Method of and apparatus for pattern recognition
First Claim
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1. A method of recognizing a pattern in a test object, said method comprising the steps of:
- specifying properties characteristic of said pattern;
specifying discrete ranges of values of said properties;
measuring the values of said properties in said test object;
arranging the measured values in at least one test histogram;
determining a reference set of values of said properties and arranging said set as at least a first reference histogram; and
comparing said test and reference histograms by determination of the value of a function which provides a measure of the amount of information necessary to express said at least one test histogram in terms of the optimum code for describing at least said first reference histogram.
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Abstract
A method of and an apparatus for analysis of patterns both in static and dynamic modes. A test histogram is described in terms of the optimum code described for a reference histogram.
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Citations
52 Claims
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1. A method of recognizing a pattern in a test object, said method comprising the steps of:
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specifying properties characteristic of said pattern; specifying discrete ranges of values of said properties; measuring the values of said properties in said test object; arranging the measured values in at least one test histogram; determining a reference set of values of said properties and arranging said set as at least a first reference histogram; and comparing said test and reference histograms by determination of the value of a function which provides a measure of the amount of information necessary to express said at least one test histogram in terms of the optimum code for describing at least said first reference histogram. - View Dependent Claims (2, 3, 4, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37)
- 29. A method as defined in claim 1 wherein said function is
- space="preserve" listing-type="equation">H(T;
R)-H(T;
T)
where ##EQU19## T is a test histogram;
R is a reference histogram;H(T;
R) is the entropy of T expressed in terms of R;b is the base of the logarithm; mi is the number of occurrences of the ith symbol in T; pi is the probability of the ith symbol occurring in R; Q is the number of different symbols in T;
##EQU20## H(T;
T) is the entropy of T expressed in terms of T; and
pi '"'"'is the probability of the ith symbol occurring in T. - space="preserve" listing-type="equation">H(T;
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- 30. A method as defined in claim 1 wherein said function is
- space="preserve" listing-type="equation">I(T;
R)-I(R;
R)
where ##EQU21## T is a test histogram;
R is a reference histogram;I(T;
R) is the information of T expressed in terms of R;b is the base of the logarithm; mi is the number of occurrences of the ith symbol in T; pi is the probability of the ith symbol occurring in R; Q is the number of different symbols in T;
##EQU22## I(R;
R) is the information of R expressed in terms of R, and ni is the number of occurrences of the ith symbol in R. - space="preserve" listing-type="equation">I(T;
- space="preserve" listing-type="equation">H(T;
R)-H(R;
R)
R is a reference histogram;
R) is the entropy of T expressed in terms of R;
##EQU24## H(R;
R) is the entropy of R expressed in terms of R;
##EQU25## ni is the number of occurrences of the ith symbol in R.
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and wherein said function is H(T;
T) and is defined as ##EQU26## wherein T is a test histogram;
H(T;
T) is the entropy of T expressed in terms of T;b is the base of the logarithm; mi is the number of occurrences is the ith symbol in T; pi '"'"' is the probability of the ith symbol occurring in T; Q is the number of different symbols in T;
##EQU27## and wherein said properties are (a) position in a field of view of said test object, and (b) the nature of the signals arising from said position, said comparison values are assigned to a position at the geometric center of said field of view, and said field is scanned over the original digitized image to produce an enhanced digitized image.
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5. A method of recognizing a pattern in a test object, said method comprising the steps of:
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specifying properties characteristic of said pattern; specifying discrete ranges of values of said properties, measuring the values of said properties in said test object; determining the number of such measured values falling in each said discrete range and arranging such number in each said range in at least one test histogram; determining a reference set of values of said properties and arranging said set as at least a first reference histogram; and comparing said test and reference histograms by determination of the value of a function which provides a measure of the amount of information necessary to express said at least one test histogram in terms of the optimum code for describing at least said first reference histogram. - View Dependent Claims (6, 7, 8)
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38. Apparatus for recognizing a pattern in a test object, said apparatus comprising, in combination:
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means for measuring in said test object the values of specified properties characteristic of said pattern, means for arranging the measured values of said properties in at least one test histogram; means for storing a reference set of values of said specified properties as at least a first reference histogram; means for comparing said test and reference histograms by determination of the value of a function which provides a measure of the amount of information necessary to express said at least one test histogram in terms of the optimum code for describing at least said first reference histogram. - View Dependent Claims (39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52)
- 50. Apparatus according to claim 38 wherein said function is
- space="preserve" listing-type="equation">H(T;
R)-H(T;
T)
where ##EQU36## T is a test histogram;
R is a reference histogram;H(T;
R) is the entropy of T expressed in terms of R;b is the base of the logarithm; mi is the number of occurrences of the ith symbol in T; pi is the probability of the ith symbol occurring in R; Q is the number of different symbols in T;
##EQU37## H(T;
T) is the entropy of T expressed in terms of T, and pi '"'"' is the probability of the ith symbol occurring in T. - space="preserve" listing-type="equation">H(T;
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- 51. Apparatus according to claim 38 wherein said function is
- space="preserve" listing-type="equation">I(T;
R)-I(R;
R)
where ##EQU38## T is a test histogram;
R is a reference histogram;I(T;
R) is the information of T expressed in terms of R;b is the base of the logarithm; mi is the number of occurrences of the ith symbol in T; pi is the probability of the ith symbol occurring in R; Q is the number of different symbols in T;
##EQU39## I(R;
R) is the information of R expressed in terms of R, and ni is the number of occurrences of the ith symbol in R. - space="preserve" listing-type="equation">I(T;
- space="preserve" listing-type="equation">H(T;
R)-H(R;
R)
R is a reference histogram;
R) is the entropy of T expressed in terms of R;
##EQU41## H(R;
R) is the entropy of R expressed in terms of ##EQU42## ni is the number of occurrences of the ith symbol in R.
Specification