# US 10,481,081 B2 · Texture analysis of a coated surface using pivot-normalization > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 10,481,081 B2 - Document ID: US10481081B2 - Status: Granted - Kind: B2 - Application number: 14/535,380 - Filed: 2014-11-07 - Published: 2015-05-14 - Granted: 2019-11-19 - Earliest claimed: 2013-11-08 - Assignees: PPG Industries Ohio, Inc. - Applicants: PPG Industries Ohio, Inc. - Inventors: Alison M. Norris - Web page: https://patentgrep.com/patent/US10481081B2 ## CPC - G01N 21/25: Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands - G01J 3/463: {Colour matching} - G01N 21/55: Specular reflectivity - G01J 2003/466: {Coded colour; Recognition of predetermined colour; Determining proximity to predetermined colour} - G01N 2201/125: Digital circuitry - G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q) - 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 A method that includes obtaining, using a processor, reflectance data from a target coating and calculating, using the processor, pivot-normalized reflectance data. The method also includes generating, using the processor, a coating formulation that is the same or substantially similar in appearance to the target coating. ## Claims ### Claim 1 A computer implemented method for efficiently analyzing multi-angle reflectance data taken from a multi-angle spectrophotometer and generating a matched coating, comprising: obtaining, using a processor, reflectance data from a target coating, wherein the obtained data comprise color responses taken from multiple angles, and the obtained data comprise two or more associated arrays including a primary array of angle data, and a secondary array of at least wavelength data; sorting, via the processor, the obtained data by the wavelength data in the secondary array; calculating, using the processor, pivot-normalized reflectance data according to: X - μ σ Equation ⁢ ⁢ ( 1 ) wherein: X is a specific data set value, μ is a sample or population average of the data set values within the secondary array, and σ is a sample or population standard deviation of the data set values within the sorted secondary array; generating a normalized, wavelength sorted hemispherical map based upon the angle data associated with the reflectance data; and based upon the normalized, wavelength sorted hemispherical map, generating, using the processor, a coating formulation that is the same in appearance to the target coating; wherein generating the coating formulation comprises: empirically correlating the wavelength-sorted reflectance data for the target coating to reflectance data sorted by wavelength for an empirical dataset; and predicting at least one texture feature of the target coating based on the correlation in reflectance data among wavelength-sorted data sets. ### Claim 2 (depends on 1) The method of claim 1, wherein predicting at least one texture feature comprises determining from the empirical correlation that a gonioapparent pigment is present. ### Claim 3 (depends on 2) The method of claim 2, further comprising determining from the empirical correlation which particular gonioapparent pigment is present at a particular flake size. ### Claim 4 (depends on 2) The method of claim 2, further comprising: determining that a first texture feature is associated with one or more first angles of reflectance data taken from the spectrophotometer. ### Claim 5 A system comprising a computer system, a processor, and a spectrophotometer in communication over a network, the system for efficiently analyzing multi-angle reflectance data taken from a multi-angle spectrophotometer and generating a matched coating, comprising: a database; and a processor in communication with the database and programmed to: obtain reflectance data from a target coating, wherein the obtained data comprise color responses taken from multiple angles, and the obtained data comprise two or more associated arrays including a primary array of angle data, and a secondary array of colorimetric data; sort, via the processor, the obtained data by the colorimetric data in the secondary array; calculate pivot-normalized reflectance data, according to: X - μ σ Equation ⁢ ⁢ ( 1 ) wherein: X is a specific data set value, μ is a sample or population average of the data set values within the secondary array, and a is a sample or population standard deviation of the data set values within the sorted secondary array; generate a normalized, wavelength sorted hemispherical map based upon the angle data associated with the reflectance data; and based upon the normalized, wavelength sorted hemispherical map, generate a coating formulation that is the same in appearance to the target coating; wherein generating the coating formulation comprises: empirically correlating the colorimetric-sorted reflectance data for the target coating to reflectance data sorted by colorimetric data for an empirical dataset; and predicting at least one texture feature of the target coating based on the correlation in reflectance data among wavelength-sorted data sets. ### Claim 6 (depends on 5) The system of claim 5, wherein the system is further programmed to: determine from the empirical correlation that a gonioapparent pigment is present. ### Claim 7 (depends on 5) The system of claim 5, wherein the system is further programmed to: determine from the empirical correlation which particular gonioapparent pigment is present at a particular flake size. ### Claim 8 (depends on 5) The system of claim 5, wherein the system is further programmed to: determine from the empirical correlation which particular gonioapparent pigment is present at a particular flake size; and determine that a first texture feature is associated with one or more first angles of reflectance data taken from the spectrophotometer. ### Claim 9 A non-transitory computer readable medium including software comprising computer-executable instructions that, when executed, cause a processor to: obtain reflectance data from a target coating, wherein the obtained data comprise color responses taken from multiple angles, and the obtained data comprise two or more associated arrays including a primary array of angle data, and a secondary array of wavelength data or colorimetric data; sort, via the processor, the obtained data by the wavelength data or colorimetric data of the secondary array; calculate pivot-normalized reflectance data, according to: X - μ σ Equation ⁢ ⁢ ( 1 ) wherein: X is a specific data set value, μ is a sample or population average of the data set values within the secondary array, and a is a sample or population standard deviation of the data set values within the sorted secondary array; generate a normalized, wavelength sorted hemispherical map based upon the angle data associated with the reflectance data; and based upon the normalized, wavelength sorted hemispherical map, generate a coating formulation that is the same in appearance to the target coating; wherein generating the coating formulation comprises: empirically correlating the wavelength- or colorimetric-sorted reflectance data for the target coating to wavelength- or colorimetric-sorted reflectance data calculated for an empirical dataset; and predicting at least one texture feature of the target coating based on the correlation in reflectance data.