Texture analysis of a coated surface using pivot-normalization

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.

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.