CA1129552A - Method for producing color representations of quantifiable data by maximizing differential perception of colors - Google Patents
Method for producing color representations of quantifiable data by maximizing differential perception of colorsInfo
- Publication number
- CA1129552A CA1129552A CA307,941A CA307941A CA1129552A CA 1129552 A CA1129552 A CA 1129552A CA 307941 A CA307941 A CA 307941A CA 1129552 A CA1129552 A CA 1129552A
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- Canada
- Prior art keywords
- color
- equivalent
- hue
- colors
- longitudenal
- Prior art date
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Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
- G01D15/00—Component parts of recorders for measuring arrangements not specially adapted for a specific variable
- G01D15/14—Optical recording elements; Recording elements using X-or nuclear radiation
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
- G01D7/00—Indicating measured values
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10S347/00—Incremental printing of symbolic information
- Y10S347/90—Data processing for electrostatic recording
Abstract
METHOD FOR PRODUCING COLOR REPRESENTATIONS OF QUANTIFIABLE
DATA BY MAXIMIZING DIFFERENTIAL PERCEPTION OF COLORS
ABSTRACT OF THE DISCLOSURE
A method is described wherein quantifiable data which have arbitrary dynamic ranges and which vary as a function of other para-meters are represented in color. A set of subranges, without re-striction in number, representing data properties are associated with a color set in such a way that the colors are perceived to be maxi-mally differentiable by interpreters, whether human, electronic, or other, by specifically incorporating information concerning the normal or anomalous characteristics of the interpreter's color perception when determing the color set. The method further provides for the realization of color displays by directly associating the colors with densities, transmittances, or illumination levels for negatives, posi-tives, or colored light emitting devices, whether the realization re-quires primary additive or primary subtractive hues.
DATA BY MAXIMIZING DIFFERENTIAL PERCEPTION OF COLORS
ABSTRACT OF THE DISCLOSURE
A method is described wherein quantifiable data which have arbitrary dynamic ranges and which vary as a function of other para-meters are represented in color. A set of subranges, without re-striction in number, representing data properties are associated with a color set in such a way that the colors are perceived to be maxi-mally differentiable by interpreters, whether human, electronic, or other, by specifically incorporating information concerning the normal or anomalous characteristics of the interpreter's color perception when determing the color set. The method further provides for the realization of color displays by directly associating the colors with densities, transmittances, or illumination levels for negatives, posi-tives, or colored light emitting devices, whether the realization re-quires primary additive or primary subtractive hues.
Description
n~CKGROUND OF T~IE INVENTION
~ 1. Field of the Invention The present invention relates generally to the color display of time; series or space series information which may be discretely sam-~led or continuous .in nature, in one or more dirnensions, or in com-bination. Mor~ particlularly, the present invention relates to a `
method of produclnq color displays of information wherein maximum clifferential perception by the interpreter oF the dlsplay is assured.
~ 1. Field of the Invention The present invention relates generally to the color display of time; series or space series information which may be discretely sam-~led or continuous .in nature, in one or more dirnensions, or in com-bination. Mor~ particlularly, the present invention relates to a `
method of produclnq color displays of information wherein maximum clifferential perception by the interpreter oF the dlsplay is assured.
2. Descriptlon of the Prior Art Pa.tents have been gran~ed to methods which convert ti~rne or space series inEon~lation whether called signals, waveforms, functions, graplls~
or ~ictures into color outputs, the colors of which were assigned on tlle basis oE sorre property of the series in question. One such patent, U.S. Patent Mo. 3,961,306, teaches a method wherein the information i.s .scalecl into .increm~ntal rancJes ancl eaCII ranCJe iS assigned a color cor-re~s[)ondincl to a sall)})le value. LL'hc colors are assigned frcm a tablc that i.s constructed be~orehand and which contaills inEorn~ation relatinq to the denslt.ies oE the various component displays required to ma]ce the as~s;.~JlIecl colors. l'hc tal)le is constructe~1 hy arb.i.trarily pickirlq co:l.ors.
~ shortcomi.llc3 o:E the ~rior art is that tlle colors MUst be chosen ' `' ', ~
. . ~:
C) ~ e}lalld arlalySed arld ~ OlT;pOn~.`ll l dellSi ti.eS Cl~OSell i.rl C) rder 1:O
;rcate an ~,.ss:iclnmel~t table. Tlli.c~ task beconlcs arcluous ~or a larclc nur!lber of rallCTeS.
~ nother shortcomin~ of -the prior art is that tllere is no -teach-~ q in any o:E thc-~ prior. art pa-tents of a method that assures ma~imal dif.Eerentlal perceptioll of the colors assi.~ned to the output. For e4.ample, the usual system for assi~nincJ colors is spectrally; where, for e~ample, lar~e samE)le values ~re assicJned colors near the violet elld and small samplc values are assi~ne(l colors neclr th(.' recl end, wlth intermediate values assiglled in betweell. Tl~hen a large nul~er of sample ~alues are displa~ed, the differences bet~7een colors assic3ned to closely ~spaced values becor~e c~uite suht].e and difficult, i not impossible, -to cliscriminate.
~ further shortcoming of tlle prior art is that there is no teach-ing of a method that takes into account color vi.sual deficiencies among observers. There are color visual anomalies wherein the ability of an .individual to perceive certain hues is either di~inished or non-existellt. In Methods based on arhitrary assignments of colors, cer-tain huès that are clearly d.is-tinquished by normaIly sighted in(lividuals are comple-tely indistinquishable to those with a color vision defi-clency. Such inclistinquishability introduces ambiguity into the color clisplay.
: ~ :
SUr~;~Ll\RY OF '1'111~ INVEMTION
- . ~ :
It is therefore an object of the present invention to provide a :~
method for Ma~ln~ color dlsplays that assues maximal differential perception of -the colors assigned :to the output. It is a further object of the present invention to provide a method that provides for ma~inal diffcren-tial perception in the casc~of human visual or elec-tro-mechanical sensitometrîc irregularities or de~iciencies. It lS a sti].l :further object of the:presellt invention to provide a method for flcxlhly ancl cllrect.].y detQrmilling the.mQxi.mally different colors in terms of pr:imary acl~:l:itive or primary suhtrackive hucs withouk the need c)f ~irst p].eassiglli.n~.l values of clensity, transmittance, or illumination lcvcl to numel^ic codes -throu~l-l the use of -tahles or matrices.
Brlefly statecl, the fore~oln~ and other objectives:are accomplished in the preserlt inven-tion by assicJning each measure of the information -2~
55;.~ ~
1~ c~splayed to a point i~ )lor ipclct sucl- that thc clistriblltion .ellsity o~ c~.ucll poillls is suhstalltially equal in cert~in s~ec1fied ways.
color c1isl1ay clyllc~mic rancJta is clefinec1, which comprises an arbitrary nun~er of subratlcJes wherein each subrange is associated wi-th a dis-tinct co]or. I.ach measure of the inforMation to be displayecl is asso-ciated with a subrancJe ancl hy means of a color contr~st parameter eacll subranclt is associated with a point in a color space such that thc distribu.ioll density of such points is su]~stantially equal.
rlle present invention ~urther provides a metllocl ~llertlby ~he spher-ical coordinates of each ~oint in the color sF)ace may be trans~ormed into Cartesian coordinates which may be directly convertt-cl into den-sitie~s transmittances or illumination levels, o~ primary hues neces-sary to-proc7uce the clisplay. The present invention also provides a ~ethod by ~hich color visual deficiencies of the interpreter may be compensated Eor.
13RIEF DES(~RIPTION OF TIIE: DRI\WI~GS
Fig. l-is a schematic aisplay of the basic construction of a color sphere used to define colors.
Fig. 2 is a schematic di9play .showing the construetion of a coordinatt? sys tem ~hich loea~tes colors determined in the method.
Fic3. 3 is a schematic drawing that shows the construction of an elemcnt of zonal area on the color sphere surfaee which is used to de-;
termine the distribution oE maximally di~ferentiable colors.
Fig. 4 is a schematic drawing illus~tra-ting a spiral path on the color sphere surface along whicli maximally differentiablt? colors are located. ~ - ~
Fig. S is a sche~atic clrawing that describes the concept of uncer-tainty in the value o~ equivalent hue.
Fig. h~ is a schema-tic drawing that shows a relationship between perceivt?d hue (1' and equivaIent hue ~ referenced to the color ~s~ ere.
.
Iig. 6n sll~ws a c~raL~hlcal relationsllip hetwee~ ~' ancl ~ .
Fig. 6C is a schematic showincJ the color sr?iral of ~ig. 4 Inodified to account ol^ a ;pec:Lfic dif~erellct betwec?n yercc!ived huc and eqillva-Lcnt IlUe .
Fig. 7 is a schematic that shows the Cartesian coordinate system X, Y, Z, in which the location of any point r, e, 0 may`~
be expressed.
Fig. 8-is a schematic that depicts the transfoxmed Cartesian system X~, ~', Z', which measures directly densities or trans-mittances for component masks for color reproduction, or the illuminat~on level of colored light emitting devices. ~ `~
Fig. 9 is a flow chart representation of a method of practicing the present invention.
Eig. 10 ~s a schematic of the separation negative (photo-graphic) embodiment of the present invention.
Fig. 11 is a schematic showing the separation positive (projection or photographic~ embodiment of the present invention.
Fig. 12 ~s a schematic showing the modulated light intensity 15 embodiment of the present invention. ~;
DESCRIPTION OF THE PRE~ED EMBODIMENT
- . : .
A measurement of a pfiysical quantity, here defined to include a purely ;
mathematical quantity or number and hereafter called the dependent quantity, whether it be a nu~m~er, a length, a mass, a time, an electric current, a temperature, a unit of lumuDous intensity,~a plane angle, a solid angle, or a quantity derived from any ccmbunation of the above or equivalent to the ;;~ same or any combination of the same (e.g. a voltage, or potential or electromotive force, is equivalent to a number of volts whether specified in~
units of abvolts or statvolts, etc. and a volt is the ccmbination kllogram 2~5 multiplied ~y meter ~red divided~by seconds cubed divided by ampere~
where a kilogram is a mass, a meter is a length, a second is a time, and an ampere is an electric c~rren~), which is itself a function of a physical~
quantity of quantities as defined, hereinafter called the independent ~ -quantity of quantities, is to ke converted into a color rQresentation of a 3Q measure of the quantity where the~measure is expressible as any numeric re-' : , .
sult after the application of any mathRmatical operation or sequence of - ~
: . :
~ -4- ~ ~
~ '' '.'` ' 1129~,52 operations to the measurement, e.g. multiplying the measurement by one, or taking 2Q times the logarithm to the base ten of the measurement. The total of all such measurements, whether they be continuous or discretely sampled will, for practical purposes, have a finite domain range of independent quan-tity or quantities. ~ithin this domain range, the maximum and minimum values of the measure of the dependent quantity define the dynamic range of the mea-sure. This dynamic range may be divided into an arbitrary unlimited number of equal or unequal subranges thereby fixing the extent of each subrange, or the extent of each su~range may be arbitrarily fixed thereby fixing the numker of subranges. The dynamic range displayed in color need not be exactly the same as the total dynamic range of the measure, but may exceed, equal, or be less than the latter quantity. Thus a specification of subrange size and number can and will determine the color display dynamic range without regard to the dynamic range of the measure.
The method concerns the assignment of max~mally diffe~nt-iable colors to the su~ranges of the color display. Measurement data for the depend- -ent quantity are converted to the measure of the quantity for each of those independent quantities or æts of independent quantities falling within the finite range extent of the color display to be produced. Each measure so found will lie within a subrange, known as an interior subrange, as defined, if the color display dynamic range is set to be equal to or greater than on either or both top and bottom of the dynamic range of the measure; if the ~;color display dynamic range is set to be less than, on either or both top and bottom of, the dynamic range of the measure, then some measures of the quantity will fall outside the available subranges. In this last case such measures may be assigned to the closest subrange, in which case such subrange will be known as an exterior subrange. The method imposes no impedlment upon the numker of subranges which may be utilized and their n~nber may e~ceed the storage capacity of any ccmputer or tabular array.
For each su~range so defined, a unique and differentiable color .
is assigned according to the following method.
'',`~' ~
,;
1~2955~
In order to describe color adequately, construct a color space, which in the preferred embodiment is sphere 1 of Fig. 1, wherein the central point 2 of sphere 1 represents neutral gray, equidistant from opposite poles representing pure white 3 and pure black 4. The axis of sphere 1 joining poles 3 and 4 and passing through neutral gray point 2 is the gray axis 5. The .
equatorial great circle 6 is formed by the intersection of the outer surface of sphere 1 with the plane 19 normal to gray axis 5 and passing through gray point 2. The three primary additive hues, red 7, green 8, and blue 9, are located on and ,~
r~
-5a~ ;
divide equatorial circle 6 into cclual segments defin.ing direetions n the ~quatorial plane~.l9 whlch are 120 apart. The three primary subtractive hues, which are complementary to the`~above:aclditive hues,, '.
are'respectively, cyan 10, magenta ll,~:and yellow'l2, and lie diame- ~`
trically opposite to their`complements on the~'equatorial circle 6. ~.
Thus an.y arbitrary visible color 13 can be represented.~as a position within or on-the sphere;and this~'position can be~descrlbed conveniently by spherical polar coordinates r, e and ~
'L`he ecluival.en-t saturation of the color, o:r purity, or relative depar~ure from neutra:l cJray, is measule~l by the raclial distance, r, Erorn center 2 of sphere 1. ~11 point.s alollcr the line seclment from central point 2 -to arbitrary color 13 or it:, extension to the sp,herical surface if arkitrarY color 13 cloes not lic on'the surface of s~here 1, continuously represellt varying propol-tions of neutral gray frorn totally neutral c~rav at ccllter 2 of sphere 1 to con;plete ahsence of neutra]. c~ray at the surEace of sphere l.
Ficr. 2 de~pict.s the determi.nation of the r~mainillg coordina-tes and ~ . The plane 15 passing throucJh and defined hy point 13 and 3ray a~is 5 COntaillS tlle line segment passing from central poi~t 2.
to color l3. l'his line SeCJment ma]ces' an ang].e, e , with respect to cJray ~is 5 measured from the direction of a reference pole, which for E)Urposes of exanll~le is taken to be black pole 4, ancl this lati~udenal angle is a continuous measure of the eqllivalent color value, or bright-ness, or-proximity -to WllitelleSS, of color 13.
Finally, a reference hue 17 is chosen which, dependi.ng upon whe-ther an additive or subtractive realization of -the method is desired, ~
.correspond to either one of -the additive primary hues or one of the sub-tractive primary hues. The~referellce hue plane 18 is the plane r)ass:ing through and cle~ined hy reference hue 17 and gra~; axis 5, and p:Lalle 18 intersects equatoria:L plane 19 along -the line 20. In a similar way, plane of cqll.Lvalent IIUC :L5, passincl through color 13, intersects c~qllaLorlal pl.alle 19 along the line 21. The ancJle ~! in equatorial plane 19, mcasur~d ~rom reEerence li.ne 20, is a conti.nuous measure o:E the C~ ;Va1ent 11~1C!, or clistlncti.ve essonce, or cJeneric class,i~icatiorl, of cok.~r 13.
The r.,etllocl seekt, to maximize the differentia]. perception of colors .
sc~ 1c(l lc~ the ~;ub.~ J1ges ~>~ c~ co].or. di.sl).1..ly. C:ons.ider Lhc ca~c in all of the cOlors of c:olo1. ;L~here :l are unarl~bicluous.l.y anc1 clis-tinctl~ ercc~ivcll~le b~r eitlleL hl~ma]l, electrc3ll!echanical, or other men-surat:i.ve me~ s. Let the radius oi. the color sphere be rS as in E`ig. 3 Thel1 ma~imally di.~ierentiable colors lie on -the surface of sphere l, sil1ce these are Lal-tl1est removed irom cJray a.~is S. ~ll colors or sub-rancres will-therefore be speci.fied by r=rS.
In acldi:~io11, -to bt? ma~imally difi-'t~rentiable, the c1esired colors wllicl1 are representecl as ~oints on this spherical s~1rEace will be dis-tributed -thereon in a manner such that the density of poin-ts be as equal as possible over the surface. To acccn~plish equa.lity oi. distribution, construct a c1ifierential zonal band 22 about sphe.re l centered a-t the latitudenal. color value angle ~ and of di.fferential ancJular wid-tl1clt~ .
The d'ifferential width of zonal hand 22 at the spherical surface will be clw ~here dw=r5~ , and the radius of t:he planar circle so .~ormecl will be rz.
Tric~onoll1etric considerati.ons show that rz - rs sin ~ and that the differenti~l ar~a oE zonal band 22 must be ~Trl ~ lrl~ .jj"~?~ . Since rs i; cons-tant for s~hele l, ecluality oE distribution recluires that the nunlber of colors lyinJ in each differential zonal band must he pro-portional to sin(~ . One embocli~ent of such a distrihution will now Ije set forth.
~ssun~e that N su~ranyes corresponding to ~i colors are desired~ -Le-t each subrancle he designated hy a subrange definer, a, that takes on in-tegral values from O to A,'where A--N-l. Eacll of the N subranye c1eEiner6 wi.ll he associatecl with a distinct color.
In orcler to deterinine the color value anc~lle ~ for each subrancJe, 'we observe from the i'oregolng trigonometric consideration-i that t~, where k i.s a constant to be determincd. Inteyrating this e~pressiol1,.c)bserving that ~ c A and ~ C11 ~e find that:
¦ t ~t~ s"~ tl~ c-~ c~r ~
'I`hus, :i.n clcl1c~r~.1.1., t.he~colc)r val~le anc3le ~' associ.ated with c!lc~ ;ub-c? . ~l~ E i. ll c~ J-, ~, w i ~ c);.vel1 by:
I s.~ e ~ s ~ ~
whi.cl1 ma~ hç rewrittel1(?-c~ c~
In orclc-.r to detcrl~ 1e the h~le anc3lt? ~'or each suLral1c!e, a spiral 28, --7-- .
1 1 2955~
.
as shown on Fig. 4, may now be constructed in a manner which satisfies the maximal differentiability requirement via equality of zonal distribution. The longitudenal hue angle will be reIated to t~e latitudenal color value angle, ë, by the equation ~-2cO, where c is the color contrast para-meter and is equal to the number of cycles in spiral 28 as it winds from 9=~ to a=~ . Color contrast parameter c controls and is a direct measure of color contrast between adjacent color coordinate pairs(~ , ~ ) associated with the definers, lQ a. These maximally differentiable colors are indicated schematically be crosses 29 on spiral 28. It will be seen that adjacent or nearly adjacent subranges differ substantially in equivalent hue, while widely different subranges differ substantially in equivalent value. Thus the color differences associated with different subran~es are clearly discernible for small as well as large differences in the value of sub- -range definAer.;~
The method is now extended to the case where a human, photoelectric, or other type of interpreter cannot perceive all of the equivalent hues of the color sphere with equal ability. In humans, those manifestin~ slightly imbalanced hue perceptive ability are known as protanomalous, deuter-anomalous, or tritanomalous observers, while those mani- -festing total inability to perceive certain hues are known as ~ -as protanopes, deuteranopes, or tritanopes. Additionally, those who can perceive no hues, but only shades of gray, are known as rod monochromats. For photoelectric or other non~
human types of interpreting devices, the detection mechanism may have an output response which varies significantly de- ~
pending upon the hue available to the input sensor. ~ ;
The extension of the method to these cases involves a coordinate transformation from ~' to ~, where ~', the ,~
-``` 1123552 perceived hue, will now be defined 0'= 2c~ and ~' will be converted into a color sphere coordinate, ~, in the following way. For every equivalent hu~, defined by an angle 01t on the color sphere as shown in Fig. 5, assign a perception wéighting value! W(0~), indicative of the relative ability of the human or electronic interpreter to perceive that equivalent hue.
For example, the perception weighting function may simply be the inverse uncertainty of the hue angle: if all the equivalent hues lying about 0H with the range ~0~ are indistinquis~able to the interpreter, then an uncertainty of ~0~,with respect to ~
~ is said to exist for the interpreter; the perception ~-weighting function would be defined then as W(~H ) = ~ ~ H
As another example, the perception weighting function W(~
may simply by the value of the measured response R(~) at the ~ ~-output of a measuring device when an input of standardized intensity of the given equivalent hue~ ~ is provided. As a third example, if the interpreter cannot perceive hues be-tween~ =o and~ = 3 , but perceives equally well all hues between~ = ~ and~= ~ ~ , then W~ ~) for ~ ~u~
W(4~)=~ for ~ < ~ < ~
In all of these examples, the transformation between ~ ~-~` and ~ is sp~ecified by:
For a given ~` , the value of ~ is ascertained as that for which ~ ~5~d~ ~ a~ 5 ~ H
Thus for the third example above, as the perceived hue, in Fig. 6A, spans the angles from ~ = to ~ = ~ , this is -~
equivalent to~ spanning the equivalent hues from~ = ~ to ;~
~ =~. Fig. 6B shows the graphical relationship between~
and ~ . As ~ = ~c~ a~ccoS (I ~3 changes as a function of the subrange definer, a, the corresponding equivalent hue _ g _ ~ ~29552 angle, ~ , takes on all ~alues except those in the range 0<~< ~. The spiral 28 of Fig. 4 would thus be modi~ied to correspond to the transformed spiral 37 of Fig. 6C.
Dlfferential perception of the colors assigned to subranges will be enhanced by transEormation of the coordinate system of the color sphere through the use of a general weighting function derived from the perception characteristics of the interpreter. The use of confusing or ill-defined colors is minimized.
lQ The method includes provision for translating the the colors defined by positions of the color sphere into vari-able density ~or transmittance~ negatives or positives for color compositing by conventional photochemical, mechanical, or ~ `~
other means, or into varying illumination levels of colored light-emitting devices. Each color previously defined by the -~
above methods ~ill be representable by the color location co~
ordinates r, ~ and ~ which are reproduced in Fig. 7. ~
Define Cartesian axes x, y and z as shown. The co- ~ -ordinates in this system will be given as a function of those `-in the previous system by ~ =rSi~ e cos~-rSX;y~5~hes~ syj : - -~~ r ~S e ~ ~5 ~ , The origin 2 of this system is ofcourse unchanged.
Now to effect direct measurement of density, (or --transmittance or illumination level), apply the following set of transformations. First normalize the above coordinates by ~- `
dividing by rs, the radius of the sphere. Then%^ ~ 'Y r5 ;
, and~~ rS must lie between ~1 and -1. Next displace the~ ;
origin by~ 1 unit in Z as indicated 41 in Fig. 8, and by -~
scaling, (optionally) reflecting, and rotating axes define a ~ ~`
new orthonormal coordinate system with axes x', y' and z' which form the basis triad for an inscribed cube 45 of color sphere 1. The major diagonal 46 of inscribed cube 45 is co---lo--1129~52 incident with gray axis 5 The example of a scaled, reflected,and rotated axl~ system shown in Fig. 8 is obtained by the transformation X ~ ( ~ ) X t (~ ) ;
~ F)X (~) y ~ (~
Additionally, if indlvidually x', y' or z' lie outside the range from O to+ 1, then they are set equal to the closest end point of this ran~e. The values of x', y' and z' correspond to the variable densities (or transmittances or illumination levels) of the negatives (or positives) of each primary sub~
tractive (or additive~ hue, with O corresponding to minimum density (or transmittance or illumination level) and tl corresponding to maximum density (or transmittance or illumi~
nation level~. -i .:
Thus the color of a subrange, for example, specified ~-. .
by the color sphere values rs, ~ and ~ , is transformed to the ~
equivalent values x, y, and z and finally to the values x', y' ~ "
and z'. These latter values are translated directly on a one-2Q to-one basis but not necessarily with linear proportionality, -~
into density (or transmittivity or illuminance level) values to be used with photographic, electronic, or other reproduction schemes to produce a composite, full-or partially-colored , .:, display. The colors thus produced are associated with the values of the corresponding subranges by means of an appro-. . ,.:.~
priate translation scale.
Referring now to Fig. 9, a plan for instructing a digital computer to perform the preferred embodiment of the - . .. .
invention is set out. At Step 100, prior to actual processing ,;
of the data, a measure of the data is constructed. In the case of a digital computer, the measure is constructed by sampling the data at incremental points in the domain of -... .. , , ~ , ... . . . .
~129552 the independent variable-. It will of course be recognized by those skilled in the art that the data could be processed in continuous fashion ~y suitably constructed analog computer.
Prior to processing, the color display dynamic range is defined, and that range is put into the computer, at Step 101. A measure of the data is put into the computer and, at Step 102, is associated with a subrange definer corresponding to a particular subrange of the color display dynamic range.
At Step lQ3, an equivalent value angle of the assigned sub-lo range is determined according to the method of the present invention. At Step 104, the equivalent hue angle of the as-signed subrange is determined with respect to a preselected color contrast parameter 105 and a perception weighting function 106 determined from the color perception data for ; ;~
the interpreter 107. It will be recalled that the color ;~
contrast parameter controls and is a direct measure o~ the hue contrast between adjacent color coordinate pairs. The perception weighting function, input at Step 106, is de- -termined from the color perception data for the interpreter, 2Q input at Step 107, and allows interpreters having color per- ;
: "
ceptual deficiencies to distinquish equally wèll all colors as-signed to the various subranges. In the case of normally ` -sighted interpreters, the perception weighting function is equal for all longitudenal equivalent hue angles.
The equivalent value angle and equivalent hue angle : ,:
determined for the subrange are converted to a set of equi-valent Cartesian coordinates at Step 108. The equivalent ~;
Cartesian coordinates are defined with respect to a reference axis, which is specified by input 109. Input 109 is specified according to whether an additive or subtractive realization of the display is desired. The equivalent Cartesian co-ordinates obtained at Step 108 are converted to a second ~12-'~;,. . .: - .
- - 11295~2 Cartesian coordinate representation at Step 110, wherein the axes of the first equ~valent Cartesian coordinates are normalized, translated, optionally reflected, scaled and rotated, such that the origin of the second Cartesian co-ordinate system is located at the reference pole of the color sphere and the reference hue is preserved. Then at Step 111, the coordinates of the assigned subrange are determined in the second Cartesian system formed in Step 110. After specifying at Step 112 whether a negative or positive realization is lQ desired, the coordinates generated in Step 111 are interpreted ;
directly in one-to-one fashion as primary~hue densities or in-tensities as Step 113, which are output as yellow/blue 114, -magenta/green 115, and cyan/red 116.
Each measure of the data is sequentially processed in the manner set forth in Fig. 9 throughout the entire domain of the independent variable and the primary components cor-responding to the entire domain are contained in outputs 114, 115 and 116. The primary color outputs may then be processed - in any of several conventional photographlc methods to form a -~
2Q final display.
One method for forming the final color display is set forth in Fig. 10, which presents a subtractive, separation ;
. .
negative (photographic~ embodiment of the present invention. ~'~
The primary subtractive hues obtained from the method as set forth in Fig. 9, wherein a subtractive primary hue is specified at Step 109 and a negative realization is specified at Step 112, are processed as follows.
The primary color outputs 114,115 and 116, in Fig. 9 become primary color inputs 117, 118 and 119 in Fig. 10.
3Q Yellow input 117 is processed to plot a negative for yellow at Step 12Q, which-in turn is exposed with blue light at Step 121. In similar fashion magenta input is processed to plot a 1 ~ 29552 negative for magenta at Step 122, which is exposed to green light at Step 123. Finally, cyan input 119 is processed to plot a negative for cyan at Step 124, which is exposed with red light at Step 125. The component exposures obtained in Steps 121, 123 and 125 were registered to form composite color realization 126.
Figs. 11 and 12 illustrate methods of producing an ~ `~
additive, positive realization of the color display formed by the method of the present invention. Primary, additive out~
lQ puts are produced according to the method as set forth in Fig.
9 by specifying an additive reference hue at Step 109 and a . ~
positive realization at Step 112. Blue input 127, corresponds to ~lue output 114, green input 128 corresponds to green out-put 115, and red input 129 corresponds to red output 116.
Blue input 127 is processed at Step 130 to form mask 131, green input 128 is processed at Step 132 to form mask 133, and ,~, - :, red input 12~ is processed at Step 134 to form mask 135. Mask ~ ~
. . . . .
131 is illuminated by a constant intensity light source 136, the light from which passes through a blue filter 137. Mask ;
2Q 133 is illuminated by a constant intensity light source 138, -the light from wAich passes through a green filter 139. ~
Mask 135 is illuminated by a constant intensity light source ~;
140, the light from which passes through red filter 141.
The light passing through masks 131, 133~and 135 is aligned and focused by alignment and focusing means 142, which includes a combination of mirrors and lenses, upon an imaging device v 143 to form a composite display. Imaging device 143 may be a projection screen or a photographic material.
Fig. 12 illustrates an alternative method of producing ..
3Q a final composite color display from blue input 160, green input 161 and red input 162. Blue input 162 operates a modulated light source 144 to produce variable intensity ,~
:
white light. Similarly,~green input 161 and red input 162 operate modulated light sources 145 and 146, respectively.
The light from modulated light source 144 passes through blue filter 147, the light from modulat~d light source 145 passes through green filter 148, and the light from modulated light source 146 passes through red filter 149 and the colored light from those sources is aligned and focused on imaging device 150 by means of alignment and focusing device 151 to ~ ;
form the final color display.
lQ Further modifications and alternative embodiments , of the method of this invention will be apparent to those skilled in the art in view of this description. Accordingly, ~-this description is to be construed as illustrative only and is for the purpose of teaching those skilled in the art the manner of carrying out the invention. For example, equivalent steps may be su~stituted for those illustrated and described herein and other conventional methods of producing color realizations may be substituted for those set forth, all as would be ap-parent to one skilled in the art after having the benefit of this description o~ the invention.
'''~' ',''', ~ ::
~.
or ~ictures into color outputs, the colors of which were assigned on tlle basis oE sorre property of the series in question. One such patent, U.S. Patent Mo. 3,961,306, teaches a method wherein the information i.s .scalecl into .increm~ntal rancJes ancl eaCII ranCJe iS assigned a color cor-re~s[)ondincl to a sall)})le value. LL'hc colors are assigned frcm a tablc that i.s constructed be~orehand and which contaills inEorn~ation relatinq to the denslt.ies oE the various component displays required to ma]ce the as~s;.~JlIecl colors. l'hc tal)le is constructe~1 hy arb.i.trarily pickirlq co:l.ors.
~ shortcomi.llc3 o:E the ~rior art is that tlle colors MUst be chosen ' `' ', ~
. . ~:
C) ~ e}lalld arlalySed arld ~ OlT;pOn~.`ll l dellSi ti.eS Cl~OSell i.rl C) rder 1:O
;rcate an ~,.ss:iclnmel~t table. Tlli.c~ task beconlcs arcluous ~or a larclc nur!lber of rallCTeS.
~ nother shortcomin~ of -the prior art is that tllere is no -teach-~ q in any o:E thc-~ prior. art pa-tents of a method that assures ma~imal dif.Eerentlal perceptioll of the colors assi.~ned to the output. For e4.ample, the usual system for assi~nincJ colors is spectrally; where, for e~ample, lar~e samE)le values ~re assicJned colors near the violet elld and small samplc values are assi~ne(l colors neclr th(.' recl end, wlth intermediate values assiglled in betweell. Tl~hen a large nul~er of sample ~alues are displa~ed, the differences bet~7een colors assic3ned to closely ~spaced values becor~e c~uite suht].e and difficult, i not impossible, -to cliscriminate.
~ further shortcoming of tlle prior art is that there is no teach-ing of a method that takes into account color vi.sual deficiencies among observers. There are color visual anomalies wherein the ability of an .individual to perceive certain hues is either di~inished or non-existellt. In Methods based on arhitrary assignments of colors, cer-tain huès that are clearly d.is-tinquished by normaIly sighted in(lividuals are comple-tely indistinquishable to those with a color vision defi-clency. Such inclistinquishability introduces ambiguity into the color clisplay.
: ~ :
SUr~;~Ll\RY OF '1'111~ INVEMTION
- . ~ :
It is therefore an object of the present invention to provide a :~
method for Ma~ln~ color dlsplays that assues maximal differential perception of -the colors assigned :to the output. It is a further object of the present invention to provide a method that provides for ma~inal diffcren-tial perception in the casc~of human visual or elec-tro-mechanical sensitometrîc irregularities or de~iciencies. It lS a sti].l :further object of the:presellt invention to provide a method for flcxlhly ancl cllrect.].y detQrmilling the.mQxi.mally different colors in terms of pr:imary acl~:l:itive or primary suhtrackive hucs withouk the need c)f ~irst p].eassiglli.n~.l values of clensity, transmittance, or illumination lcvcl to numel^ic codes -throu~l-l the use of -tahles or matrices.
Brlefly statecl, the fore~oln~ and other objectives:are accomplished in the preserlt inven-tion by assicJning each measure of the information -2~
55;.~ ~
1~ c~splayed to a point i~ )lor ipclct sucl- that thc clistriblltion .ellsity o~ c~.ucll poillls is suhstalltially equal in cert~in s~ec1fied ways.
color c1isl1ay clyllc~mic rancJta is clefinec1, which comprises an arbitrary nun~er of subratlcJes wherein each subrange is associated wi-th a dis-tinct co]or. I.ach measure of the inforMation to be displayecl is asso-ciated with a subrancJe ancl hy means of a color contr~st parameter eacll subranclt is associated with a point in a color space such that thc distribu.ioll density of such points is su]~stantially equal.
rlle present invention ~urther provides a metllocl ~llertlby ~he spher-ical coordinates of each ~oint in the color sF)ace may be trans~ormed into Cartesian coordinates which may be directly convertt-cl into den-sitie~s transmittances or illumination levels, o~ primary hues neces-sary to-proc7uce the clisplay. The present invention also provides a ~ethod by ~hich color visual deficiencies of the interpreter may be compensated Eor.
13RIEF DES(~RIPTION OF TIIE: DRI\WI~GS
Fig. l-is a schematic aisplay of the basic construction of a color sphere used to define colors.
Fig. 2 is a schematic di9play .showing the construetion of a coordinatt? sys tem ~hich loea~tes colors determined in the method.
Fic3. 3 is a schematic drawing that shows the construction of an elemcnt of zonal area on the color sphere surfaee which is used to de-;
termine the distribution oE maximally di~ferentiable colors.
Fig. 4 is a schematic drawing illus~tra-ting a spiral path on the color sphere surface along whicli maximally differentiablt? colors are located. ~ - ~
Fig. S is a sche~atic clrawing that describes the concept of uncer-tainty in the value o~ equivalent hue.
Fig. h~ is a schema-tic drawing that shows a relationship between perceivt?d hue (1' and equivaIent hue ~ referenced to the color ~s~ ere.
.
Iig. 6n sll~ws a c~raL~hlcal relationsllip hetwee~ ~' ancl ~ .
Fig. 6C is a schematic showincJ the color sr?iral of ~ig. 4 Inodified to account ol^ a ;pec:Lfic dif~erellct betwec?n yercc!ived huc and eqillva-Lcnt IlUe .
Fig. 7 is a schematic that shows the Cartesian coordinate system X, Y, Z, in which the location of any point r, e, 0 may`~
be expressed.
Fig. 8-is a schematic that depicts the transfoxmed Cartesian system X~, ~', Z', which measures directly densities or trans-mittances for component masks for color reproduction, or the illuminat~on level of colored light emitting devices. ~ `~
Fig. 9 is a flow chart representation of a method of practicing the present invention.
Eig. 10 ~s a schematic of the separation negative (photo-graphic) embodiment of the present invention.
Fig. 11 is a schematic showing the separation positive (projection or photographic~ embodiment of the present invention.
Fig. 12 ~s a schematic showing the modulated light intensity 15 embodiment of the present invention. ~;
DESCRIPTION OF THE PRE~ED EMBODIMENT
- . : .
A measurement of a pfiysical quantity, here defined to include a purely ;
mathematical quantity or number and hereafter called the dependent quantity, whether it be a nu~m~er, a length, a mass, a time, an electric current, a temperature, a unit of lumuDous intensity,~a plane angle, a solid angle, or a quantity derived from any ccmbunation of the above or equivalent to the ;;~ same or any combination of the same (e.g. a voltage, or potential or electromotive force, is equivalent to a number of volts whether specified in~
units of abvolts or statvolts, etc. and a volt is the ccmbination kllogram 2~5 multiplied ~y meter ~red divided~by seconds cubed divided by ampere~
where a kilogram is a mass, a meter is a length, a second is a time, and an ampere is an electric c~rren~), which is itself a function of a physical~
quantity of quantities as defined, hereinafter called the independent ~ -quantity of quantities, is to ke converted into a color rQresentation of a 3Q measure of the quantity where the~measure is expressible as any numeric re-' : , .
sult after the application of any mathRmatical operation or sequence of - ~
: . :
~ -4- ~ ~
~ '' '.'` ' 1129~,52 operations to the measurement, e.g. multiplying the measurement by one, or taking 2Q times the logarithm to the base ten of the measurement. The total of all such measurements, whether they be continuous or discretely sampled will, for practical purposes, have a finite domain range of independent quan-tity or quantities. ~ithin this domain range, the maximum and minimum values of the measure of the dependent quantity define the dynamic range of the mea-sure. This dynamic range may be divided into an arbitrary unlimited number of equal or unequal subranges thereby fixing the extent of each subrange, or the extent of each su~range may be arbitrarily fixed thereby fixing the numker of subranges. The dynamic range displayed in color need not be exactly the same as the total dynamic range of the measure, but may exceed, equal, or be less than the latter quantity. Thus a specification of subrange size and number can and will determine the color display dynamic range without regard to the dynamic range of the measure.
The method concerns the assignment of max~mally diffe~nt-iable colors to the su~ranges of the color display. Measurement data for the depend- -ent quantity are converted to the measure of the quantity for each of those independent quantities or æts of independent quantities falling within the finite range extent of the color display to be produced. Each measure so found will lie within a subrange, known as an interior subrange, as defined, if the color display dynamic range is set to be equal to or greater than on either or both top and bottom of the dynamic range of the measure; if the ~;color display dynamic range is set to be less than, on either or both top and bottom of, the dynamic range of the measure, then some measures of the quantity will fall outside the available subranges. In this last case such measures may be assigned to the closest subrange, in which case such subrange will be known as an exterior subrange. The method imposes no impedlment upon the numker of subranges which may be utilized and their n~nber may e~ceed the storage capacity of any ccmputer or tabular array.
For each su~range so defined, a unique and differentiable color .
is assigned according to the following method.
'',`~' ~
,;
1~2955~
In order to describe color adequately, construct a color space, which in the preferred embodiment is sphere 1 of Fig. 1, wherein the central point 2 of sphere 1 represents neutral gray, equidistant from opposite poles representing pure white 3 and pure black 4. The axis of sphere 1 joining poles 3 and 4 and passing through neutral gray point 2 is the gray axis 5. The .
equatorial great circle 6 is formed by the intersection of the outer surface of sphere 1 with the plane 19 normal to gray axis 5 and passing through gray point 2. The three primary additive hues, red 7, green 8, and blue 9, are located on and ,~
r~
-5a~ ;
divide equatorial circle 6 into cclual segments defin.ing direetions n the ~quatorial plane~.l9 whlch are 120 apart. The three primary subtractive hues, which are complementary to the`~above:aclditive hues,, '.
are'respectively, cyan 10, magenta ll,~:and yellow'l2, and lie diame- ~`
trically opposite to their`complements on the~'equatorial circle 6. ~.
Thus an.y arbitrary visible color 13 can be represented.~as a position within or on-the sphere;and this~'position can be~descrlbed conveniently by spherical polar coordinates r, e and ~
'L`he ecluival.en-t saturation of the color, o:r purity, or relative depar~ure from neutra:l cJray, is measule~l by the raclial distance, r, Erorn center 2 of sphere 1. ~11 point.s alollcr the line seclment from central point 2 -to arbitrary color 13 or it:, extension to the sp,herical surface if arkitrarY color 13 cloes not lic on'the surface of s~here 1, continuously represellt varying propol-tions of neutral gray frorn totally neutral c~rav at ccllter 2 of sphere 1 to con;plete ahsence of neutra]. c~ray at the surEace of sphere l.
Ficr. 2 de~pict.s the determi.nation of the r~mainillg coordina-tes and ~ . The plane 15 passing throucJh and defined hy point 13 and 3ray a~is 5 COntaillS tlle line segment passing from central poi~t 2.
to color l3. l'his line SeCJment ma]ces' an ang].e, e , with respect to cJray ~is 5 measured from the direction of a reference pole, which for E)Urposes of exanll~le is taken to be black pole 4, ancl this lati~udenal angle is a continuous measure of the eqllivalent color value, or bright-ness, or-proximity -to WllitelleSS, of color 13.
Finally, a reference hue 17 is chosen which, dependi.ng upon whe-ther an additive or subtractive realization of -the method is desired, ~
.correspond to either one of -the additive primary hues or one of the sub-tractive primary hues. The~referellce hue plane 18 is the plane r)ass:ing through and cle~ined hy reference hue 17 and gra~; axis 5, and p:Lalle 18 intersects equatoria:L plane 19 along -the line 20. In a similar way, plane of cqll.Lvalent IIUC :L5, passincl through color 13, intersects c~qllaLorlal pl.alle 19 along the line 21. The ancJle ~! in equatorial plane 19, mcasur~d ~rom reEerence li.ne 20, is a conti.nuous measure o:E the C~ ;Va1ent 11~1C!, or clistlncti.ve essonce, or cJeneric class,i~icatiorl, of cok.~r 13.
The r.,etllocl seekt, to maximize the differentia]. perception of colors .
sc~ 1c(l lc~ the ~;ub.~ J1ges ~>~ c~ co].or. di.sl).1..ly. C:ons.ider Lhc ca~c in all of the cOlors of c:olo1. ;L~here :l are unarl~bicluous.l.y anc1 clis-tinctl~ ercc~ivcll~le b~r eitlleL hl~ma]l, electrc3ll!echanical, or other men-surat:i.ve me~ s. Let the radius oi. the color sphere be rS as in E`ig. 3 Thel1 ma~imally di.~ierentiable colors lie on -the surface of sphere l, sil1ce these are Lal-tl1est removed irom cJray a.~is S. ~ll colors or sub-rancres will-therefore be speci.fied by r=rS.
In acldi:~io11, -to bt? ma~imally difi-'t~rentiable, the c1esired colors wllicl1 are representecl as ~oints on this spherical s~1rEace will be dis-tributed -thereon in a manner such that the density of poin-ts be as equal as possible over the surface. To acccn~plish equa.lity oi. distribution, construct a c1ifierential zonal band 22 about sphe.re l centered a-t the latitudenal. color value angle ~ and of di.fferential ancJular wid-tl1clt~ .
The d'ifferential width of zonal hand 22 at the spherical surface will be clw ~here dw=r5~ , and the radius of t:he planar circle so .~ormecl will be rz.
Tric~onoll1etric considerati.ons show that rz - rs sin ~ and that the differenti~l ar~a oE zonal band 22 must be ~Trl ~ lrl~ .jj"~?~ . Since rs i; cons-tant for s~hele l, ecluality oE distribution recluires that the nunlber of colors lyinJ in each differential zonal band must he pro-portional to sin(~ . One embocli~ent of such a distrihution will now Ije set forth.
~ssun~e that N su~ranyes corresponding to ~i colors are desired~ -Le-t each subrancle he designated hy a subrange definer, a, that takes on in-tegral values from O to A,'where A--N-l. Eacll of the N subranye c1eEiner6 wi.ll he associatecl with a distinct color.
In orcler to deterinine the color value anc~lle ~ for each subrancJe, 'we observe from the i'oregolng trigonometric consideration-i that t~, where k i.s a constant to be determincd. Inteyrating this e~pressiol1,.c)bserving that ~ c A and ~ C11 ~e find that:
¦ t ~t~ s"~ tl~ c-~ c~r ~
'I`hus, :i.n clcl1c~r~.1.1., t.he~colc)r val~le anc3le ~' associ.ated with c!lc~ ;ub-c? . ~l~ E i. ll c~ J-, ~, w i ~ c);.vel1 by:
I s.~ e ~ s ~ ~
whi.cl1 ma~ hç rewrittel1(?-c~ c~
In orclc-.r to detcrl~ 1e the h~le anc3lt? ~'or each suLral1c!e, a spiral 28, --7-- .
1 1 2955~
.
as shown on Fig. 4, may now be constructed in a manner which satisfies the maximal differentiability requirement via equality of zonal distribution. The longitudenal hue angle will be reIated to t~e latitudenal color value angle, ë, by the equation ~-2cO, where c is the color contrast para-meter and is equal to the number of cycles in spiral 28 as it winds from 9=~ to a=~ . Color contrast parameter c controls and is a direct measure of color contrast between adjacent color coordinate pairs(~ , ~ ) associated with the definers, lQ a. These maximally differentiable colors are indicated schematically be crosses 29 on spiral 28. It will be seen that adjacent or nearly adjacent subranges differ substantially in equivalent hue, while widely different subranges differ substantially in equivalent value. Thus the color differences associated with different subran~es are clearly discernible for small as well as large differences in the value of sub- -range definAer.;~
The method is now extended to the case where a human, photoelectric, or other type of interpreter cannot perceive all of the equivalent hues of the color sphere with equal ability. In humans, those manifestin~ slightly imbalanced hue perceptive ability are known as protanomalous, deuter-anomalous, or tritanomalous observers, while those mani- -festing total inability to perceive certain hues are known as ~ -as protanopes, deuteranopes, or tritanopes. Additionally, those who can perceive no hues, but only shades of gray, are known as rod monochromats. For photoelectric or other non~
human types of interpreting devices, the detection mechanism may have an output response which varies significantly de- ~
pending upon the hue available to the input sensor. ~ ;
The extension of the method to these cases involves a coordinate transformation from ~' to ~, where ~', the ,~
-``` 1123552 perceived hue, will now be defined 0'= 2c~ and ~' will be converted into a color sphere coordinate, ~, in the following way. For every equivalent hu~, defined by an angle 01t on the color sphere as shown in Fig. 5, assign a perception wéighting value! W(0~), indicative of the relative ability of the human or electronic interpreter to perceive that equivalent hue.
For example, the perception weighting function may simply be the inverse uncertainty of the hue angle: if all the equivalent hues lying about 0H with the range ~0~ are indistinquis~able to the interpreter, then an uncertainty of ~0~,with respect to ~
~ is said to exist for the interpreter; the perception ~-weighting function would be defined then as W(~H ) = ~ ~ H
As another example, the perception weighting function W(~
may simply by the value of the measured response R(~) at the ~ ~-output of a measuring device when an input of standardized intensity of the given equivalent hue~ ~ is provided. As a third example, if the interpreter cannot perceive hues be-tween~ =o and~ = 3 , but perceives equally well all hues between~ = ~ and~= ~ ~ , then W~ ~) for ~ ~u~
W(4~)=~ for ~ < ~ < ~
In all of these examples, the transformation between ~ ~-~` and ~ is sp~ecified by:
For a given ~` , the value of ~ is ascertained as that for which ~ ~5~d~ ~ a~ 5 ~ H
Thus for the third example above, as the perceived hue, in Fig. 6A, spans the angles from ~ = to ~ = ~ , this is -~
equivalent to~ spanning the equivalent hues from~ = ~ to ;~
~ =~. Fig. 6B shows the graphical relationship between~
and ~ . As ~ = ~c~ a~ccoS (I ~3 changes as a function of the subrange definer, a, the corresponding equivalent hue _ g _ ~ ~29552 angle, ~ , takes on all ~alues except those in the range 0<~< ~. The spiral 28 of Fig. 4 would thus be modi~ied to correspond to the transformed spiral 37 of Fig. 6C.
Dlfferential perception of the colors assigned to subranges will be enhanced by transEormation of the coordinate system of the color sphere through the use of a general weighting function derived from the perception characteristics of the interpreter. The use of confusing or ill-defined colors is minimized.
lQ The method includes provision for translating the the colors defined by positions of the color sphere into vari-able density ~or transmittance~ negatives or positives for color compositing by conventional photochemical, mechanical, or ~ `~
other means, or into varying illumination levels of colored light-emitting devices. Each color previously defined by the -~
above methods ~ill be representable by the color location co~
ordinates r, ~ and ~ which are reproduced in Fig. 7. ~
Define Cartesian axes x, y and z as shown. The co- ~ -ordinates in this system will be given as a function of those `-in the previous system by ~ =rSi~ e cos~-rSX;y~5~hes~ syj : - -~~ r ~S e ~ ~5 ~ , The origin 2 of this system is ofcourse unchanged.
Now to effect direct measurement of density, (or --transmittance or illumination level), apply the following set of transformations. First normalize the above coordinates by ~- `
dividing by rs, the radius of the sphere. Then%^ ~ 'Y r5 ;
, and~~ rS must lie between ~1 and -1. Next displace the~ ;
origin by~ 1 unit in Z as indicated 41 in Fig. 8, and by -~
scaling, (optionally) reflecting, and rotating axes define a ~ ~`
new orthonormal coordinate system with axes x', y' and z' which form the basis triad for an inscribed cube 45 of color sphere 1. The major diagonal 46 of inscribed cube 45 is co---lo--1129~52 incident with gray axis 5 The example of a scaled, reflected,and rotated axl~ system shown in Fig. 8 is obtained by the transformation X ~ ( ~ ) X t (~ ) ;
~ F)X (~) y ~ (~
Additionally, if indlvidually x', y' or z' lie outside the range from O to+ 1, then they are set equal to the closest end point of this ran~e. The values of x', y' and z' correspond to the variable densities (or transmittances or illumination levels) of the negatives (or positives) of each primary sub~
tractive (or additive~ hue, with O corresponding to minimum density (or transmittance or illumination level) and tl corresponding to maximum density (or transmittance or illumi~
nation level~. -i .:
Thus the color of a subrange, for example, specified ~-. .
by the color sphere values rs, ~ and ~ , is transformed to the ~
equivalent values x, y, and z and finally to the values x', y' ~ "
and z'. These latter values are translated directly on a one-2Q to-one basis but not necessarily with linear proportionality, -~
into density (or transmittivity or illuminance level) values to be used with photographic, electronic, or other reproduction schemes to produce a composite, full-or partially-colored , .:, display. The colors thus produced are associated with the values of the corresponding subranges by means of an appro-. . ,.:.~
priate translation scale.
Referring now to Fig. 9, a plan for instructing a digital computer to perform the preferred embodiment of the - . .. .
invention is set out. At Step 100, prior to actual processing ,;
of the data, a measure of the data is constructed. In the case of a digital computer, the measure is constructed by sampling the data at incremental points in the domain of -... .. , , ~ , ... . . . .
~129552 the independent variable-. It will of course be recognized by those skilled in the art that the data could be processed in continuous fashion ~y suitably constructed analog computer.
Prior to processing, the color display dynamic range is defined, and that range is put into the computer, at Step 101. A measure of the data is put into the computer and, at Step 102, is associated with a subrange definer corresponding to a particular subrange of the color display dynamic range.
At Step lQ3, an equivalent value angle of the assigned sub-lo range is determined according to the method of the present invention. At Step 104, the equivalent hue angle of the as-signed subrange is determined with respect to a preselected color contrast parameter 105 and a perception weighting function 106 determined from the color perception data for ; ;~
the interpreter 107. It will be recalled that the color ;~
contrast parameter controls and is a direct measure o~ the hue contrast between adjacent color coordinate pairs. The perception weighting function, input at Step 106, is de- -termined from the color perception data for the interpreter, 2Q input at Step 107, and allows interpreters having color per- ;
: "
ceptual deficiencies to distinquish equally wèll all colors as-signed to the various subranges. In the case of normally ` -sighted interpreters, the perception weighting function is equal for all longitudenal equivalent hue angles.
The equivalent value angle and equivalent hue angle : ,:
determined for the subrange are converted to a set of equi-valent Cartesian coordinates at Step 108. The equivalent ~;
Cartesian coordinates are defined with respect to a reference axis, which is specified by input 109. Input 109 is specified according to whether an additive or subtractive realization of the display is desired. The equivalent Cartesian co-ordinates obtained at Step 108 are converted to a second ~12-'~;,. . .: - .
- - 11295~2 Cartesian coordinate representation at Step 110, wherein the axes of the first equ~valent Cartesian coordinates are normalized, translated, optionally reflected, scaled and rotated, such that the origin of the second Cartesian co-ordinate system is located at the reference pole of the color sphere and the reference hue is preserved. Then at Step 111, the coordinates of the assigned subrange are determined in the second Cartesian system formed in Step 110. After specifying at Step 112 whether a negative or positive realization is lQ desired, the coordinates generated in Step 111 are interpreted ;
directly in one-to-one fashion as primary~hue densities or in-tensities as Step 113, which are output as yellow/blue 114, -magenta/green 115, and cyan/red 116.
Each measure of the data is sequentially processed in the manner set forth in Fig. 9 throughout the entire domain of the independent variable and the primary components cor-responding to the entire domain are contained in outputs 114, 115 and 116. The primary color outputs may then be processed - in any of several conventional photographlc methods to form a -~
2Q final display.
One method for forming the final color display is set forth in Fig. 10, which presents a subtractive, separation ;
. .
negative (photographic~ embodiment of the present invention. ~'~
The primary subtractive hues obtained from the method as set forth in Fig. 9, wherein a subtractive primary hue is specified at Step 109 and a negative realization is specified at Step 112, are processed as follows.
The primary color outputs 114,115 and 116, in Fig. 9 become primary color inputs 117, 118 and 119 in Fig. 10.
3Q Yellow input 117 is processed to plot a negative for yellow at Step 12Q, which-in turn is exposed with blue light at Step 121. In similar fashion magenta input is processed to plot a 1 ~ 29552 negative for magenta at Step 122, which is exposed to green light at Step 123. Finally, cyan input 119 is processed to plot a negative for cyan at Step 124, which is exposed with red light at Step 125. The component exposures obtained in Steps 121, 123 and 125 were registered to form composite color realization 126.
Figs. 11 and 12 illustrate methods of producing an ~ `~
additive, positive realization of the color display formed by the method of the present invention. Primary, additive out~
lQ puts are produced according to the method as set forth in Fig.
9 by specifying an additive reference hue at Step 109 and a . ~
positive realization at Step 112. Blue input 127, corresponds to ~lue output 114, green input 128 corresponds to green out-put 115, and red input 129 corresponds to red output 116.
Blue input 127 is processed at Step 130 to form mask 131, green input 128 is processed at Step 132 to form mask 133, and ,~, - :, red input 12~ is processed at Step 134 to form mask 135. Mask ~ ~
. . . . .
131 is illuminated by a constant intensity light source 136, the light from which passes through a blue filter 137. Mask ;
2Q 133 is illuminated by a constant intensity light source 138, -the light from wAich passes through a green filter 139. ~
Mask 135 is illuminated by a constant intensity light source ~;
140, the light from which passes through red filter 141.
The light passing through masks 131, 133~and 135 is aligned and focused by alignment and focusing means 142, which includes a combination of mirrors and lenses, upon an imaging device v 143 to form a composite display. Imaging device 143 may be a projection screen or a photographic material.
Fig. 12 illustrates an alternative method of producing ..
3Q a final composite color display from blue input 160, green input 161 and red input 162. Blue input 162 operates a modulated light source 144 to produce variable intensity ,~
:
white light. Similarly,~green input 161 and red input 162 operate modulated light sources 145 and 146, respectively.
The light from modulated light source 144 passes through blue filter 147, the light from modulat~d light source 145 passes through green filter 148, and the light from modulated light source 146 passes through red filter 149 and the colored light from those sources is aligned and focused on imaging device 150 by means of alignment and focusing device 151 to ~ ;
form the final color display.
lQ Further modifications and alternative embodiments , of the method of this invention will be apparent to those skilled in the art in view of this description. Accordingly, ~-this description is to be construed as illustrative only and is for the purpose of teaching those skilled in the art the manner of carrying out the invention. For example, equivalent steps may be su~stituted for those illustrated and described herein and other conventional methods of producing color realizations may be substituted for those set forth, all as would be ap-parent to one skilled in the art after having the benefit of this description o~ the invention.
'''~' ',''', ~ ::
~.
Claims (11)
1. A method for displaying in color, in a manner which shall be maximally differentiable to an interpreter, any measure of a physical quantity which is itself a function of a physical quantity, whether continuous or discretely sampled, which com-prises the following steps:
defining a color display dynamic range, which includes a plurality of subranges;
associating said measure of said physical quantity with a subrange;
associating said subrange with a point of a color sphere, wherein each point of said color sphere is defined by a radial distance, a latitudenal equivalent value angle and a longitudenal equivalent hue angle, such that the distribution density of said latitudenal equivalent value angles of said points is substanti-ally proportional to the sine of said latitudenal equivalent value angle and said longitudenal equivalent hue angle is determined by a preselected color contrast parameter that relates the latitudenal equivalent value angle and longitudenal equivalent hue angle associated with said point, and wherein the distribution density of said longitudenal equivalent hue angles is substantially pro-portional to a weighting function determined by the ability of an interpreter to identify unambiguously the hue corresponding to each of said longitudenal equivalent hue angles;
converting the spherical coordinate representation of said point into an equivalent first Cartesian coordinate repre-sentation with a longitudenal reference axis chosen to correspond to a primary reference hue angle;
creating a second Cartesian coordinate system by scaling, translating, and rotating the axes of said first Cartesian coordinate system so that the origin thereby created corresponds to a pole of the color sphere and the axes thereby created make equal angles with the polar axis of said color sphere, with the longitudenal direction of said reference axis preserved after transformation;
converting said first Cartesian coordinate representa-tion of said point into a representation in said second Cartesian coordinate system;
interpreting the coordinates of said point in said second coordinate system directly in the manner of a one-to-one transformation as the amounts of each of the primary hues necessary to produce the color associated with said subrange and said measure associated therewith;
and compositing the amounts of said primary hues corresponding to said measure into a final display.
defining a color display dynamic range, which includes a plurality of subranges;
associating said measure of said physical quantity with a subrange;
associating said subrange with a point of a color sphere, wherein each point of said color sphere is defined by a radial distance, a latitudenal equivalent value angle and a longitudenal equivalent hue angle, such that the distribution density of said latitudenal equivalent value angles of said points is substanti-ally proportional to the sine of said latitudenal equivalent value angle and said longitudenal equivalent hue angle is determined by a preselected color contrast parameter that relates the latitudenal equivalent value angle and longitudenal equivalent hue angle associated with said point, and wherein the distribution density of said longitudenal equivalent hue angles is substantially pro-portional to a weighting function determined by the ability of an interpreter to identify unambiguously the hue corresponding to each of said longitudenal equivalent hue angles;
converting the spherical coordinate representation of said point into an equivalent first Cartesian coordinate repre-sentation with a longitudenal reference axis chosen to correspond to a primary reference hue angle;
creating a second Cartesian coordinate system by scaling, translating, and rotating the axes of said first Cartesian coordinate system so that the origin thereby created corresponds to a pole of the color sphere and the axes thereby created make equal angles with the polar axis of said color sphere, with the longitudenal direction of said reference axis preserved after transformation;
converting said first Cartesian coordinate representa-tion of said point into a representation in said second Cartesian coordinate system;
interpreting the coordinates of said point in said second coordinate system directly in the manner of a one-to-one transformation as the amounts of each of the primary hues necessary to produce the color associated with said subrange and said measure associated therewith;
and compositing the amounts of said primary hues corresponding to said measure into a final display.
2. The method as claimed in claim 1, wherein said creating step additionally includes reflecting an axis of said first Cartesian axes.
3. The method as claimed in claim 1, wherein said radial distance associated with every point is equal to the radius of said color sphere.
4. The method as claimed in claim 1, wherein said weighting function is equal for all longitudenal equivalent hue angles.
5. The method as claimed in claim 1, wherein said weighting function is specifically inversely related to the relative un-certainty in perceiving each color as represented by each longi-tudenal equivalent hue angle.
6. The method as claimed in claim 1, wherein said weighting function is specifically directly related to the relative ampli-tude of a measured response at the output of a measuring device when an input of standardized intensity is provided for each longi-tudenal equivalent hue angle.
7. The method as claimed in claim 1, wherein said weighting function is specifically zero over a portion of the range of longitudenal equivalent hue angles.
8. The method as claimed in claim 1, including the further step of: forming a schematic and systematic representation of the colors associated with each of said measures, whereby the interpreter may correlate said colors with said measures.
9. The method as claimed in claim 1, wherein:
said interpreting step includes associating said second Cartesian coordinates of said point with corresponding densities in masks which control the amount and location of subtractive primary hue dyes on a substrate;
and said compositing step includes registering and pro-ducing said primary hues on an integral substrate.
said interpreting step includes associating said second Cartesian coordinates of said point with corresponding densities in masks which control the amount and location of subtractive primary hue dyes on a substrate;
and said compositing step includes registering and pro-ducing said primary hues on an integral substrate.
10. The method as claimed in claim 1, wherein:
said interpreting step includes associating said second Cartesian coordinate representation of said point with corresponding transmittances masks for constant intensity light sources directed to an imaging device;
and said compositing step includes aligning the images formed on said imaging device.
said interpreting step includes associating said second Cartesian coordinate representation of said point with corresponding transmittances masks for constant intensity light sources directed to an imaging device;
and said compositing step includes aligning the images formed on said imaging device.
11. The method as claimed in claim 1, wherein:
said interpreting step includes modulating variable inten-sity light sources associated with each additive primary hue to form an image on an imaging device;
and said compositing step includes aligning said images formed on said imaging device.
said interpreting step includes modulating variable inten-sity light sources associated with each additive primary hue to form an image on an imaging device;
and said compositing step includes aligning said images formed on said imaging device.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US05/858,524 US4169285A (en) | 1977-12-07 | 1977-12-07 | Method for producing color representations of quantifiable data by maximizing differential perception of colors |
| US858,524 | 1977-12-07 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1129552A true CA1129552A (en) | 1982-08-10 |
Family
ID=25328517
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA307,941A Expired CA1129552A (en) | 1977-12-07 | 1978-07-24 | Method for producing color representations of quantifiable data by maximizing differential perception of colors |
Country Status (3)
| Country | Link |
|---|---|
| US (1) | US4169285A (en) |
| CA (1) | CA1129552A (en) |
| GB (1) | GB2009934B (en) |
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| US4352105A (en) * | 1979-09-25 | 1982-09-28 | Radiation Dynamics, Inc. | Display system |
| US4467461A (en) * | 1981-01-05 | 1984-08-21 | Conoco Inc. | Interactive color analysis of geophysical data |
| US4675696A (en) * | 1982-04-07 | 1987-06-23 | Canon Kabushiki Kaisha | Recording apparatus |
| US4736307A (en) * | 1982-04-21 | 1988-04-05 | Neuroscience, Inc. | Microcomputer-based system for the on-line analysis and topographic display of human brain electrical activity |
| US4836026A (en) * | 1984-06-01 | 1989-06-06 | Science Applications International Corporation | Ultrasonic imaging system |
| US4979129A (en) * | 1987-02-09 | 1990-12-18 | Ricoh Company | Digital color converting apparatus for color image processor |
| US5912656A (en) * | 1994-07-01 | 1999-06-15 | Ohmeda Inc. | Device for producing a display from monitored data |
| US7966234B1 (en) | 1999-05-17 | 2011-06-21 | Jpmorgan Chase Bank. N.A. | Structured finance performance analytics system |
| US6618500B1 (en) * | 1999-12-07 | 2003-09-09 | Sony Corporation | Color conversion matrix based on minimal surface theory |
| US6210006B1 (en) * | 2000-02-09 | 2001-04-03 | Titmus Optical, Inc. | Color discrimination vision test |
| US7392210B1 (en) | 2000-04-07 | 2008-06-24 | Jpmorgan Chase Bank, N.A. | Workflow management system and method |
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| US6429868B1 (en) | 2000-07-13 | 2002-08-06 | Charles V. Dehner, Jr. | Method and computer program for displaying quantitative data |
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| KR100467600B1 (en) * | 2002-07-30 | 2005-01-24 | 삼성전자주식회사 | Method for color correction |
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| US7634435B2 (en) | 2003-05-13 | 2009-12-15 | Jp Morgan Chase Bank | Diversified fixed income product and method for creating and marketing same |
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| KR100587333B1 (en) * | 2003-11-07 | 2006-06-08 | 엘지전자 주식회사 | Method and apparatus of color display for incomplete color blindness |
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| US8558843B2 (en) * | 2010-08-26 | 2013-10-15 | Nicoline Kinch | Method for identifying, selecting and matching colors |
| US9171481B2 (en) * | 2010-08-26 | 2015-10-27 | Nicoline Kinch | Method for identifying, displaying, selecting, naming and matching colors |
| US8681171B2 (en) * | 2010-08-26 | 2014-03-25 | Nicoline Kinch | Method for identifying, displaying, selecting, naming and matching colors |
| JP5645091B2 (en) * | 2010-09-16 | 2014-12-24 | ビバコンピュータ株式会社 | COLOR INFORMATION GENERATION DEVICE, COLOR INFORMATION GENERATION METHOD, AND RECORDING MEDIUM |
| JP2012209733A (en) * | 2011-03-29 | 2012-10-25 | Fuji Xerox Co Ltd | Color gamut outline information generating device and program |
| WO2018137736A1 (en) * | 2017-01-25 | 2018-08-02 | Techkon Gmbh | Method and device for representing colours of a colour space |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US3961306A (en) * | 1971-10-28 | 1976-06-01 | Seiscom Delta Inc. | Method of forming color graphic displays from input data |
-
1977
- 1977-12-07 US US05/858,524 patent/US4169285A/en not_active Expired - Lifetime
-
1978
- 1978-07-20 GB GB7830538A patent/GB2009934B/en not_active Expired
- 1978-07-24 CA CA307,941A patent/CA1129552A/en not_active Expired
Also Published As
| Publication number | Publication date |
|---|---|
| US4169285A (en) | 1979-09-25 |
| GB2009934B (en) | 1982-07-21 |
| GB2009934A (en) | 1979-06-20 |
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