Method for controlling the inking of a printing press by determining color value gradients

Method and apparatus for the determination of the color value gradients of a picture element of a printed image when there are changes in the layer thicknesses of the inks used in the printing, the picture element (4) is photo-electrically scanned in the visible range of the spectrum and also in the near infrared range. From the scanning signals thereby obtained, color coordinates or an approximated subjectively equidistant color system and at least one infrared value is formed. The color value gradients are then calculated from these color coordinates and the at least one infrared value.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates generally to a method for the determination 
of color value gradients of a picture element of a printed image when 
there are changes in the layer thicknesses of the inks used in the 
printing, whereby the picture element is photo-electrically scanned in the 
visible region of the spectrum, and the color value gradients are derived 
from the scanning signals thereby obtained. 
2. Background Information 
The regulation of inking in modern printing presses, in particular in 
offset printing, can be advantageously done on the basis of color 
differences. A typical regulation method based on control by color 
differences is described in European Patent No. B2-0 228 347 and in German 
Patent No. 195 15 499 C2, for example. In this method, a sheet to be 
printed with the printing press is divided colorimetrically into a number 
of test areas with regard to a selected system of color coordinates. From 
the color coordinates obtained in this manner, the color difference 
vectors are calculated to obtain the desired color coordinates with 
respect to said color coordinate system. These color difference vectors 
are converted by means of color value gradients into layer thickness 
change vectors, and the inking of the printing press is regulated on the 
basis of the layer thickness change vectors converted from the color 
difference vectors. The test areas used are the fields of the color test 
strips printed at the same time as the printed image itself. 
Scanning devices have recently become available that make it possible to 
survey the entire image content of a printed sheet by dividing it into a 
large number of relatively small picture elements at reasonable cost and 
in a very short time, using colorimetric or spectro-photometric 
techniques. These scanning devices meet the theoretical instrumentation 
requirements because they not only use simultaneously printed test strips 
for the regulation of the inking of a printing press, but also acquire the 
color information from all the picture elements of the entire actual 
printed image for this purpose. One problem with this method, which is 
sometimes called "measurement in the image", however, results from the 
problem of the black fraction that is present in four-color printing 
which, as is known, is the result of contributions not only from the color 
black itself, but also from the colors superimposed on one another. A 
reliable determination of the color value gradients necessary for the 
calculation of the input variables for the color regulation for all the 
very different printing situations that can arise in a printed image is 
not possible using current methods. An additional problem results from the 
enormously large computer capacity required, which in practice results in 
unreasonably long computing times. 
OBJECT OF THE INVENTION 
On the basis of the known art, one object of the present invention is to 
significantly improve a method of the type described above so that it can 
also be used for the "measurement in the image". In particular, an object 
of the invention is to make it possible to determine color value gradients 
on any desired picture elements of a printed image, thereby making it 
possible to reliably separate all the participating print colors, in 
particular including the print color black. An additional object of the 
invention is to make it possible to determine the color value gradients 
with a reasonable expenditure of time and effort and at high speed, and 
thereby create the conditions for a feasible computer regulation of the 
printing press on the basis of "measurements in the printed image." 
SUMMARY OF THE INVENTION 
The present invention teaches that these objects can be accomplished by the 
method wherein, from the scanning signals of the visible region of the 
spectrurn, color coordinates (L,a,b) of an approximately subjectively 
equidistant color system are formed, that the picture element is also 
scanned photo-electrically in the near-infrared region of the spectrum, 
that from the scanning signals of the infrared range, at least one 
infrared value is formed (I), and that the color value gradients (S) are 
calculated from the color coordinates and the at least one infrared value. 
Particularly advantageous configurations and refinements of the present 
invention are described herebelow. 
A possible advantageous refinement of the invention includes the fact that 
the color coordinates and the infrared value color value gradients S can 
be taken from a pre-defined table. The table can be calculated using a 
mathematical model of the printing press used to produce the printed image 
from measurements taken on the full-tone areas printed with the printing 
press, and taking into consideration the characteristics of the printing 
press. 
Still another advantageous refinement in accordance with the present 
invention includes that for a specified first number of discrete half-tone 
value combinations R.sub.iR, color value gradients S.sub.iR corresponding 
to the colors used in the printing can be calculated and stored in a 
half-tone color table RFT, that for the picture element 4, the 
corresponding half-tone value combination R of the colors used in the 
printing can be calculated from the color coordinates L,a,b and the at 
least one infrared value I, and that the color value gradients S.sub.iR 
from the half-tone color table RFT are assigned to the picture element, 
when the corresponding discrete half-tone value combination R.sub.iR of 
the gradients in question is closest to the half-tone value combination R 
calculated for the picture element. 
A further possible advantageous refinement of the present invention resides 
in the method wherein a four-dimensional color space is formed, the 
coordinates of which are the color coordinates L,a,b and the infrared 
value I, that in this four-dimensional color space, a specified second 
number of discrete color sites F.sub.iF are defined, for each of these 
discrete color sites the corresponding half-tone value combination R of 
the colors used in the printing is calculated, this half-tone combination 
R is replaced by the closest discrete half-tone value combination R.sub.iR 
taken from the half-tone color value table RFT and the discrete color 
sites F.sub.iF are stored in correspondence to the discrete half-tone 
value combinations R.sub.iR in a half-tone index table RIT, and that for 
the determination of the color value gradients of the picture element from 
the color coordinates L,a,b and the infrared value I of this picture 
element, the coordinates of a color site are formed in the 
four-dimensional color space, this color site is replaced by the closest 
discrete color site F.sub.iF, the discrete half-tone value combination 
R.sub.iR corresponding to this discrete color site F.sub.iF is taken from 
the half-tone index table RIT, the color value gradient S.sub.iR 
corresponding to this discrete half-tone value combination R.sub.iR is 
taken from the half-tone color table RFT, and this color value gradient 
S.sub.iR is assigned to the picture element. 
In accordance with another possible refinement of the present invention the 
half-tone value combination R.sub.iR and the color value gradients 
S.sub.iR are determined by interpolation from the half-tone color table 
RFT. 
In at least one embodiment of the present invention the term 
"four-dimensional" as used herein, can possibly refer to a 
four-dimensional array or matrix. 
The above discussed embodiments of the present invention will be described 
further hereinbelow with reference to the accompanying figures. When the 
word "invention" is used in this specification, the word "invention" 
includes "inventions", that is plural of "invention". By stating 
"invention", the Applicants do not in any way admit that the present 
application does not include more than one patentably and non-obviously 
distinct invention, and maintains that this application may include more 
than one patentably and non-obviously distinct invention. The Applicants 
hereby assert that the disclosure of the application may include more than 
one invention, and, in the event that there is more than one invention, 
that these inventions may be patentable and non-obvious one with respect 
to the other.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
In the sole FIGURE, a printing press 1, in particular a multi-color offset 
printing press, produces printed sheets 3 that have the desired printed 
image and any additional printing control elements that may be necessary. 
The printed sheets are extracted from the current printing process and fed 
to a spectro-photometric scanning device 2. This scanning device scans the 
printed sheets essentially over the entire surface, picture element by 
picture element. The size of the individual picture element 4 is typically 
approximately 2.5 mm.times.2.5 mm, which corresponds to approximately 
130,000 picture elements 4 on a printed sheet 3 of conventional 
dimensions. The scanned values--typically spectral remission 
values--generated by the scanning device 2 are analyzed in an analysis 
device 5 that essentally comprises a computer and are processed into input 
variables for a control device 9 associated with the printing press 1 
which, for its part, controls the ink dispensing mechanisms of the 
printing press 1 on the basis of these input variables. The input 
variables, in the case of an offset printing press 1, are typically zonal 
layer thickness changes for the individual printing inks used in the 
printing. The above mentioned input variables or layer thickness changes 
are determined by a comparison of the scanned values or of variables 
derived from them, in particular color measurements (color sites or color 
vectors) of an OK sheet 3, or correctly colored sheet, with the 
corresponding variables of a printed sheet 3 taken from the current 
printing process, in the sense that the changes in the settings of the 
inking mechanisms of the printing press 11 effected by the input variables 
or layer thickness changes result in the best possible approximation of 
the color impression of the printed sheets 3 currently being printed to 
the OK sheets 3. For comparison, instead of an OK sheet 3, an additional 
reference can also be used, for example an approximately corresponding 
specification or corresponding values obtained from preliminary printing 
stages. 
In one possible embodiment of the present invention the scanning device 2 
can comprise a single device capable of scanning in both the visible 
region of the spectrum and the infra-red region of the spectrum. In one 
possible embodiment the scanning device 2 can include an arrangement for 
scanning in the infra-red region and arrangement for scanning in the 
visible region of the spectrum. It is also possible that the scanning 
device 2 could include two separate devices, with one device used to scan 
in the visible region of the spectrum and another to scan in the infra-red 
region of the spectrum. 
The system illustrated essentially corresponds to that extent to 
conventional systems and methods for inking regulation of printing presses 
1, such as, for example, those described in detail in DE-A 44 15 486, and 
therefore does not require any additional explanation for a technician 
skilled in the art. 
A first essential aspect of the present invention is the inclusion of the 
printing color black in the determination of the color value gradients and 
the input variables calculated using this color for the control of the 
printing press. For this purpose, the printed sheets 3 are surveyed not 
only in the visible spectral range (approximately 400-700 nm), but also in 
at least one point in the near-infrared, where only the print color black 
has a significant absorption. It is thereby possible to selectively detect 
the influence of the print color black on the color impression. The 
remission spectra of the individual picture elements 4 therefore consist 
of remission values in the visible spectral range, typically 16 remission 
values at intervals of 20 nm each, and one remission value in the 
near-infrared range. From the remission values of the visible spectral 
range, color values (color coordinates, color vectors, color sites) 
regarding a selected color space are calculated. Preferably, a 
subjectively equidistant color space is selected for this purpose, 
typically something like the L,a,b, color space defined by the CIE 
(Commission Internationale de l'Eclairage). The calculation of the color 
values L,a,b from the spectral remission values of the visible spectral 
range is standardized by CIE and therefore does not require any 
explanation. The remission value in the near-infrared is converted into an 
infrared value I, which corresponds qualitatively to the brightness value 
L of the color space. This conversion is done in a manner analogous to the 
calculation formula for L according to the equation: 
##EQU1## 
where I.sub.i indicates the infrared remission measured in the picture 
element 4 in question and I.sub.in the infrared remission measured at an 
unprinted point on the printed sheet 43. 
The infrared value I, like the brightness value L, can therefore assume 
essentially only values from 0-100. The calculation of the color values 
L,a,b and of the infrared value I from the spectral remission values 
occurs in the evaluation device 5. For the sake of completeness, it should 
be noted that the color values L,a,b (or corresponding values of another 
color space) could also be determined without spectral scanning, using 
suitable colorimetric devices. 
The color and infrared values L,a,b and I available after the scanning of a 
printed sheet 3 for each individual picture element 4 form the starting 
point for the calculation of the color value gradient, and thereby the 
input variables for the printing press control device 9. These 
calculations are also performed in the evaluation device 5. For the 
following description, the value quadruples, or set of four values, 
determined for each picture element 4 and comprising the three color 
values L,a,b (or the corresponding values of another color system) and the 
infrared value I are designated, for purposes of simplification, as a 
(four-dimensional) color vector F of the picture element 4 in question, 
i.e.: 
EQU F=(L, a, b, I) 
In this case, the term "color site" in the four-dimensional color space is 
used to designate a point in the color space, the four coordinates of 
which are the four components of the color vector. The color difference of 
a picture element 4 from a reference picture element 4 or from the 
corresponding picture element 4 of a reference, typically of an OK sheet 
3, is designated the color difference vector .DELTA.F, which is calculated 
according to the equation: 
EQU .DELTA.F=(.DELTA.L, .DELTA.a, .DELTA.b, .DELTA.I)=F.sub.i -F.sub.r 
=(L.sub.i -L.sub.r, a.sub.i -a.sub.r, b.sub.i -b.sub.r, I.sub.i -I.sub.r) 
where the values designated by the index i are those of the picture element 
4 in question and the values designated by the index r are those of the 
components of the color vector of the reference picture element 4 or of 
the corresponding picture element 4 of the OK sheet 3. The color vectors 
of the picture elements of the OK sheet or of another reference are 
frequently also designated the desired color vectors. As the color 
difference .DELTA.E between two picture elements 4 of a picture element 4 
and of the corresponding picture element 4 of the OK sheet 3 is the 
absolute amount of the color difference vector .DELTA.F in question, i.e. 
EQU .DELTA.E=.vertline..DELTA.F.vertline.={(L.sub.i -L.sub.r).sup.2 +(a.sub.i 
-a.sub.r).sup.2 +(b.sub.i -b.sub.r).sup.2 +(I.sub.i -I.sub.r).sup.2 
}.sup.0.5 
where the indices i and r have the same meaning as indicated above. The 
calculator in the evaluation device 5 calculates the color difference 
vector .DELTA.F for each picture element 4 of the current printed sheet 3 
from the color vectors F determined on this sheet and on the OK sheet 3. 
The input variables to be determined for the printing press control device 
9, i.e. the zonal relative layer thickness changes for the individual 
printing inks used in the printing, are also illustrated in the form of 
vectors for .DELTA.D, which is also illustrated below in the form of a 
vector and is called the layer thickness change vector .DELTA.D for short: 
EQU .DELTA.D=(.DELTA.D.sub.c, .DELTA.D.sub.g, .DELTA.D.sub.m, .DELTA.D.sub.s) 
The indices c, g, m and s thereby stand for the colors cyan (c), yellow 
(g), magenta (m) and black (s), and the correspondingly indexed components 
of the vector are the relative layer thickness changes for the color 
indicated by the index. The current layer thicknesses themselves can be 
illustrated as the layer thickness vector D: 
EQU D=(D.sub.c, D.sub.g, D.sub.m, D.sub.s) 
where the indices have the same meanings as indicated above. 
According to the teaching of the above mentioned EP-B2 0 228, 347, for 
example, the relative layer thickness changes .DELTA.D of the individual 
printing inks being used necessary for the compensation of a color 
deviation from the reference (OK sheet 3) can be calculated from the color 
difference vectors .DELTA.F determined from a current printed sheet 3 with 
respect to the reference (OK sheet 3) according to the equation 
EQU .DELTA.F=S*.DELTA.D 
where S is a sensitivity matrix that contains as coefficients the partial 
derivatives of the four components L, a, b, I of the color vector F 
according to the four components D.sub.c, D.sub.g, D.sub.m, D.sub.s of the 
layer thickness vector D: 
##EQU2## 
The coefficients of the sensitivity matrix S are generally designated color 
value gradients. In the following description, the summary term 
"sensitivity matrix" will be used for these 16 color value gradients. 
The sensitivity matrix S is a linear substitution model for the 
relationship between the changes in the layer thicknesses of the printing 
inks used in the printing and the resulting changes in the printed 
impression of the picture element 4 printed with the changed layer 
thickness values. The sensitivity matrix S is not identical for all color 
sites in the color space, but strictly speaking is valid only in the 
immediate vicinity of a color site, i.e. strictly speaking, a unique 
sensitivity matrix S must be used for each measured color vector F of the 
individual picture elements 4 in the equation .DELTA.F=S*.DELTA.D. 
On the assumption that the sensitivity matrices S are known, the matrix 
equation .DELTA.F=S*.DELTA.D can be solved for .DELTA.D, 
(.DELTA.D=S.sup.-1 *.DELTA.F) according to the known rules of matrix 
calculations. 
The visual color impression (technically the color value, color site or 
color vector) of a picture element 4 is determined in offset half-tone 
printing by the percentage half-tone, or raster, value (surface coverage) 
of the printing inks used, and to a lesser extent by the layer thicknesses 
of the inks. The half-tone values or coverages (0-100%) are defined by the 
basic printing plate and are practically unchanged. Under some printing 
conditions, an influence can be exerted on the printed impression and thus 
on the regulation of the printing press only by means of the layer 
thicknesses of the printing inks used. The expressions "half-tone value" 
and "coverage" are used synonymously below. The totality of all possible 
combinations R of percentage half-tone values of the printing inks used 
(generally cyan, yellow, magenta, black) are designated the half-tone 
space (four-dimensional) below. 
In other possible embodiments of the present invention it is possible that 
the half-tone values could be considered or referred to as grid values, 
screen values or lattice values. 
Under specified printing conditions (characteristics of the printing press, 
nominal layer thicknesses, stock to be printed, inks used etc.), each 
half-tone value combination R corresponds to a precisely defined color 
impression or color vector F of the picture element 4 printed with this 
half-tone value combination R. There is thus a clear correspondence 
between the half-tone value combination R and the color site or color 
vector F. The half-tone space can be uniquely simulated in the color 
space, whereby, however, the color space is not completely occupied, 
because it also contains unprintable color sites. On the other hand, there 
is in general no unique relationship. The color vector F that belongs to 
an arbitrary half-tone value combination R can be determined empirically 
by test printings or by means of a suitable model that describes the 
printing process under the printing conditions with sufficient accuracy. A 
suitable model is given, for example, by the known Neugebauer equations 
for four-color offset printing. The model requires a knowledge of the 
remission spectra of single-color full tones (or solid colors), several 
overprints of full tones and several half-tone fields of all the printing 
inks used in the printing at the nominal layer thicknesses of the inks. 
These remission spectra can be measured very easily by means of a test 
printing. If the characteristics of the printing press 1 are known, all 
that is required is simple measurements on fill tones. 
Using the model described above, it is possible, using the methods of the 
known art, to determine the (16) coefficients of the sensitivity matrix S 
corresponding to this half-tone value combination for an arbitrary 
half-tone value combination R. All that is necessary is to change the 
nominal layer thicknesses of the printing inks used in the model, 
preferably by 1% each, for example, and with these changed layer 
thicknesses to calculate the corresponding color vectors and the 
corresponding color difference vectors with respect to the color vector 
resulting from the nominal layer thicknesses. These color difference 
vectors .DELTA.F and the underlying layer thickness change vectors 
.DELTA.D are inserted into the equation .DELTA.F=S*.DELTA.D and the 
equation is solved for the coefficients of the sensitivity matrix S. 
In accordance with an additional essential aspect of the invention, on the 
basis of the model described above, the invention teaches that a limited 
number of potential half-tone value combinations R of the corresponding 
color vector F and the corresponding sensitivity matrix S are calculated 
in advance and are stored in the form of a table. This table, which 
contains the totality of all the sensitivity matrices S and color vectors 
F calculated in this manner, is designated the half-tone color table (RFT) 
below. 
For the calculation of the layer thickness change vectors .DELTA.D from the 
equation .DELTA.F=S*.DELTA.D, as described above, a knowledge of the 
sensitivity matrix S corresponding to each respective color site or color 
vector F, or in general to each picture element 4, is necessary. To obtain 
this information, the invention also teaches that the corresponding 
half-tone value combination R is calculated from the color vector F of the 
respective picture element 4 according to an additional and particularly 
advantageous calculation method that is described in greater detail below, 
and on the basis of this half-tone value combination R, the corresponding 
sensitivity matrix S is taken from the previously calculated 
half-tone-color table. In this manner, it is possible without an excessive 
amount of computer time and effort to rapidly determine the required 
sensitivity matrix for each picture element 4. 
The invention also teaches that, in the half-tone space, a number of, for 
example, 1296 equidistant discrete half-tone value combinations R.sub.iR 
(6 each discrete half-tone percentages A.sub.C, A.sub.G, A.sub.M, A.sub.S 
for the ink colors cyan, yellow, magenta and black) can be determined as 
follows: 
______________________________________ 
I 0 1 2 3 4 5 
______________________________________ 
A.sub.C 0 20 40 60 80 100% 
A.sub.G 0 20 40 60 80 100% 
A.sub.M 0 20 40 60 80 100% 
A.sub.S 0 20 40 60 80 100% 
______________________________________ 
These 1296 discrete half-tone value combinations R.sub.iR are numbered 
sequentially according to the following formula with a unique half-tone 
index iR: 
EQU iR=i(A.sub.C)*5.sup.0 +i(A.sub.G)*5.sup.1 +i(A.sub.M)*5.sup.2 
i(A.sub.S)*5.sup.3 
i(AC) . . . is thereby defined as the value of the index i for the 
respective discrete half-tone value of the respective color. For each of 
these 1296 discrete half-tone value combinations R.sub.iR, a sensitivity 
matrix S.sub.iR is calculated and stored in the half-tone-color table. The 
calculated color vector F.sub.iR corresponding to the discrete half-tone 
value combinations R.sub.iR is also stored in the table. In total, 
therefore, the half-tone-color table RFT contains 1296 color vectors 
R.sub.IR and 1296 corresponding sensitivity matrices S.sub.iR. 
The quantification of the half-tone space is preferably done in two stages. 
In the first stage, the corresponding color vectors and the corresponding 
sensitivity matrices are calculated for only 256 discrete half-tone value 
combinations (corresponding to four discrete half-tone percentages 0%, 
40%, 80% and 100% for each of the colors cyan, yellow, magenta and black), 
using the offset printing model. In the second stage, the corresponding 
color vectors and sensitivity matrices for the missing half-tone 
percentages 20% and 60% are calculated by linear interpolation from the 
color vectors and sensitivity matrices of the respective 16 closest 
discrete half-tone value combinations. 
The result is a total of, again, 1296 discrete half-tone value combinations 
R.sub.iR with 1296 corresponding discrete color vectors F.sub.iR and 1296 
corresponding sensitivity matrices S.sub.iR. Of course, the half-tone 
space can also be reduced to another number of discrete half-tone 
combinations, for example 625 or 2401, although the number 1296 represents 
a substantially optimal compromise between accuracy and computer time in 
actual practice. 
A color vector F determined for a picture element 4 is then assigned to the 
sensitivity matrix, the corresponding discrete half-tone value combination 
R.sub.iR of which is closest to the half-tone value combination R 
calculated from the color vector F. In other words, the calculated 
half-tone value combination R is replaced by the respective closest 
discrete half-tone value combination R.sub.iR and is given the previously 
calculated sensitivity matrix S.sub.iR for this discrete half-tone value 
combination R.sub.iR. 
In one variant of the method, the half-tone value combinations (R.sub.iR) 
and the color value gradients (S.sub.iR) can be determined by 
interpolation from the half-tone color table (RFT). 
The invention also teaches, for the determination of the half-tone value 
combination R from the color vector F, that the color space (including the 
infrared value I four-dimensionally) is subjected to a quantification, 
i.e. it is divided into a number of sub-spaces. For that purpose, in the 
color space, a number of discrete color sites F.sub.iF, each with discrete 
coordinates, are defined. The quantification of the four-dimensional color 
space can be done, for example, so that each dimension L, a, b, I of the 
color space can assume only 11 discrete values, which gives a total of 
14,641 discrete color sites F.sub.iF : 
______________________________________ 
I 0 1 2 3 4 5 6 7 8 9 10 
______________________________________ 
L 0 10 20 30 40 50 60 70 80 90 100 
a -75 -60 -45 -30 -15 0 15 30 45 60 75 
b -45 -30 -15 0 15 30 45 60 75 90 105 
l 0 10 20 30 40 50 60 70 80 90 100 
______________________________________ 
These 14,641 discrete color sites F.sub.iF are numbered with a unique color 
site index iF according to the formula indicated below: 
EQU iF=i(L)*11.sup.0 +i(a)*11.sup.1 +i(b)*11.sup.2 +i(I)*11.sup.3 
For these discrete color sites F.sub.iF of the color space, the 
particularly advantageous calculation method described in greater detail 
is used to find the corresponding half-tone value combinations R.sub.iF, 
and, to the extent that they do not coincide with a discrete half-tone 
value combination R.sub.iR, they are replaced by the respective closest 
discrete half-tone value combination R.sub.iR. The result is a unique, 
previously calculated simulation of the 14,641 discrete color sites 
F.sub.iF of the (four-dimensional) color space on the 1296 discrete 
half-tone value combinations R.sub.iR of the (likewise four-dimensional) 
half-tone space. This simulation, as noted above, is calculated in advance 
and is stored in a table designated the half-tone index table (RIT) below. 
To determine the half-tone value combinations R from the color vectors F 
determined for the picture elements 4, each color vector F determined for 
a picture element 4 is replaced by the closest discrete color site 
F.sub.iF. From the half-tone index table RIT, the discrete half-tone value 
combination R.sub.iR corresponding to this discrete color site F.sub.iF is 
taken, and on the basis of this R.sub.iR, the corresponding sensitivity 
matrix S.sub.iR is read from the half-tone color table RFT, establishing a 
correspondence with the color vector F and thus the picture element 4. In 
this manner, using relatively little computer time and capacity, for each 
arbitrary picture element 4, the sensitivity matrix S can be determined on 
the basis of the color vector F with sufficient precision for practical 
purposes. 
In the preceding portion of the explanation, it was assumed that the 
corresponding half-tone value combinations R can be calculated from the 
color vectors F. The following sections explain an additional essential 
teaching of the invention, namely how this can be done particularly 
advantageously. 
First the (four-dimensional) color space is divided into 81 partial areas 
T.sub.iT as follows: 
__________________________________________________________________________ 
I 0 1 2 
__________________________________________________________________________ 
L(0 . . . 120) 
0 . . . 20 . . . 40 
40 . . . 60 . . . 80 
80 . . . 100 . . . 120 
a(-90 . . . +90) 
-90 . . . -60 . . . -30 
-30 . . . 0 . . . +30 
+30 . . . +60 . . . +90 
b(-60 . . . +120) 
-60 . . . -30 . . . 0 
0 . . . +30 . . . +60 
+60 . . . +90 . . . +120 
I(0 . . . 120) 
0 . . . 20 . . . 40 
40 . . . 60 . . . 80 
80 . . . 100 . . . 120 
__________________________________________________________________________ 
The total of 81 partial areas T.sub.iT are assigned a unique identifying 
partial area index iT according to the following formula: 
EQU iT=i(L)*3.sup.0 +i(a)*3.sup.1 +i(b)*3.sup.2 +i(I)*3.sup.3 
Within each partial area T.sub.iT, the relationship between the color 
vector F and the corresponding half-tone value combination R written as a 
half-tone vector A is given a linear approximation by the following matrix 
equation: 
EQU A=U.sub.iT *F 
where A is the half-tone vector with the half-tone percentage values 
A.sub.C, A.sub.G, A.sub.M, A.sub.S of the four colors being used as 
components, and U.sub.iT is a conversion matrix with 16 coefficients which 
are the partial derivations (gradients) of the components of the half-tone 
vector according to the components of the color vector. If the conversion 
matrices U.sub.iT of the individual partial areas T.sub.it are known, then 
for each color vector F, the corresponding half-tone vector A or the 
corresponding half-tone value combination R can be calculated. 
The problem is therefore reduced to the calculation of the conversion 
matrices U.sub.iT for the individual partial areas T.sub.iT, or more 
accurately for the color vectors F.sub.iT of their midpoints. The 
calculation of the conversion matrices is performed on the basis of a 
weighted linear equation to calculate the most probable values with the 
values of the half-tone color table RFT described above, i.e. the 1296 
discrete half-tone value combinations R.sub.iR and the corresponding 
discrete color vectors F.sub.iR. For the equation to calculate the most 
probable values, the essential requirement for each partial area T.sub.iT 
is essentially only the inversion of a 4.times.4 matrix. The weight of the 
interpolation nodes, i.e. the discrete color sites F.sub.iR of the 
half-tone color table, for the calculation of the most probable values, is 
determined on the basis of a suitable function with the color difference 
between the interpolation nodes and the respective color vector F.sub.iT 
as a parameter. The calculation of the most probable values is linear, 
i.e. there are discontinuities at the transitions between the individual 
partial areas T.sub.iT, but they are irrelevant for actual practical 
applications. 
The sensitivity matrices S determined on the basis of the above 
explanations for the individual picture elements 4, or the color value 
gradients that form these matrices, can now be used for the calculation of 
the input variables described above for the regulation of the inking of 
the printing press. 
One feature of the invention resides broadly in the method for the 
determination of the color value gradients of a picture element of a 
printed image when there are changes in the layer thicknesses of the inks 
used in the printing, whereby the picture element is photo-electrically 
scanned in the visible region of the spectrum, and the color value 
gradients are derived from the scanning signals thereby obtained, 
characterized by the fact that from the scanning signals of the visible 
region of the spectrum, color coordinates (L,a,b) of an approximately 
subjectively equidistant color system are formed, that the picture element 
4 is also scanned photo-electrically in the near-infrared region of the 
spectrum, that from the scanning signals of the infrared range, at least 
one infrared value is formed I, and that the color value gradients S are 
calculated from the color coordinates and the at least one infrared value. 
Another feature of the invention resides broadly in the method 
characterized by the fact that the color coordinates and the infrared 
value color value gradients S are taken from a pre-defined table. 
Yet another feature of the invention resides broadly in the method 
characterized by the fact that the table is calculated using a 
mathematical model of the printing press 1 used to produce the printed 
image from measurements taken on the full-tone areas printed with the 
printing press 1, and taking into consideration the characteristics of the 
printing press 1. 
Still another feature of the invention resides broadly in the method 
characterized by the fact that for a specified first number of discrete 
half-tone value combinations R.sub.iR, color value gradients SIR 
corresponding to the colors used in the printing are calculated and stored 
in a half-tone color table RFT, that for the picture element 4, the 
corresponding half-tone value combination R of the colors used in the 
printing is calculated from the color coordinates L,a,b and the at least 
one infrared value I, and that the color value gradients S.sub.iR from the 
half-tone color table RFT are assigned to the picture element 4, when the 
corresponding discrete half-tone value combination R.sub.iR of the 
gradients in question is closest to the half-tone value combination R 
calculated for the picture element 4. 
A further feature of the invention resides broadly in the method 
characterized by the fact that a four-dimensional color space is formed, 
the coordinates of which are the color coordinates L,a,b and the infrared 
value I, that in this four-dimensional color space, a specified second 
number of discrete color sites F.sub.iF are defined, for each of these 
discrete color sites the corresponding half-tone value combination R of 
the colors used in the printing is calculated, this half-tone combination 
R is replaced by the closest discrete half-tone value combination R.sub.iR 
taken from the half-tone color value table RFT and the discrete color 
sites F.sub.iF are stored in correspondence to the discrete half-tone 
value combinations R.sub.iR in a half-tone index table RIT, and that for 
the determination of the color value gradients of the picture element 4 
from the color coordinates L,a,b and the infrared value I of this picture 
element 4, the coordinates of a color site are formed in the 
four-dimensional color space, this color site is replaced by the closest 
discrete color site F.sub.iF, the discrete half-tone value combination 
R.sub.iR corresponding to this discrete color site F.sub.iF is taken from 
the half-tone index table RIT, the color value gradient S.sub.iR 
corresponding to this discrete half-tone value combination R.sub.iR is 
taken from the half-tone color table RFT, and this color value gradient 
S.sub.iR is assigned to the picture element 4. 
Another feature of the invention resides broadly in the method 
characterized by the fact that the half-tone value combination R.sub.iR 
and the color value gradients S.sub.iR are determined by interpolation 
from the half-tone color table RFT. 
The Commission Internationale de l'Eclairage, or International Commission 
on Illumination, (CIE), has a headquarters at Kegelgasse 27, A-1030 Wien, 
AUSTRIA, has been recognized as an international standardization body in 
matters relating to the science and art of lighting. 
The components disclosed in the various publications, disclosed or 
incorporated by reference herein, may be used in the embodiments of the 
present invention, as well as, equivalents thereof. 
The appended drawings in their entirety, including all dimensions, 
proportions and/or shapes in at least one embodiment of the invention, are 
accurate and to scale and are hereby included by reference into this 
specification. 
All or substantially all, of the components and methods of the various 
embodiments may be used with at least one embodiment or all of the 
embodiments, if more that one embodiment is described herein. 
All of the patents, patent applications and publications recited herein, 
and in the Declaration attached hereto, are hereby incorporated by 
reference as if set forth in their entirety herein. 
The corresponding foreign patent publication applications, namely, Federal 
Republic of Germany Patent Application No. 197 49 064.9, filed on Nov. 6, 
1997, having inventors Hans Ott and Kurt Ruegg, and DE-OS 197 49 064.6 and 
DE-PS 197 49 064.6, as well as their published equivalents, and other 
equivalents or corresponding applications, if any, in corresponding cases 
in the Federal Republic of Germany and elsewhere, and the references cited 
in any of the documents cited herein, are hereby incorporated by reference 
as if set forth in their entirety herein. 
The details in the patents, patent applications and publications may be 
considered to be incorporable, at applicant's option, into the claims 
during prosecution as further limitations in the claims to patentably 
distinguish any amended claims from any applied prior art. 
Although only a few exemplary embodiments of this invention have been 
described in detail above, those skilled in the art will readily 
appreciate that many modifications are possible in the exemplary 
embodiments without materially departing from the novel teachings and 
advantages of this invention. Accordingly, all such modifications are 
intended to be included within the scope of this invention as defined in 
the following claims. In the claims, means-plus-function clause are 
intended to cover the structures described herein as performing the 
recited function and not only structural equivalents but also equivalent 
structures. 
The invention as described hereinabove in the context of the preferred 
embodiments is not to be taken as limited to all of the provided details 
thereof, since modifications and variations thereof may be made without 
departing from the spirit and scope of the invention.