CN104933706B - A kind of imaging system color information scaling method - Google Patents

A kind of imaging system color information scaling method Download PDF

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CN104933706B
CN104933706B CN201510289303.4A CN201510289303A CN104933706B CN 104933706 B CN104933706 B CN 104933706B CN 201510289303 A CN201510289303 A CN 201510289303A CN 104933706 B CN104933706 B CN 104933706B
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CN104933706A (en
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宫睿
王娇阳
许洁
邵晓鹏
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Xidian University
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Xidian University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/80—Analysis of captured images to determine intrinsic or extrinsic camera parameters, i.e. camera calibration

Abstract

Its CIEXYZ tristimulus values is calculated the invention discloses a kind of imaging system color information scaling method, including by the spectral reflectance of demarcation colour atla and the spectral intensity distribution of Calibrating source, and changes to color space CIELAB coordinate；Same Scene under same imaging circumstances is imaged using with reference to imaging system and imaging system to be calibrated, it is digital drive values to obtain digital image colors information, and mapping matrix between CIELAB coordinates and digital drive values is obtained by being fitted；For the imaging system to be calibrated digital picture that scene obtains under any imaging circumstances, using corresponding mapping matrix, the digital drive values of every pixel are predicted to corresponding CIELAB coordinates, then digital drive values after predicting to demarcation, complete accurately color information demarcation between two imaging systems.The present invention realizes accurate transmission and presentation of the digital image colors information in various equipment rooms, and calibration algorithm is accurate, and method implements simple, strong applicability.

Description

A kind of imaging system color information scaling method
Technical field
The invention belongs to Digital image technology field, more particularly to a kind of imaging system color information scaling method.
Background technology
Image be the mankind obtain and exchange external information main source, imaging system then be obtain digital picture can not or Scarce hardware device.Imaging system is that a kind of be distributed scene brightness according to geometric optics or physioptial rule is converted to light The system of electric transducer Illumination Distribution, its digital picture obtained can be widely applied to photograph, record, investigate, remote sensing mapping etc. Field.In some application demands, it is desirable to the digitized map that different imaging systems are recorded to Same Scene under same imaging circumstances As having identical color information, i.e. digital drive values (R, G, B) are identical, when these Digital Image Transmissions to any output equipment During display, visually consistent color perception amount is also brought along, consequently facilitating digital image colors information is between various equipment Accurate transmission and presentation.
However, different imaging systems are due to sensor type, running parameter setting, spectral response characteristic and imaging circumstances Etc. have differences, they under same imaging circumstances Same Scene obtain imaging results simultaneously differ, cause these into As system finally obtain image color information exist it is larger different, this limit to a certain extent imaging system the army and the people lead Further apply in domain.
The content of the invention
It is an object of the invention to provide a kind of imaging system color information scaling method, it is intended to solves different imaging systems Because sensor type, running parameter setting, spectral response characteristic and imaging circumstances etc. have differences, to same imaging Under environment Same Scene obtain imaging results and differ, cause imaging system finally obtain image color information exist compared with It is big different, imaging system is limited to a certain extent Military and civil fields are further applied the problem of.
The present invention is achieved in that a kind of imaging system color information scaling method, the imaging system color information Scaling method includes：
CIEXYZ tri- is calculated and is pierced by the spectral reflectance of demarcation colour atla and the spectral intensity distribution of Calibrating source first Swash value, and change to uniform color space CIELAB coordinate；
Then, using Same Scene under same imaging circumstances is carried out with reference to imaging system and imaging system to be calibrated into Picture, it is digital drive values to obtain digital image colors information, is obtained by being fitted between CIELAB coordinates and digital drive values Mapping matrix；
For the imaging system to be calibrated digital picture that scene obtains under any imaging circumstances, using corresponding mapping square Battle array, the digital drive values of every pixel are predicted to corresponding CIELAB coordinates, then digital drive values after predicting to demarcation, complete two Accurate color information demarcation between imaging system.
Further, the imaging system color information scaling method specifically includes following steps：
Step 1: selection demarcation colour atla and Calibrating source, demarcation colour atla is no less than 24 tinctorial patterns, N number of according to demarcation colour atla The spectral reflectance ρ of tinctorial patterniThe spectral intensity of (λ) and Calibrating source is distributedWith reference to CIE1931 standard colorimetric systems Color matching functionThe demarcation N number of tinctorial pattern of colour atla is calculated in CIE1931 by following two formula CIEXYZ tristimulus values (X under standard colorimetric systemi,Yi,Zi)；
Pass throughCalibrating source is calculated under CIE1931 standard colorimetric systems with following formula CIEXYZ tristimulus values (XW,YW,ZW)；
Wherein, Δ λ is used spectrum sample interval when calculating, and takes 5nm, and i is the sequence number of the demarcation N number of tinctorial pattern of colour atla, i =1,2,3 ..., N；
Step 2: (the X that step 1 is obtainedi,Yi,Zi) and (XW,YW,ZW) following two formula is substituted into, calculate each Coordinate of the tinctorial pattern in uniform color space CIELAB
Step 3: being respectively adopted with reference to imaging system and imaging system to be calibrated, N number of tinctorial pattern under Calibrating source is carried out Imaging, record obtain the color information of digital picture, read each tinctorial pattern corresponding digital drive values in two imaging systems (RSi,GSi,BSi) and (RTi,GTi,BTi)；
Step 4: for imaging system to be calibrated, the N number of tinctorial pattern CIELAB coordinates obtained according to step 2The N number of tinctorial pattern digital drive values (R obtained with step 3Ti,GTi,BTi), under being gone out using least square fitting By (R in formulaTi,GTi,BTi) prediction is extremelyMapping matrix MT, MTFor 3 × 11 matrixes；
Step 5: for reference imaging system, the N number of tinctorial pattern CIELAB coordinates obtained according to step 2 The N number of tinctorial pattern digital drive values (R obtained with step 3Si,GSi,BSi), using least square fitting go out by Predict to (RSi,GSi,BSi) mapping matrix HSI, HSIFor 3 × 10 matrixes；
Step 6: for the imaging system to be calibrated digital picture that any scene obtains under any imaging circumstances, use The mapping matrix M that step 4 is obtainedT, by following formula, by the digital drive values (R of every pixelTj',GTj',BTj') predict correspondingly CIELAB space coordinatesWherein j=1,2,3 ..., N', N' are that imaging system to be calibrated obtains numeral The total number-of-pixels of image；
Step 7: obtain CIELAB space coordinates of the imaging system to be calibrated per pixel for step 6The mapping matrix H obtained using step 5SI, by following formula, predict number after being demarcated corresponding to every pixel Word drive value (RSj',GSj',BSj'), that is, the color information demarcation between two imaging systems is completed, makes imaging system to be calibrated The digital picture that certain scene obtains under any imaging circumstances has the digital drive values consistent with reference imaging system；
Imaging system color information scaling method provided by the invention, realize the color information mark between different imaging systems It is fixed, make them consistent to the color information that same scene imaging obtains under same imaging circumstances, i.e., digital drive values are identical；With Demarcation colour atla spectral reflectance is calculated into the link of its CIELAB coordinate with Calibrating source spectral intensity distributed intelligence, CIELAB The selection of uniform color space can make the sign of color information and transmit to have more versatility；CIELAB is established by mapping matrix The mode of mathematical between coordinate and digital drive values, the color for being capable of more accurate characterization difference imaging system acquisition are believed Breath.The inventive method is implemented simply, and calibration algorithm is accurate, strong applicability, is advantageous to digital image colors information in distinct device Between accurate transmission and presentation.
Brief description of the drawings
Fig. 1 is imaging system color information scaling method flow chart provided in an embodiment of the present invention；
Fig. 2 is the calculating process of target designation parameter CIELAB coordinates provided in an embodiment of the present invention；
Fig. 3 is imaging system color information scaling method specific implementation flow chart provided in an embodiment of the present invention.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to Limit the present invention.
The present invention carries out the demarcation of image color information by certain Processing Algorithm to different imaging systems, obtains them The digital drive values (R, G, B) that the digital picture taken is consistent, overcome and rung by sensor type, running parameter setting, spectrum Color information difference caused by answering characteristic and imaging circumstances, ensure that different imaging systems obtain to Same Scene under same imaging circumstances The digital picture taken has consistent color information, and this is by the optimization and its extension of application field to imaging system picture quality Produce significant impetus.
1-3 is explained in detail to the imaging system color information calibration process of the present invention below in conjunction with the accompanying drawings.
As shown in figure 1, the imaging system color information scaling method of the embodiment of the present invention comprises the following steps：
S101：Its CIEXYZ tri- is calculated by the spectral reflectance of demarcation colour atla and the spectral intensity distribution of Calibrating source Values, and change to uniform color space CIELAB coordinate；
S102：Using Same Scene under same imaging circumstances is carried out with reference to imaging system and imaging system to be calibrated into Picture, it is digital drive values to obtain digital image colors information, is obtained by being fitted between CIELAB coordinates and digital drive values Mapping matrix；
S103：For the imaging system to be calibrated digital picture that scene obtains under any imaging circumstances, can use corresponding Mapping matrix, the digital drive values of every pixel are predicted to corresponding CIELAB coordinates, then predict to its demarcation after numeral drive Dynamic value, that is, complete accurately color information demarcation between two imaging systems.
In embodiment, using Canon's 5D Mark III slr cameras as with reference to imaging system, using the micro- one cameras of Nikon J4 as Imaging system to be calibrated, by the micro- one cameras of Nikon J4, certain scene obtains the digital drive values of digital picture under any imaging circumstances (RTj',GTj',BTj') obtain calibrated digital drive values (RSj',GSj',BSj'), it is allowed to mono- anti-with Canon 5D Mark III Camera is identical.
As shown in Figures 2 and 3, the imaging system color information scaling method of the embodiment of the present invention specifically includes following step Suddenly：
Step 1: selection demarcation colour atla and Calibrating source, GretagMacbethColorChe typically can be selected in demarcation colour atla Cker, should be no less than 24 tinctorial patterns, and standard illuminants D series, such as D65 can be selected in Calibrating source.According to the demarcation N number of tinctorial pattern of colour atla Spectral reflectance ρiThe spectral intensity of (λ) and Calibrating source is distributedWith reference to the color of CIE1931 standard colorimetric systems With functionThe demarcation N number of tinctorial pattern of colour atla is calculated in CIE1931 reference colours by formula (1)~(2) CIEXYZ tristimulus values (X under degree systemi,Yi,Zi)；
CIEXYZ tristimulus values of the Calibrating source under CIE1931 standard colorimetric systems is calculated by formula (2)~(3) (XW,YW,ZW)；
Wherein, Δ λ is used spectrum sample interval when calculating, and it is the sequence of the demarcation N number of tinctorial pattern of colour atla typically to take 5nm, i Number, i=1,2,3 ..., N；
Step 2: (the X that step 1 is obtainedi,Yi,Zi) and (XW,YW,ZW) formula (4)~(5) are substituted into, calculate each color Coordinate of the sample in uniform color space CIELAB
Step 3: being respectively adopted with reference to imaging system and imaging system to be calibrated, N number of tinctorial pattern under Calibrating source is carried out Imaging, the color information that they obtain digital picture is recorded, read each tinctorial pattern corresponding numeral in two imaging systems and drive Dynamic value (RSi,GSi,BSi) and (RTi,GTi,BTi)；
Step 4: for imaging system to be calibrated, the N number of tinctorial pattern CIELAB coordinates obtained according to step 2The N number of tinctorial pattern digital drive values (R obtained with step 3Ti,GTi,BTi), formula is gone out using least square fitting (6) by (R inTi,GTi,BTi) prediction is extremelyMapping matrix MT, MTFor 3 × 11 matrixes；
Step 5: for reference imaging system, the N number of tinctorial pattern CIELAB coordinates obtained according to step 2 The N number of tinctorial pattern digital drive values (R obtained with step 3Si,GSi,BSi), using least square fitting go out in formula (7) byPredict to (RSi,GSi,BSi) mapping matrix HSI, HSIFor 3 × 10 matrixes；
6th, for the imaging system to be calibrated digital picture that any scene obtains under any imaging circumstances, using step The four mapping matrix M obtainedT, by formula (8), by the digital drive values (R of every pixelTj',GTj',BTj') predict corresponding to CIELAB space coordinatesWherein j=1,2,3 ..., N', N' are that imaging system to be calibrated obtains digitized map The total number-of-pixels of picture；
Step 7: obtain CIELAB space coordinates of the imaging system to be calibrated per pixel for step 6 The mapping matrix H obtained using step 5SI, by formula (9), predict digital drive values (R after being demarcated corresponding to every pixelSj', GSj',BSj'), that is, the color information demarcation between two imaging systems is completed, makes imaging system to be calibrated in any imaging circumstances The digital picture that certain lower scene obtains has the digital drive values consistent with reference imaging system；
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention All any modification, equivalent and improvement made within refreshing and principle etc., should be included in the scope of the protection.

Claims (1)

  1. A kind of 1. imaging system color information scaling method, it is characterised in that the imaging system color information scaling method bag Include：
    CIEXYZ tristimulus values is calculated by the spectral reflectance of demarcation colour atla and the spectral intensity distribution of Calibrating source first, And change to color space CIELAB coordinate；
    Then, Same Scene under same imaging circumstances is imaged using with reference to imaging system and imaging system to be calibrated, obtained It is digital drive values to obtain digital image colors information, passes through the mapping square for being fitted and obtaining between CIELAB coordinates and digital drive values Battle array；
    For the imaging system to be calibrated digital picture that scene obtains under any imaging circumstances, using corresponding mapping matrix, The digital drive values of every pixel are predicted to corresponding CIELAB coordinates, then digital drive values after predicting to demarcation, complete twenty percent As accurately color information demarcation between system；
    The imaging system color information scaling method specifically includes following steps：
    Step 1: selection demarcation colour atla and Calibrating source, demarcation colour atla is no less than 24 tinctorial patterns, according to the demarcation N number of tinctorial pattern of colour atla Spectral reflectance ρiThe spectral intensity of (λ) and Calibrating source is distributedWith reference to the color of CIE1931 standard colorimetric systems With functionThe demarcation N number of tinctorial pattern of colour atla is calculated in CIE1931 standards by following two formula CIEXYZ tristimulus values (X under colorimeter systemi,Yi,Zi)；
    Pass throughCalibrating source is calculated under CIE1931 standard colorimetric systems with following formula CIEXYZ tristimulus values (XW,YW,ZW)；
    Wherein, Δ λ is used spectrum sample interval when calculating, and takes 5nm, and i is the sequence number of the demarcation N number of tinctorial pattern of colour atla, i=1, 2,3,…,N；
    Step 2: (the X that step 1 is obtainedi,Yi,Zi) and (XW,YW,ZW) following two formula is substituted into, calculate each tinctorial pattern In color space CIELAB coordinate
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    Step 3: be respectively adopted with reference to imaging system and imaging system to be calibrated, N number of tinctorial pattern under Calibrating source is carried out into Picture, record obtain the color information of digital picture, read each tinctorial pattern corresponding digital drive values in two imaging systems (RSi,GSi,BSi) and (RTi,GTi,BTi)；
    Step 4: for imaging system to be calibrated, the N number of tinctorial pattern CIELAB coordinates obtained according to step 2With N number of tinctorial pattern digital drive values (R that step 3 is obtainedTi,GTi,BTi), gone out using least square fitting in following formula by (RTi,GTi, BTi) prediction is extremelyMapping matrix MT, MTFor 3 × 11 matrixes；
    <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>L</mi> <mi>i</mi> <mo>*</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>a</mi> <mi>i</mi> <mo>*</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>b</mi> <mi>i</mi> <mo>*</mo> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msub> <mi>M</mi> <mi>T</mi> </msub> <msup> <mrow> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>R</mi> <mrow> <mi>T</mi> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>G</mi> <mrow> <mi>T</mi> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>B</mi> <mrow> <mi>T</mi> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msubsup> <mi>R</mi> <mrow> <mi>T</mi> <mi>i</mi> </mrow> <mn>2</mn> </msubsup> <mo>,</mo> <msubsup> <mi>G</mi> <mrow> <mi>T</mi> <mi>i</mi> </mrow> <mn>2</mn> </msubsup> <mo>,</mo> <msubsup> <mi>B</mi> <mrow> <mi>T</mi> <mi>i</mi> </mrow> <mn>2</mn> </msubsup> <mo>,</mo> <msub> <mi>R</mi> <mrow> <mi>T</mi> <mi>i</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>G</mi> <mrow> <mi>T</mi> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>G</mi> <mrow> <mi>T</mi> <mi>i</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>B</mi> <mrow> <mi>T</mi> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>B</mi> <mrow> <mi>T</mi> <mi>i</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>R</mi> <mrow> <mi>T</mi> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <mi>T</mi> <mi>i</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>G</mi> <mrow> <mi>T</mi> <mi>i</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>B</mi> <mrow> <mi>T</mi> <mi>i</mi> </mrow> </msub> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>;</mo> </mrow>
    Step 5: for reference imaging system, the N number of tinctorial pattern CIELAB coordinates obtained according to step 2And step The rapid three N number of tinctorial pattern digital drive values (R obtainedSi,GSi,BSi), using least square fitting go out byPrediction To (RSi,GSi,BSi) mapping matrix HSI, HSIFor 3 × 10 matrixes；
    <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>R</mi> <mrow> <mi>S</mi> <mi>i</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>G</mi> <mrow> <mi>S</mi> <mi>i</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>B</mi> <mrow> <mi>S</mi> <mi>i</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msub> <mi>H</mi> <mrow> <mi>S</mi> <mi>I</mi> </mrow> </msub> <msup> <mrow> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>,</mo> <msubsup> <mi>L</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mo>,</mo> <msubsup> <mi>a</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mo>,</mo> <msubsup> <mi>b</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mo>,</mo> <msubsup> <mi>L</mi> <mi>i</mi> <mrow> <mo>*</mo> <mn>2</mn> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>a</mi> <mi>i</mi> <mrow> <mo>*</mo> <mn>2</mn> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>b</mi> <mi>i</mi> <mrow> <mo>*</mo> <mn>2</mn> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>L</mi> <mi>i</mi> <mrow> <mo>*</mo> <mn>3</mn> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>a</mi> <mi>i</mi> <mrow> <mo>*</mo> <mn>3</mn> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>b</mi> <mi>i</mi> <mrow> <mo>*</mo> <mn>3</mn> </mrow> </msubsup> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>;</mo> </mrow>
    Step 6: for the imaging system to be calibrated digital picture that any scene obtains under any imaging circumstances, using step The four mapping matrix M obtainedT, by following formula, by the digital drive values (R of every pixelTj',GTj',BTj') predict corresponding to CIELAB space coordinatesWherein j=1,2,3 ..., N', N' are that imaging system to be calibrated obtains digitized map The total number-of-pixels of picture；
    <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msup> <msubsup> <mi>L</mi> <mi>j</mi> <mo>*</mo> </msubsup> <mo>&amp;prime;</mo> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <msubsup> <mi>a</mi> <mi>j</mi> <mo>*</mo> </msubsup> <mo>&amp;prime;</mo> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <msubsup> <mi>b</mi> <mi>j</mi> <mo>*</mo> </msubsup> <mo>&amp;prime;</mo> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msub> <mi>M</mi> <mi>T</mi> </msub> <msup> <mrow> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>,</mo> <msubsup> <mi>R</mi> <mrow> <mi>T</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>,</mo> <msubsup> <mi>G</mi> <mrow> <mi>T</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>,</mo> <msubsup> <mi>B</mi> <mrow> <mi>T</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>,</mo> <msup> <msubsup> <mi>R</mi> <mrow> <mi>T</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mn>2</mn> </msup> <mo>,</mo> <msup> <msubsup> <mi>G</mi> <mrow> <mi>T</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mn>2</mn> </msup> <mo>,</mo> <msup> <msubsup> <mi>B</mi> <mrow> <mi>T</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mn>2</mn> </msup> <mo>,</mo> <msubsup> <mi>R</mi> <mrow> <mi>T</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>&amp;CenterDot;</mo> <msubsup> <mi>G</mi> <mrow> <mi>T</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>,</mo> <msubsup> <mi>G</mi> <mrow> <mi>T</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>&amp;CenterDot;</mo> <msubsup> <mi>B</mi> <mrow> <mi>T</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>,</mo> <msubsup> <mi>B</mi> <mrow> <mi>T</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>&amp;CenterDot;</mo> <msubsup> <mi>R</mi> <mrow> <mi>T</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>,</mo> <msubsup> <mi>R</mi> <mrow> <mi>T</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>&amp;CenterDot;</mo> <msubsup> <mi>G</mi> <mrow> <mi>T</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>&amp;CenterDot;</mo> <msubsup> <mi>B</mi> <mrow> <mi>T</mi> <mi>j</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>;</mo> </mrow>
    Step 7: obtain CIELAB space coordinates of the imaging system to be calibrated per pixel for step 6Adopt The mapping matrix H obtained with step 5SI, by following formula, predict digital drive values (R after being demarcated corresponding to every pixelSj', GSj',BSj'), that is, the color information demarcation between two imaging systems is completed, makes imaging system to be calibrated in any imaging circumstances The digital picture that certain lower scene obtains has the digital drive values consistent with reference imaging system；
    <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msup> <msub> <mi>R</mi> <mrow> <mi>S</mi> <mi>j</mi> </mrow> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <msub> <mi>G</mi> <mrow> <mi>S</mi> <mi>j</mi> </mrow> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <msub> <mi>B</mi> <mrow> <mi>S</mi> <mi>j</mi> </mrow> </msub> <mo>&amp;prime;</mo> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msub> <mi>H</mi> <mrow> <mi>S</mi> <mi>I</mi> </mrow> </msub> <msup> <mrow> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>,</mo> <msup> <msubsup> <mi>L</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <msup> <msubsup> <mi>a</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <msup> <msubsup> <mi>b</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <msup> <msubsup> <mi>L</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mrow> <mo>&amp;prime;</mo> <mn>2</mn> </mrow> </msup> <mo>,</mo> <msup> <msubsup> <mi>a</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mrow> <mo>&amp;prime;</mo> <mn>2</mn> </mrow> </msup> <mo>,</mo> <msup> <msubsup> <mi>b</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mrow> <mo>&amp;prime;</mo> <mn>2</mn> </mrow> </msup> <mo>,</mo> <msup> <msubsup> <mi>L</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mrow> <mo>&amp;prime;</mo> <mn>3</mn> </mrow> </msup> <mo>,</mo> <msup> <msubsup> <mi>a</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mrow> <mo>&amp;prime;</mo> <mn>3</mn> </mrow> </msup> <mo>,</mo> <msup> <msubsup> <mi>b</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mrow> <mo>&amp;prime;</mo> <mn>3</mn> </mrow> </msup> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>.</mo> </mrow> 3
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