Method of simply setting expansion regions for conversion of values of colors according to xyz notation system into values of colors according to Munsell notation system

A method of expanding the regions in which conversion of color values in the CIE notation system to values in the Munsell notation system can be made. On a conventional Munsell chromaticity diagram having equi-hue lines and equi-chroma loci and superimposed on a CIE set of coordinates in a conventional conversion diagram, the respective equi-hue lines are extended outwardly from the outermost equi-chroma locus in a direction in alignment with respective lines connecting the respective intersections of the outermost equi-chroma locus with the respective equi-hue lines and the intersections of the next inward equi-chroma locus with the respective equi-hue lines, the extension being to points along the extended equi-hue lines which are integral multiples of a value d which is equal to .sqroot.(x.sub.1 -x.sub.2).sup.2 +(y.sub.1 -y.sub.2).sup.2 where x.sub.1 and y.sub.1 are the CIE notation values of the points of intersection of the respective equi-hue lines and the outermost equi-chroma locus, and x.sub.2 and y.sub.2 are the CIE notation values of the points of intersection of the respective equi-hue lines and the next inward equi-chroma locus. The points along the extended equi-hue lines are joined with corresponding points on adjacent equi-hue lines to form further equi-chroma loci outwardly of the outermost equi-chroma locus.

This invention relates to converting values which numerically express a 
color from the so-called CIE notation system to the Munsell notation 
system, and more particularly to a method of expanding the regions in 
which conversion of values can be made to ranges outside those covered by 
existing tables and diagrams of correlated values of the CIE notation 
system and the Munsell system. 
BACKGROUND OF THE INVENTION AND PRIOR ART 
It is widely accepted that the Munsell notation system of numerical values 
for designating a color is a most excellent system for expressing the 
color of an object because of the high correspondence of the values 
according to the Munsell system and the luminosity of the color of the 
object. However, it is not very easy to convert the tristimulus values X, 
Y and Z according to the CIE notation system, which are calculated on the 
basis of a colorimetric value, into a value according to the Munsell 
notation system. 
The Optical Society of America considered the relation between the values 
according to the CIE notation system and the values according to the 
Munsell notation system, and in 1943 proposed a revised Munsell notation 
system, known as the Munsell Renotation System, but hereinafter referred 
to simply as the Munsell notation system. According to this system, the 
relation between the visual reflection power Y(%) and Munsell lightness V 
is determined by using a quinary formula experimentarily obtained. For the 
conversion of the chromaticity values according to the CIE notation 
system, an equi-hue locus and an equi-chroma locus must be found on a 
chromaticity-Munsell notation conversion diagram, which is a CIE 193 (x, 
y)--chromaticity diagram corresponding to Munsell lightness value V close 
to the value V for the particular color as converted from the CIE notation 
system, and which has Munsell equi-hue lines and equi-chroma loci 
superimposed therein, from which the Munsell values for hue and chroma as 
marked on the diagram can be determined. 
This conversion process is described in ASTM Designation D 1535-80 Standard 
Method of SPECIFYING COLOR BY THE MUNSELL SYSTEM. Using this process, it 
is fundamentally possible to convert a value according to the CIE notation 
system into a value according to the Munsell notation system. 
However, the relation between a value according to the CIE notation system 
and a value according to the Munsell notation system can be expressed by a 
numerical formula only for the relation between the visual reflection 
power Y and the Munsell lightness V. Therefore, in order to convert a 
value according to the Munsell notation system, it is necessary to carry 
out the troublesome steps of using the chromaticity-Munsell notation 
conversion diagrams. 
For this reason it is thought that the values according to the Munsell 
notation system have not been widely utilized, although they have a high 
correspondency to the luminosity of colors. 
Recently, however, the complexity of the conversion because of the 
necessity of using the chromaticity-Munsell notation conversion diagrams 
have been overcome by the utilization of computers, so that it has become 
possible to carry out the conversion very easily and speedily. Therefore, 
it is possible that the Munsell notation system will be utilized to a 
greater extent in the future. 
However, the tables of numerical values representing the relation between 
the values of visual reflection power according to the CIE notation system 
and the lightness values according to the Munsell notation system and the 
chromaticity-Munsell notation conversion diagrams proposed by the Optical 
Society of America do not fully cover the whole range of colors of 
objects. They cover only a limited range of colors of objects. This has 
been an obstacle to the utilization of the values according to the Munsell 
notation system. 
The values according to the CIE notation system of certain colors, 
especially those having high visibilities, are substantially incapable of 
being converted into values according to the Munsell notation system by 
the system presently available. 
The above drawbacks of the Munsell notation system have not heretofore 
posed any big problems. This may be due to the fact that the Munsell 
notation system has not been utilized very much in practice. 
There has also been developed a new color-expressing notation system for 
colored materials, namely the HC*B* system, which is based on and is 
derived from the Munsell notation system. 
In the HC*B* notation system, the values designating colors are determined 
on the basis of hue H, lightness V and chroma C according to the Munsell 
notation system, and the system is described in Japanese Patent 
Application No. 205282/1981, "Apparatus for Measuring and Displaying 
Values C* of Density and Degrees of Fastness of Colors". 
In order to be able to make sufficient use of not only the values according 
to the Munsell notation system but also those according to the HC*B* 
notation system, it is very inconvenient that regions in the range of 
colors exist in which it is substantially not possible to convert, by the 
system presently available, values according to the CIE notation system of 
colors of objects into values according to the Munsell notation system. 
OBJECTS AND BRIEF SUMMARY OF INVENTION 
It is accordingly an object of the invention to provide a method of 
obtaining Munsell notation system values for colors outside the range of 
colors presently included in conventional tables and chromaticity diagrams 
for conversion from the CIE notation system and the Munsell notation 
system. 
The method which achieves this object according to the invention comprises 
the steps of, on a conventional Munsell chromaticity diagram having 
equi-hue lines and equi-chroma loci and superimposed on a CIE set of 
coordinates in a conventional conversion diagram, extending the respective 
equi-hue lines outwardly from the outermost equi-chroma locus in a 
direction in alignment with respective lines connecting the respective 
intersections of the outermost equi-chroma locus with the respective 
equi-hue lines and the intersections of the next inward equi-chroma locus 
with the respective equi-hue lines, the extension being to points along 
the extended equi-hue lines which are integral multiples of a value d 
which is equal to .sqroot.(x.sub.1 -x.sub.2).sup.2 +(y.sub.1 
-y.sub.2).sup.2 where x.sub.1 and y.sub.1 are the CIE notation values of 
the points of intersection of the respective equi-hue lines and the 
outermost equi-chroma locus, and x.sub.2 and y.sub.2 are the CIE notation 
values of the points of intersection of the respective equi-hue lines and 
the next inward equi-chroma locus; and joining the points along the 
extended equi-hue lines with corresponding points on adjacent equi-hue 
lines to form further equi-chroma loci outwardly of the said outermost 
equi-chroma locus.

DETAILED DESCRIPTION OF THE INVENTION 
In order to obtain Munsell values for ranges of colors beyond the 
conventional conversion tables and diagrams, the equi-hue lines on the 
existing conventional x, y-chromaticity diagrams must be extended and 
equi-chroma loci beyond the equichroma loci in the existing conventional 
chromaticity conversion diagrams must be provided. However, it is not easy 
to extend these lines and provide these loci in accordance with the 
uniformity in perception with respect to a hue and a chroma as determined 
by the Optical Society of America. Therefore, an approximate extension of 
the equi-hue lines and the provision of approximate equichroma loci are 
carried out by a simple method. 
To this end, as shown in FIG. 1, a straight line 20 connecting the 
outermost intersecting points x.sub.1 and y.sub.1 between an equi-hue line 
21 and an equi-chroma locus 22 and the second outermost intersecting 
points x.sub.2 and y.sub.2 of the equi-hue line 21 and the next inward 
equi-chroma locus 23 spaced from each other a distance corresponding to 
two chromas along the equi-hue lines 21 on a conventional x, 
y-chromaticity-Munsell notation conversion diagram is extended outward as 
shown at 20a. Two points 24 and 25 which are spaced outwardly from the 
point x.sub.1, y.sub.1 by a distance d=.sqroot.(x.sub.1 -x.sub.2).sup.2 
+(y.sub.1 -y.sub.2).sup.2, and a distance 2d, respectively, are marked on 
the resulting extended line. These points are connected to corresponding 
points on extended lines of equi-hue lines on opposite sides of the 
first-mentioned equi-hue line to form an expanded region of the conversion 
diagram. 
The relation between the values according to the CIE notation system in the 
expanded region formed by the above-described method and values according 
to the Munsell notation system can, in addition to being derived from the 
conversion diagrams, be set forth in tabular form, as shown in Table 1. 
Examples of the regions of the known conversion diagrams and newly formed 
expanded regions formed according to the present invention are shown in 
FIGS. 2a and 2b and 3a and 3b. In these figures, the Munsell chromaticity 
diagrams, or parts thereof, with their equi-hue lines generally indicated 
at EL and chroma loci CL are superimposed on the x, y coordinates of the 
CIE diagram. FIGS. 2a and 3a show regions which have already been 
established for Munsell lightness values V=3 and V=4, and FIGS. 2b and 3b 
show the expanded regions for these values of V prepared according to the 
present invention. 
In this simple expansion method according to this invention, an 
uncomplicated, linear expansion operation using only the outermost and 
second outermost intersecting points is carried out. It is conceivable, of 
course, that a more exact and scientific expansion method utilizing all of 
the tables of already known numerical values could be employed. Both of 
these types of expansion methods are mathematic expansion methods, which 
may not correspond exactly with experimental results. However, an object 
of the expansion operation according to the present invention is to make 
it possible to obtain substantially accurate values according to the 
Munsell notation system which correspond to values according to the CIE 
notation system which heretofore could not be converted into values 
according to the Munsell notation system. It is considered that the 
results obtained by the simple expansion method according to the present 
invention and those obtained by a more exact method will not differ very 
greatly. 
Even if a more strict mathematic expansion system, or an expansion system 
based on sufficient psychological experiments is employed in the future, 
the tables of numerical values obtained according to the present simple 
method will not be required to be corrected very much. Consequently, it is 
believed that the values according to the CIE notation system which lie 
outside known conversion tables and diagrams can be converted into 
sufficiently accurate values according to the Munsell notation system by 
conversion diagrams as shown in FIGS. 2b and 3b and tables similar to 
Table 1 showing the relation between the values in the two notation 
systems obtained according to the present method. 
An example of the conversion of values according to the CIE notation system 
into values according to the Munsell notation system using expanded 
conversion diagrams prepared according to the method according to the 
present invention will now be described with reference to a specific color 
for which values according to the CIE notation system which could not 
heretofore be converted into values according to the Munsell notation 
system, are converted into such values. 
Values according to the CIE notation system, X=18.87, Y=9.56, Z=0.91, which 
represent bright red, are converted into values according to the Munsell 
notation system as follows. (1) The chromaticity coordinates x, y are 
calculated from the XYZ values as follows: 
##EQU1## 
(2) The Munsell lightness V is determined from the value of Y. The Munsell 
lightness V can be obtained from the Y-V tables of JIS (Japan Industrial 
Standard Z8721, or can be determined by carrying out a computation in 
accordance with the known formula expressing the relation between Y and V, 
as follows: 
Y=1.2219V-0.23111V.sup.2 +0.23951V.sup.3 -0.021009V.sup.4 +0.0008404V.sup.5 
V=3.6 corresponding to Y=9.56 is obtained by either method. (3) Since the 
lightness V is 3.60, the hues H and chromas C are read from the conversion 
diagrams for values V=3 and V=4, and an interpolation corresponding to 0.6 
lightness value is carried out with respect to the hue and chroma as 
described in ASTM Designation D1535-80 to obtain values according to the 
Munsell notation system. (4) Using the conversion diagram for V=3, point 
(x, y) as determined in paragraph (1) above is plotted as P.sub.3 in FIG. 
4, which is an enlarged part of FIG. 2a. FIG. 2a can be used since P.sub.3 
lies within the known conversion diagram. Interpolation is carried out on 
the basis of the four values according to the Munsell notation system of 
the intersections around P.sub.3, i.e. 10R 3/12, 10 R 3/14, 7.5R 3/12, 
7.5R 3/14, by which the following results are obtained: 
Hue: 9.3R, Chroma: 12.8 
Value according to the Munsell notation system: 9/3R 3/12. (5) Using the 
conversion diagram for V=4, an attempt is made to plot point (x, y) as 
determined in paragraph (1) above as P.sub.4 in FIG. 5, which is an 
enlarged part of FIG. 3a and including an expanded part from FIG. 3b. The 
points having known hues and chromas are included within the regions below 
and to the left of the solid lines, and P.sub.4 cannot be located in these 
regions so as to be surrounded by four known values in the Munsell 
notation system. Therefore, if only the conventional conversion diagram is 
used, the hue and chroma values in the Munsell notation system 
corresponding to the point P.sub.4 cannot be obtained. When the conversion 
diagram is expanded according to the present invention, the Munsell 
notation system values in the regions within the broken lines in FIG. 5 
can be obtained. Interpolation operations are carried out using the four 
values according to the Munsell notation system, i.e. 10R 4/16, 10R 4/18, 
7.5R 4/16, 7.5R 4/18, which surround the point P.sub.4, to obtain the 
following results. 
Hue: 8.3R, Chroma: 17.0 
Value according to the Munsell notation system: 8.3R 4/17.0 (6) 
Interpolation of hue and chroma values in the Munsell notation system for 
the lightness values 3 and 4 is carried out according to the technique of 
ASTM Designation D1535-80 to obtain hue and chroma values for the 
lightness of 3.6, and the following results are obtained. 
Hue: 9.3R+0.6(8.3R-9.3R)=8.7R 
Chroma: 12.8+0.6(17.0-12.8).div.15.3 
The values for the color of this example according to the Munsell notation 
system are: 
Hue: 8.7R, Lightness: 3.6, Chroma: 15.3 (i.e. Munsell 8.7R 3.6/15.3). 
As described above, the values of colors according to the CIE notation 
system which are outside the range of the known conversion diagrams, 
cannot, without more, be converted into values according to the Munsell 
notation system. When the expansion method according to the present 
invention is used, the above drawback can be eliminated, i.e. the values 
according to the Munsell notation system for colors in any region can be 
obtained. 
In the above Example of the present invention, the procedure for converting 
values according to the CIE notation system into values according the 
Munsell notation system by using the conversion diagrams and making 
calculations with figures written down on paper is described. For carrying 
out such a conversion in actual practice, a computer is preferably used to 
shorten the calculation time and save labor. In such a case, essentially 
the same procedure as described above is carried out. The data for the 
exanded areas of the various conversion diagrams for the different values 
of V in the CIE system, an example of which is shown in Table 1, is stored 
in a computer memory along with the data for the known regions of the 
conversion diagrams, and the conversion can be carried out simply and 
speedily in accordance with a simple program. 
The present invention thus provides a way to overcome the problem that, 
with the known conversion diagrams and data therefrom, it is impossible in 
practice to carry out conversion of values according to the CIE notation 
system into values according to the Munsell notation system. 
When the expansion areas of the conversion diagrams and the data based 
therein are provided, values according to the Munsell notation system for 
all colors can be obtained reliably. Accordingly, the provision of the 
expanded areas and data based thereon make it possible to utilize the 
Munsell notation system values effectively for industrial purposes. 
TABLE 1 
__________________________________________________________________________ 
V = 9, Yc (%) = 78.66 
2.5 5.0 7.5 10.0 
H V/C 
x y V/C 
x y V/C 
x y V/C 
x y 
__________________________________________________________________________ 
R /8 0.3885 
0.3187 
/8 0.3973 
0.3286 
/8 0.4073 
0.3413 
/8 0.4160 
0.35296 
/10 
0.4105 
0.3191 
/10 
0.4242 
0.3316 
/10 
0.4334 
0.3478 
/10 
0.4440 
0.36202 
YR /8 0.4213 
0.3678 
/8 0.4228 
0.3809 
/10 
0.4490 
0.4097 
/10 
0.4457 
0.4261 
/10 
0.4499 
0.3806 
/10 
0.4508 
0.3959 
/12 
0.4760 
0.4264 
/12 
0.4715 
0.4453 
Y /14 
0.4768 
0.4685 
/22 
0.4878 
0.5135 
/20 
0.4731 
0.5272 
/20 
0.4603 
0.5415 
/16 
0.4967 
0.4843 
/24 
0.4926 
0.5178 
/22 
0.4799 
0.5356 
/22 
0.4666 
0.5510 
GY /20 
0.4420 
0.5633 
/20 
0.4158 
0.5857 
/20 
0.3623 
0.6186 
/20 
0.2985 
0.6056 
/22 
0.4486 
0.5758 
/22 
0.4208 
0.6015 
/22 
0.3644 
0.6452 
/22 
0.2938 
0.6364 
G /18 
0.2549 
0.5206 
/14 
0.2417 
0.4319 
/14 
0.2293 
0.4115 
/14 
0.2193 
0.3890 
/20 
0.2468 
0.5446 
/16 
0.2306 
0.4478 
/16 
0.2167 
0.4245 
/16 
0.2061 
0.3984 
BG /12 
0.2255 
0.3629 
/12 
0.2165 
0.3432 
/12 
0.2069 
0.3227 
/8 0.2302 
0.3096 
/14 
0.2128 
0.3690 
/14 
0.2029 
0.3459 
/14 
0.1923 
0.3228 
/10 
0.2103 
0.3074 
B /6 0.2451 
0.3021 
/6 0.2431 
0.2908 
/6 0.2439 
0.2835 
/6 0.2475 
0.2772 
/8 0.2222 
0.2969 
/8 0.2187 
0.2811 
/8 0.2190 
0.2709 
/8 0.2238 
0.2620 
PB /4 0.2849 
0.2963 
/4 0.2881 
0.2951 
/4 0.2929 
0.2941 
/6 0.2782 
0.2646 
/6 0.2723 
0.2863 
/6 0.2771 
0.2845 
/6 0.2843 
0.2830 
/8 0.2654 
0.2442 
P /6 0.2876 
0.2679 
/6 0.2939 
0.2680 
/8 0.3123 
0.2648 
/8 0.3260 
0.2724 
/8 0.2789 
0.2493 
/8 0.2875 
0.2490 
/10 
0.3126 
0.2508 
/10 
0.3302 
0.2603 
RP /8 0.3410 
0.2810 
/8 0.3561 
0.2916 
/8 0.3674 
0.3005 
/8 0.3780 
0.3096 
/10 
0.3498 
0.2710 
/10 
0.3691 
0.2844 
/10 
0.3836 
0.2958 
/10 
0.3970 
0.3074 
__________________________________________________________________________