Color separating method and apparatus using statistical techniques

Claim 1

An apparatus for analyzing the colors of a print painted with n distinct colors C i where i ranges from unity to n, and wherein each of the colors has a predetermined spectral reflectivity distribution having a set of mean values of reflectivities, comprising: first means for representing the spectral reflectivity distribution of a light reflected from an elemental area of the print by electrical signals x 1 to x r , where x represents the spectral intensity r representing a position in the color spectrum is an integer, and wherein the spectral intensity varies as random variables of multiple numbers in accordance with a predetermined conditional probability density function p(x|C i ); second means for representing the spectral reflectivity distribution per unit area of said print by electrical signal X' 1 to X' n ; means for multiplying the set of X' 1 to X' n and the inverse matrix of said mean values of reflectivities to generate a probability P(C i ) in accordance with which each of said colors occurs in said print; means for computing the product P(C i )p(x|C i ) by substituting x 1 to x r for x; and means for detecting C i which maximizes the value of said product.

Claim 2

An apparatus for analyzing the colors of a print painted with n distinct colors C i where i ranges from unity to n, and wherein each of the colors has a predetermined spectral reflectivity distribution having a set of mean values of reflectivities, comprising: first means for representing the spectral reflectivity distribution of a light reflected from an elemental area of the print by electrical signals x 1 to x r , where x represents the spectral intensity r representing a position in the color spectrum is an integer, and wherein the spectral intensity varies as random variables of multiple numbers in accordance with a predetermined conditional probability density function p(x|C i ); second means for representing the spectral reflectivity distribution per unit area of said print by electrical signal X' 1 to X' n ; means for multiplying the set of X' 1 to X' n and the inverse matrix of said mean values of reflectivities to generate a probability P(C i ) in accordance with which each of said colors occurs in said print; means for computing the product P(C i )p(x|C i ) by substituting x 1 to x r for x; and means for detecting C i which maximizes the value of said product.

Claim 14

An apparatus for analyzing the colors of a print painted with N distinct colors C i where i ranges from unity to N, and wherein each of the colors has a predetermined spectral reflectivity distribution which substantially follows a normal density function of multiple random variables, said apparatus comprising: a variable range focus lens system for collecting light reflected from an elemental area of the print and a larger area encompassing a plurality of such elemental areas; means for separating the collected light into a plurality of spectral components; means for converting the separated spectral components into corresponding first electrical quantities x l to x n when said lens system is at a first range focus to provide collection of light from the elemental area and into second electrical quantities X 1 to X n when said lens system is at a second range focus to provide collection of light from the larger area; means for demultiplying the second electrical quantities X 1 to X n by the size of said larger area to derive third electrical quantities X 1 ' to X n ' representing the spectral reflectivity per unit area of the larger area; means coupled to said converting means for generating fourth electrical quantities μ l .sup.(i) to μ n .sup.(i) representing a set of mean values of said first electrical quantities x l to x n ; first means for mathematically manipulating said fourth electrical quantities to produce an inverse matrix of said fourth electrical quantities; means for multiplying said third electrical quantities X 1 ' to X n ' by said inverse matrix to generate fifth electrical quantities representing a probability P(C i ) in accordance with which of said colors appears in said print; second means for mathematically manipulating said fifth electrical quantities with a conditional probability density function p(x|C i ) by substituting x l to x n for x to produce products P(C i )p(x 1 |C i ) to P(C i ) p (x N |C i ); and means for detecting a C i which maximizes the value of said products.

Claim 15

An apparatus for analyzing the colors of a print painted with N distinct colors C i where i ranges from unity to N, and wherein each of the colors has a predetermined spectral reflectivity distribution which substantially follows a normal density function of multiple random variables, said apparatus comprising: a variable range focus lens system for collecting light reflected from an elemental area of the print and a larger area encompassing a plurality of such elemental areas; means for separating the collected light into a plurality of spectral components; means for converting the separated spectral components into corresponding first electrical quantities x l to x n when said lens system is at a first range focus to provide collection of light from the elemental area and into second electrical quantities X 1 to X n when said lens system is at a second range focus to provide collection of light from the larger area; means for demultiplying the second electrical quantities X 1 to X n by the size of said larger area to derive third electrical quantities X 1 ' to X n ' representing the spectral reflectivity per unit area of the larger area; means coupled to said converting means for generating fourth electrical quantities μ l .sup.(i) to μ n .sup.(i) representing a set of mean values of said first electrical quantities x l to x n ; first means for mathematically manipulating said fourth electrical quantities to produce an inverse matrix of said fourth electrical quantities; means for multiplying said third electrical quantities X 1 ' to X n ' by said inverse matrix to generate fifth electrical quantities representing a probability P(C i ) in accordance with which of said colors appears in said print; second means for mathematically manipulating said fifth electrical quantities with a conditional probability density function p(x|C i ) by substituting x l to x n for x to produce products P(C i )p(x 1 |C i ) to P(C i ) p (x N |C i ); and means for detecting a C i which maximizes the value of said products.

Claim 20

A method for analyzing a print painted with n different colors C i to form a colored pattern, where i ranges from unity to n, wherein each of the areas painted with a same color has a particular intensity distribution in the color spectrum with a tendency to vary as random variables from a distribution of mean values in accordance with a predetermined conditional probability density function p(x|C i ) where x represents the spectral intensity of an elemental area, and each of the painted areas of the same color has a probability of occurrence P(C i ) in said print, comprising: placing said print with respect to a first optical system; collecting spectral information from a predetermined area within said print with said optical system; selectively filtering said collected spectral information to produce macroscopic spectral data of said predetermined area; converting said macroscopic spectral data into macroscopic electronic data; demultiplying the converted data by the size of said predetermined area to produce electronic data representing spectral data per unit area of said predetermined area; mathematically manipulating said demultiplied electronic data and said mean values to determine said probability P(C i ); placing said print with respect to a second optical system; scanning said print with said second optical system along each of a plurality of line paths; selectively filtering the output from said second optical system to produce microscopic spectral data representing said spectral intensity x; converting said microscopic spectral data x into microscopic electronic data x; mathematically manipulating said conditional probability density function p(x|C i ) with said converted electronic data x to determine the conditional probabilities of said electronic data x given that said data x belong to a said C i and manipulating said probability P(C i ) with said conditional probabilities to produce a set of products of said probability and said conditional probability; and detecting a C i which maximizes said products.

Claim 21

A method for analyzing a print painted with n different colors C i to form a colored pattern, where i ranges from unity to n, wherein each of the areas painted with a same color has a particular intensity distribution in the color spectrum with a tendency to vary as random variables from a distribution of mean values in accordance with a predetermined conditional probability density function p(x|C i ) where x represents the spectral intensity of an elemental area, and each of the painted areas of the same color has a probability of occurrence P(C i ) in said print, comprising: placing said print with respect to a first optical system; collecting spectral information from a predetermined area within said print with said optical system; selectively filtering said collected spectral information to produce macroscopic spectral data of said predetermined area; converting said macroscopic spectral data into macroscopic electronic data; demultiplying the converted data by the size of said predetermined area to produce electronic data representing spectral data per unit area of said predetermined area; mathematically manipulating said demultiplied electronic data and said mean values to determine said probability P(C i ); placing said print with respect to a second optical system; scanning said print with said second optical system along each of a plurality of line paths; selectively filtering the output from said second optical system to produce microscopic spectral data representing said spectral intensity x; converting said microscopic spectral data x into microscopic electronic data x; mathematically manipulating said conditional probability density function p(x|C i ) with said converted electronic data x to determine the conditional probabilities of said electronic data x given that said data x belong to a said C i and manipulating said probability P(C i ) with said conditional probabilities to produce a set of products of said probability and said conditional probability; and detecting a C i which maximizes said products.