Patent US5749020A successfully refreshed from Google Patents.
US5749020A
Expired / Lapsed
US
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Coordinitization of tone reproduction curve in terms of basis functions
Assignee: Xerox Corp
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Filing: 1996-11-21
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Granted: 1998-05-05
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Expires: 2016-11-21
Abstract
Abstract Fundamental machine functions such as the Tone Reproduction Curve need to be divided into regions of smaller units so that each unit can be interrelated to some aspects of the internal machine process. A first step toward that is by decomposing measured TRC in terms of what are known as "orthogonal basis functions". Two significant applications for orthogonal basis functions may be extensive use in color controls to maintain color consistency for every page, every time and all the time. The use of basis functions might also lead to a new soft sensor for use in certain machines.
Inventors
- 👤 Lingappa K. Mestha
- 👤 Yao Rong Wang
- 👤 Sohail A. Dianat
- 👤 Pramod P. Khargonekar
- 👤 Daniel E. Koditschek
- 👤 Eric Jackson
- 👤 Tracy E. Thieret
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-29 14:53
CPC Classifications
G; G03; G03G; G03G15/00; G03G15/50; G03G15/5033; G03G15/5041; G03G2215/00; G03G2215/00025; G03G2215/00029; G03G2215/00033; G03G2215/00037; G03G2215/00042
Claims Analysis
Total Claims: 33
Claim 1
Independent Claim
120 words
In an imaging system having a control including a set of actuators for projecting an image onto an imaging surface, a method of machine control comprising the steps of; modeling the imaging system with respect to the actuators for producing a predicted tone reproduction curve, the predicted tone reproduction curve being defined by the expression C.sub.i ≈Ci =α.sub.1i Ψ.sub.1 +α.sub.2i Ψ.sub.2 +α.sub.3i Ψ.sub.3 +C, where α's are coefficients, ψ's are basis functions, and C represents a toner reproduction curve, obtaining a discrete number of tone reproduction samples, melding the predicted tone reproduction curve and the discrete number of tone reproduction samples to provide a reconstructed tone reproduction curve, and responding to the reconstructed tone reproduction curve to control machine operation.
Claim 2
Dependent Claim
120 words
In an imaging system having a control including a set of actuators for projecting an image onto an imaging surface, a method of machine control comprising the steps of; modeling the imaging system with respect to the actuators for producing a predicted tone reproduction curve, the predicted tone reproduction curve being defined by the expression C.sub.i ≈Ci =α.sub.1i Ψ.sub.1 +α.sub.2i Ψ.sub.2 +α.sub.3i Ψ.sub.3 +C, where α's are coefficients, ψ's are basis functions, and C represents a toner reproduction curve, obtaining a discrete number of tone reproduction samples, melding the predicted tone reproduction curve and the discrete number of tone reproduction samples to provide a reconstructed tone reproduction curve, and responding to the reconstructed tone reproduction curve to control machine operation.
Claim 3
Dependent Claim
28 words
The method of claim 1 wherein in the expression, C.sub.i ≈Ci =α.sub.1i Ψ.sub.1 +α.sub.2i Ψ.sub.2 +α.sub.3i Ψ.sub.3 +C, the alpha coefficients are known in terms of said actuators.
Claim 4
Dependent Claim
23 words
The method of claim 1 wherein the actuators include at least one of imaging surface voltage, developer bias voltage, and projecting system power.
Claim 5
Dependent Claim
166 words
In an imaging system having tone reproduction curves for a set of actuators for projecting an image onto an imaging surface, a method of decomposing the tone reproduction curves into basis functions comprising the steps of: defining the complete space of tone reproduction curve variance upon actuator change, approximating to a suitable geometric shape said complete space defined by a covariance matrix of size n×n, defined by ##EQU10## where Σε n ×n and!n equals the total number of samples per tone reproduction curve, C j equals ith TRC, C equals average of N number of TRC's, T represents the matrix transpose, and N equals a set of tone reproduction curves, forming singular value decomposition on the covariance matrix to provide ##EQU11## wherein the vectors, Ψ i , in the equation correspond to an i-th basis function, and π corresponds to the matrix containing eigenvalues, and providing a linear combination of the basis functions representing a complete tone reproduction curve defined by ##EQU12## with α's representing coefficients.
Claim 6
Dependent Claim
166 words
In an imaging system having tone reproduction curves for a set of actuators for projecting an image onto an imaging surface, a method of decomposing the tone reproduction curves into basis functions comprising the steps of: defining the complete space of tone reproduction curve variance upon actuator change, approximating to a suitable geometric shape said complete space defined by a covariance matrix of size n×n, defined by ##EQU10## where Σε n ×n and!n equals the total number of samples per tone reproduction curve, C j equals ith TRC, C equals average of N number of TRC's, T represents the matrix transpose, and N equals a set of tone reproduction curves, forming singular value decomposition on the covariance matrix to provide ##EQU11## wherein the vectors, Ψ i , in the equation correspond to an i-th basis function, and π corresponds to the matrix containing eigenvalues, and providing a linear combination of the basis functions representing a complete tone reproduction curve defined by ##EQU12## with α's representing coefficients.
Claim 7
Dependent Claim
113 words
In an imaging system having tone reproduction curves for a set of actuators for projecting an image onto an imaging surface, a method of decomposing the tone reproduction curves into basis functions comprising the steps of: defining a complete space of tone reproduction curve variance upon actuator change, approximating to a suitable geometric shape said complete space defined by a covariance matrix and a given number of samples per tone reproduction curve and a given subset of tone reproduction curve samples, forming singular value decomposition on the covariance matrix to provide vectors corresponding to an i-th basis function, and providing a linear combination of the basis functions representing a complete tone reproduction curve.
Claim 8
Dependent Claim
113 words
In an imaging system having tone reproduction curves for a set of actuators for projecting an image onto an imaging surface, a method of decomposing the tone reproduction curves into basis functions comprising the steps of: defining a complete space of tone reproduction curve variance upon actuator change, approximating to a suitable geometric shape said complete space defined by a covariance matrix and a given number of samples per tone reproduction curve and a given subset of tone reproduction curve samples, forming singular value decomposition on the covariance matrix to provide vectors corresponding to an i-th basis function, and providing a linear combination of the basis functions representing a complete tone reproduction curve.
Claim 9
Dependent Claim
37 words
The method of claim 5 wherein the tone reproduction curve represented by a linear combination of basis functions is defined by ##EQU13## where α's are coefficients, ψ's are basis functions, and C represents a toner reproduction curve.
Claim 10
Dependent Claim
39 words
The method of claim 5 wherein the tone reproduction curve represented by a linear combination of basis functions is defined by C.sub.i ≈Ci =α.sub.1i Ψ.sub.1 +α.sub.2i Ψ.sub.2 +α.sub.3i Ψ.sub.3 +C, the α coefficients being in terms of said actuators.
Claim 11
Dependent Claim
55 words
The method of claim 5 wherein the covariance matrix defined by ##EQU14## where Σ n ×n and! n equals the total number of samples per tone reproduction curve, C j equals the ith TRC, Cequals average of N number of TRC's, T represents the matrix transpose, and N equals a set of tone reproduction curves.
Claim 12
Dependent Claim
43 words
The method of claim 5 wherein the step of forming singular value decomposition on the covariance matrix includes the step of providing ##EQU15## wherein the vectors, Ψ i , correspond to an i-th basis function and π corresponds to the matrix containing eigenvalues.
Claim 13
Dependent Claim
89 words
In an imaging system for projecting an image onto an imaging surface, the imaging system having a control including actuators and a model of tone reproduction curve response, a method of reconstructing a tone reproduction curve for use in controlling the imaging system operation comprising the steps of: predicting a tone reproduction curve for a given set of actuator conditions, sensing a discrete number of tone reproduction samples, and merging the discrete number of tone reproduction samples with the tone reproduction curve to provide a reconstructed tone reproduction curve.
Claim 14
Dependent Claim
89 words
In an imaging system for projecting an image onto an imaging surface, the imaging system having a control including actuators and a model of tone reproduction curve response, a method of reconstructing a tone reproduction curve for use in controlling the imaging system operation comprising the steps of: predicting a tone reproduction curve for a given set of actuator conditions, sensing a discrete number of tone reproduction samples, and merging the discrete number of tone reproduction samples with the tone reproduction curve to provide a reconstructed tone reproduction curve.
Claim 15
Dependent Claim
42 words
The method of claim 10 wherein the model of tone reproduction curve response is defined by the expression C.sub.i ≈Ci =α.sub.1i Ψ.sub.1 +α.sub.2i Ψ.sub.2 +α.sub.3i Ψ.sub.3 +C where α's are coefficients, ψ's are basis functions, and C represents a toner reproduction curve.
Claim 16
Dependent Claim
27 words
The method of claim 10 wherein the reconstructed tone reproduction curve is defined by α.sub.i =(C-C).sup.T Ψ.sub.j where the subscript j corresponds to a basis function number.
Claim 17
Dependent Claim
123 words
In an imaging system for projecting an image onto an imaging surface, the imaging system having a control including actuators and a model of tone reproduction curve response, the model of tone reproduction curve response being defined by C.sub.i ≈Ci =α.sub.1i Ψ.sub.1 +α.sub.2i Ψ.sub.2 +α.sub.3i Ψ.sub.3 +C where α's are coefficients, ψ's are basis functions, and C represents a toner reproduction curve, a method of reconstructing a tone reproduction curve for use in controlling the imaging system operation comprising the steps of: predicting a tone reproduction curve for a given set of actuator conditions, sensing a discrete number of tone reproduction samples, and merging the discrete number of tone reproduction samples with the tone reproduction curve to provide a reconstructed tone reproduction curve.
Claim 18
Dependent Claim
123 words
In an imaging system for projecting an image onto an imaging surface, the imaging system having a control including actuators and a model of tone reproduction curve response, the model of tone reproduction curve response being defined by C.sub.i ≈Ci =α.sub.1i Ψ.sub.1 +α.sub.2i Ψ.sub.2 +α.sub.3i Ψ.sub.3 +C where α's are coefficients, ψ's are basis functions, and C represents a toner reproduction curve, a method of reconstructing a tone reproduction curve for use in controlling the imaging system operation comprising the steps of: predicting a tone reproduction curve for a given set of actuator conditions, sensing a discrete number of tone reproduction samples, and merging the discrete number of tone reproduction samples with the tone reproduction curve to provide a reconstructed tone reproduction curve.
Claim 19
Dependent Claim
100 words
In an imaging system having a control including a set of actuators for projecting an image onto an imaging surface, a method of reconstructing a tone reproduction curve for use in controlling the imaging system operation comprising the steps of providing a model of the imaging system with respect to the actuators for producing a predicted tone reproduction curve, obtaining a discrete number of tone reproduction samples, melding the predicted tone reproduction curve and the discrete number of tone reproduction samples to provide a reconstructed tone reproduction curve, and responding to the reconstructed tone reproduction curve to control machine operation.
Claim 20
Dependent Claim
100 words
In an imaging system having a control including a set of actuators for projecting an image onto an imaging surface, a method of reconstructing a tone reproduction curve for use in controlling the imaging system operation comprising the steps of providing a model of the imaging system with respect to the actuators for producing a predicted tone reproduction curve, obtaining a discrete number of tone reproduction samples, melding the predicted tone reproduction curve and the discrete number of tone reproduction samples to provide a reconstructed tone reproduction curve, and responding to the reconstructed tone reproduction curve to control machine operation.
Claim 21
Dependent Claim
38 words
The method of claim 14 wherein the predicted tone reproduction curve is defined by C.sub.i ≈Ci =α.sub.1i Ψ.sub.1 +α.sub.2i Ψ.sub.2 +α.sub.3i Ψ.sub.3 +C where α's are coefficients, ψ's are basis functions, and C represents a toner reproduction curve.
Claim 22
Dependent Claim
88 words
In an imaging system having a control including a set of actuators for projecting an image onto an imaging surface, a method of machine control comprising the steps of; modeling the imaging system with respect to the actuators for producing a predicted tone reproduction curve, obtaining a discrete number of tone reproduction samples, providing a look up table responding to the tone reproduction samples to produce a reconstructed tone reproduction curve, and comparing the predicted tone reproduction curve and the reconstructed tone reproduction curve to adjust machine operation.
Claim 23
Dependent Claim
88 words
In an imaging system having a control including a set of actuators for projecting an image onto an imaging surface, a method of machine control comprising the steps of; modeling the imaging system with respect to the actuators for producing a predicted tone reproduction curve, obtaining a discrete number of tone reproduction samples, providing a look up table responding to the tone reproduction samples to produce a reconstructed tone reproduction curve, and comparing the predicted tone reproduction curve and the reconstructed tone reproduction curve to adjust machine operation.
Claim 24
Dependent Claim
51 words
The method of claim 16 wherein the predicted tone reproduction curve is defined by the expression C.sub.i ≈Ci =α.sub.1i Ψ.sub.1 +α.sub.2i Ψ.sub.2 +α.sub.3i Ψ.sub.3 +C where α's are coefficients, ψ's are basis functions, and C represents a toner reproduction curve, wherein the α coefficients are known in terms of said actuators.
Claim 25
Dependent Claim
45 words
The method of claim 16 wherein the look up table is defined by the matrix II.sup.+ =ΣII(II.sup.T ΣII).sup.-1, wherein π corresponds to the matrix containing eigenvalues, and incorporates an estimated linear reconstruction defined by =II.sup.+ c where II + represents a least squares optimal reconstruction.
Claim 26
Dependent Claim
19 words
The method of claim 16 wherein the actuators are imaging surface voltage, developer bias voltage, and projecting system power.
Claim 27
Dependent Claim
20 words
The method of claim 16 wherein the look up table incorporates a covariance matrix of elements containing tone reproduction samples.
Claim 28
Dependent Claim
26 words
The method of claim 20 including a matrix multiplier responding to sensed samples and to the look up table to reproduce a complete tone reproduction curve.
Claim 29
Dependent Claim
93 words
In an imaging system having a control including a set of actuators for projecting an image onto an imaging surface, a method of machine control comprising the steps of: providing a model of the imaging system with respect to actuators for producing a predicted tone reproduction curve, the model including a linear combination of basis functions derived by decomposing sample tone reproduction curves, producing a discrete number of tone reproduction samples, and melding the predicted tone reproduction curve and the tone reproduction samples to provide a reconstructed tone reproduction curve for machine control.
Claim 30
Dependent Claim
93 words
In an imaging system having a control including a set of actuators for projecting an image onto an imaging surface, a method of machine control comprising the steps of: providing a model of the imaging system with respect to actuators for producing a predicted tone reproduction curve, the model including a linear combination of basis functions derived by decomposing sample tone reproduction curves, producing a discrete number of tone reproduction samples, and melding the predicted tone reproduction curve and the tone reproduction samples to provide a reconstructed tone reproduction curve for machine control.
Claim 31
Dependent Claim
67 words
In an imaging system having a control including a set of actuators for projecting an image onto an imaging surface, a method of machine control comprising the steps of: providing a linear combination of basis functions, producing a discrete number of tone reproduction samples, and melding the linear combination of basis functions and the tone reproduction samples to provide a reconstructed tone reproduction curve for machine control.
Claim 32
Dependent Claim
67 words
In an imaging system having a control including a set of actuators for projecting an image onto an imaging surface, a method of machine control comprising the steps of: providing a linear combination of basis functions, producing a discrete number of tone reproduction samples, and melding the linear combination of basis functions and the tone reproduction samples to provide a reconstructed tone reproduction curve for machine control.
Claim 33
Dependent Claim
20 words
The method of claim 23 wherein the linear combination of basis functions is derived by decomposing sample tone reproduction curves.
References Cited (Backward Citations)
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 2001-05-04 | 2001-11-03 | 2002-05-05 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 2005-05-04 | 2005-11-03 | 2006-05-05 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 2009-05-04 | 2009-11-03 | 2010-05-05 | $7700.00 | Window Closed / Lapsed |