area of natural language semantics where embodiment, grounding, andsituatedness seem to play an important role is that of color terms In their anthropologicaland linguistic work in the late sixties, Berlin and Kay [Berlin & Kay 1969] were lookingfor semantic universals in the domain of color terms, hoping to refute the Sapir-Whorfhypothesis which claims that there are no semantic universals, and that each languageperforms the coding of experience into language in a unique and arbitrary manner Thelatter is of course in direct opposition to theories of embodied semantics, since these dopredict the existence of universals, based on the observation that all people share a commonphysiology, regardless of the language they speak or the culture they live in Berlin and Kayfound that there are indeed semantic universals in the domain of color, particularly in the

widely diering languages to identify (1) the best examples and (2) the boundaries of basiccolor categories on a chart of color samples, they found that (1) the best examples (foci)

of basic color categories are the same within small tolerances for speakers of any languagethat has (the equivalent of) the basic color term in question, and (2) there is a hierarchy oflanguages with respect to how many and which basic color terms they possess, such that,

7 According to Webster's online dictionary, \a branch of semiotics dealing with the relations between signs and what they refer to and including theories of denotation, extension, naming, and truth".

8 In English, there are eleven basic color terms: white, black, red, green, yellow, blue, brown, purple, pink, orange, grey.

roughly speaking, a language that hasi+1 basic color terms has all the basic color terms of

same ones (with respect to their extensions) It is of course apparent from these results that(basic) color categories are characterized by graded membership functions, with some colorsclearly being non-members, some being prime examples, some being borderline examples,and with other degrees of membership in between

[Kay & McDaniel 1978] have made the ... Outline of the Model< /h3>

I will dene a computational model of human color perception and color naming, i.e

data about the neurophysiology and psychophysics of color perception, and. .. dene a computational model of color perception andcolor naming, i.e a semantic model of (basic) color terms grounded in color perception, that is partly based on neurophysiological data and that... existence proof of the following kind: It ispossible to dene an adequate model of the semantics of natural language color terms, and

an adequate model of color naming and color pointing