# US 11,906,360 B2 · Generating spectra from tristimulus values

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 11,906,360 B2
- Document ID: US11906360B2
- Status: Granted
- Kind: B2
- Application number: 17/913,845
- Filed: 2020-03-25
- Published: 2023-07-06
- Granted: 2024-02-20
- Earliest claimed: 2020-03-25
- Assignees: GMG GmbH & Co. KG
- Applicants: GMG GmbH & Co. KG
- Inventors: Patrick Herzog
- Web page: https://patentgrep.com/patent/US11906360B2

## CPC

- G01J 3/465: {taking into account the colour perception of the eye; using tristimulus detection}
- G01J 3/462: {Computing operations in or between colour spaces; Colour management systems}
- G01J: MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY (light sources F21, H01J, H01K, H05B; investigating properties of materials by optical means G01N)

## Abstract

To bring color, described by Lab values only, back into the spectral domain the invention discloses a method for automatically generating reflectance spectrum values from tristimulus values using a computer system administrating a database with data matrices of reflectance spectra of different colors differentiated by at least the process parameters print technology, substrate and print order of inks, wherein a) given tristimulus values of a color are classified with regard to the process parameters, b) in the database the data matrices of reflectance spectra of the respective color with the most matching process parameters are identified and c) the identified data matrix is used to define the reflectance spectrum values for the respective color.

## Claims

### Claim 1

Method for automatically generating reflectance spectrum values from tristimulus values using a computer system administrating a database with data matrices of reflectance spectra of different colors differentiated by one or more process parameters, wherein the one or more process parameters include print technology, substrate, and print order of inks, the method comprising:
a) classifying given tristimulus values of a color with regard to the one or more process parameters,
b) identifying in the database a data matrix of reflectance spectra of said color with matches of the one or more process parameters matching most, and
c) using the data matrix of reflectance spectra of said color identified in step b) to define the reflectance spectrum values for said color and selecting the one or more process parameters for a print process as needed, based on the reflectance spectrum values for said color;
wherein the data matrix of reflectance spectra of said color identified in step b) is reduced to basis vector data within a PCA (principal component analysis) process to yield correct tristimulus values of the reflectance spectra, based on an equation
r=μ+(x−μCT)*(BCT)−1B
wherein r be the spectral reflectance, μ be a mean vector of the data matrix of reflectance spectra of said color identified in step b), x be a vector of tristimulus values, C be a color matching function weighted by a given illuminant, and B be a matrix of the PCA (principal component analysis) basis vectors.

### Claim 2 (depends on 1)

Method according to claim 1, further comprising:
d) using the data matrix of reflectance spectra of said color identified in step b) as a reference spectrum to calculate resulting tristimulus values,
e) comparing the calculated tristimulus values to the given tristimulus values to define differences,
f) using the differences to adjust the reference spectrum resulting in a synthesized spectrum.

### Claim 3 (depends on 2)

Method according to claim 2, wherein the adjustment of the reference spectrum is based on an equation
r=ro+(x−roCT)*(BCT)−1B
wherein r be a spectral reflectance, C be the color matching functions, weighted by a given illuminant, x be the vector of tristimulus values CIEXYZ, B be the matrix of 3 chosen basis vectors, ro be the reference spectrum.

### Claim 4 (depends on 3)

Method according to claim 3, wherein B represents the matrix of the first 3 basis vectors resulting from the PCA (principal component analysis) process with the dimension (3×36).

### Claim 5 (depends on 2)

Method according to claim 2, wherein the synthesized spectrum is investigated for negative reflectance and, if negative reflectance exist, further comprising:
i) clipping all spectral samples that are below a given threshold t to said given threshold t to generate a clipped spectrum,
ii) applying a smoothing filter to said clipped spectrum, as the clipping may have introduced edges, to generate a smoothed clipped spectrum, and
iii) using the smoothed clipped spectrum as the reference spectrum.

### Claim 6 (depends on 5)

Method according to claim 5, wherein the given threshold t is t>0.

### Claim 7 (depends on 5)

Method according to claim 5, further comprising transforming the tristimulus values and the reference spectrum into a non-linear domain by applying a non-linear transfer function r′=f(r), the non-linear transfer function being a root function, and reducing the tristimulus values and the reference spectrum within the PCA (principal component analysis) process to produce revised basis vector data of reflectance spectra.

### Claim 8 (depends on 1)

Method according to claim 1, wherein the data base is a database with generic basis vector data of reflectance spectra of different colors, further comprising using a further data base with process related data matrices of reference spectra of different colors so that the specific properties of the process are then taken from the reference spectra, while a correction shift is performed by using the generic basis vectors.

### Claim 9 (depends on 1)

Method according to claim 1, further comprising producing a number of different reflectance spectra sets and evaluating a quality of the number of different reflectance spectra sets with regard to a success of the spectral synthesis to decide for a best result.