System for composing color transforms using class information

Details System for composing color transforms using class information System for composing color transforms using class information

1999-05-13

2001-08-21

Grant, II, Jerome (Department: 2624)

Image analysis

Image transformation or preprocessing

C345S156000

Reexamination Certificate

active

06278805

ABSTRACT:

BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention is directed to a system that composes color transforms as needed and, more particularly, to a system where the accuracy of a composed transform is improved by automatically selecting the input and output transforms of the composed transform, based on the classes of the transforms in the sequence to be composed.
2. Description of the Related Art
Complex mathematical functions, such as color transform functions, are often represented by tabular functions, which are tables containing function values. Each value in the table is the value of the function for a particular set of input values. The complete table is made by calculating and storing in the table the output values of the function at a uniform sampling over the desired range of input values. The tabular function is evaluated by finding the table entries which are closest to the input values and then interpolating between the tabulated values to produce an approximation to the actual value of the function.
FIG. 1
depicts a one-dimensional tabular function y=f(x) where calculated values
12
are stored in the table
10
and an input value (x) selects a table entry
14
which contains the output value (y).
FIG. 2
illustrates a three-dimensional tabular function t=f(x,y,z) where calculated values are stored in a table
16
and input values (x,y,z) select a table entry
18
which is the output value (t).
This method of evaluating complex functions has several advantages in a computer system. It can represent complex functions very compactly, the functions can be evaluated very quickly, and two tabular functions can be combined (or composed) into a single tabular function.
The method has the disadvantage of reduced accuracy, which are caused by a number of factors collectively referred to as interpolation error. Several techniques have been developed to reduce interpolation error, such as increasing the number of tabular function values and using different interpolation methods. Another common method is to construct the tabular function as a series of tabular functions which are evaluated in a specific sequence to produce the overall, or net, function value.
One particular method, commonly used for color transformation functions, combines a set of nine tabular functions into a grouped tabular function (GTF) as depicted in FIG.
3
. It could be used, for example, for the conversion between the RGB for a scanner and RGB for a monitor, which requires three functions, each of which is a function of the same three inputs: f1(r, g, b)=r′, f2(r, g, b)=g′, and f3(r, g, b)=b′.
The first three tabular functions form a set of one dimensional tables in which there is one tabular function for each input value (x′=f1(x), y′=f2(y), z′=f3(z)). These are the “input” tables
32
,
34
and
36
. The second three tabular functions form a set of multi-dimensional tables in which each dimension of a table corresponds to a particular input (u′=f4(x′,y′,z′), v′=f5(x′,y′,z′), w′=f6(x′,y′,z′)). These are the “grid” or “lattice” tables
38
,
40
and
42
. The last three tabular functions form a set of one dimensional tables which produce the actual function values (u=f7(u′), v=f8(v′), w=f9(w′)). These are the “output” tables
44
,
46
and
48
. This is the input tables (I), lattice tables (L), and output tables (O) or ILO form of a GTF
52
as depicted in FIG.
4
. Judicious partitioning of the mathematical functions being represented by the GTF into the three tabular functions can dramatically reduce the interpolation error of the GTF.
It is common to use two tabular functions sequentially and is therefore useful to combine the two tabular functions into a single net tabular function using functional composition. The net tabular function uses the input value of the first tabular function and produces output function values of the second tabular function.
A sequence of two GTFs
62
and
64
in the ILO form, that is, GTF
1
followed by GTF
2
as depicted in
FIG. 5
, is typically composed into a net GTF
66
as follows:
1) form the net GTF with the same input and lattice table sizes as GTF
1
and the output table sizes of GTF
2
.
2) copy the input table entries of GTF
1
into the net GTF input table entries.
3) copy the output table entries of GTF
2
into the net GTF output table entries.
4) calculate the net GTF lattice tables:
for each lattice table position m
for each GTF
1
lattice table n
get the GTF
1
lattice table value LTVALUE at position m
apply LTVALUE to GTF
1
output table n to get OTVALUE
apply OTVALUE to GTF
2
input table n to get OIVALUE
store OIVALUE in position n of the set of input values
for each net GTF lattice table n apply the set of input values to GTF
2
lattice table n to get LTVALUE
store LTVALUE into net GTF lattice table n at position m
The net GTF has: 1) input tables which are the same as the input tables of GTF
1
, 2) output tables which are the same as GTF
2
, and 3) lattice tables which are the combination of the lattice tables of GTF
1
, the output tables of GTF
1
, the input tables of GTF
2
, and the lattice tables of GTF
2
.
However, this partitioning of the net GTF into its constituent tabular functions may not be optimal for the mathematical function that it represents, i.e. the input tables of GTF
1
and the output tables of GTF
2
may not be the most judicious selection of input and output functions for the net function.
One method of reducing interpolation error is to add pre-existing and previously created prefix and suffix identity GTFs to the beginning and end of the sequence of GTFs and create a net GTF from the prefix, sequence GTF(s) and suffix GTF. The pre-existing identity GTFs are designed for known or pre-existing sequence GTFs and various known combinations thereof. When the previously described method of functional composition is used, this results in a net GTF which has the input tables of the prefix GTF and the output tables of the suffix GTF. If the input and output tables are appropriate for the net GTF, the interpolation error of the net GTF will be reduced. The identity GTFs are constructed such that each of their functions corresponds to f(x)=x. This is typically done by filling the input tables with the values of the desired input functions, filling the lattice table entries with an identity function, and filling the output tables with the inverse of the function in the input tables.
For this method to work properly, the prefix and suffix GTFs must be selected carefully, because an improper choice could easily result in greater interpolation error. One method of selecting the prefix and suffix GTFs is to associate information about the GTFs with the GTFs, in particular information which identifies the specific nature, or type, of the input values for the GTFs and the specific nature, or type, of the output from the GTFs. The specific knowledge of the particular types of the input values (for example, scanner, camera, etc.) and output values (for example, to a paper printer, photo printer, etc.) allows the determination of appropriate functions for the input and output tables of the net GTF. A table
70
as depicted in
FIG. 6
is constructed which lists the specific prefix and suffix GTFs to use for each combination of types. As shown in
FIG. 6
, a particular combination may require using both prefix and suffix GTFs, or neither prefix nor suffix GTF. During operation of this method, the prefix and suffix GTFs discussed above are created ahead of time and stored. At the time a GTF is created, the builder determines, using his experience and knowledge about the color device which provides the input image or receives the output image, which types should be associated with the GTF by reviewing the table of available types. The appropriate types are stored with the GTF. When the GTF is

Affiliated with

Also associated with

Rating

System for composing color transforms using class information does not yet have a rating. At this time, there are no reviews or comments for this patent.

If you have personal experience with System for composing color transforms using class information, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and System for composing color transforms using class information will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFUS-PAI-O-2454314