CN108519157B - A kind of generation of metamerism spectrum and evaluation method and system for light source detection - Google Patents
A kind of generation of metamerism spectrum and evaluation method and system for light source detection Download PDFInfo
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Abstract
The invention proposes a kind of metamerism spectrum generations for light source detection and evaluation method and system, by being sampled and being screened in huge library of spectra, utilize color science relevant calculation formula, in conjunction with based on the method for carrying out degree of metameris evaluation under single light source, the spectrum for realizing metamerism is generated.It is sampled based on standard item color spectrum library, since data volume is very big, can screen to obtain the metamerism color with being worth compared with high reference, improve the accuracy of metamerism collection.It is easy to implement in terms of generation.Metamerism evaluation is carried out based on single light source, there is higher independence, reduces the dependence to testing light source, meets the needs evaluated various light sources, increases the efficiency of light source evaluation.
Description
Technical Field
The invention belongs to the technical field of printed light source detection, and particularly relates to a metamerism spectrum generation and evaluation method and system for light source detection.
Background
In the field of color reproduction and light source control, metamerism refers to a pair of colors with different spectral stimuli that have the same color appearance under the same viewing conditions (e.g., light source or viewer), and when one or more of these conditions is changed, the color changes, resulting in a mismatch between the two colors.
With the development of the illumination light source market, the light sources are various at present, human eyes can hardly directly distinguish the quality of the illumination light sources, and a scientific and effective method which can help to screen the illumination light sources is needed. In addition, in the color production industry such as printing and packaging, the light source is indispensable, for example, in the light box used in the printing quality detection, after a period of time, the light source will be degraded, so that the light source used is no longer standard, and at this time, a convenient and effective method is also needed for the quality control of the light source. In color science, tristimulus values are a measure of the relationship between color light and vision, and represent color by data, and its calculation formula is based on spectral stimulus, standard observer function, and light source spectral distribution function. Obviously, if the spectral stimuli are different and the spectral distribution of the light source is changed, metamerism is generated. The metamerism phenomenon is utilized, and great benefits can be brought to the related field of light source quality control.
At present, in the field of metamerism, various generation methods such as a three-function combination method, a polynomial method, a variational calculation method, a metamerism black method, and the like are proposed in the industry. Because the three-function combination method can only generate three groups of metamerism colors in one calculation, the calculation efficiency is low. In addition, existing metameric black generation methods, which are simply enumerated within a reasonable range, have a small number of samples and are impractical to source. Currently, the CIE1976L a b uniform color space system is widely used for evaluating the metamerism degree as a method for calculating color difference, and the method has strong dependence on light sources and has limitation on the selected metameric color pair when detecting and evaluating uncertain light sources.
In view of the above problems, a standard metamerism test standard which is easy to obtain and use is lacking in the current field of light source detection. For the light source and spectrum evaluation in the current color imaging field, the current generation and evaluation technology cannot meet the applicability, the standard and the rationality.
Disclosure of Invention
The invention aims to solve the problems in the background art and provides a metamerism spectrum generation and evaluation method for light source detection.
The technical scheme of the invention is a metamerism spectrum generation and evaluation method for light source detection, which comprises the following steps:
step 1, performing typical sample sampling in a large amount of collected spectral data sets to obtain C typical color samples,
step 2, decomposing in the color space to obtain C color samples NiBasic color stimulus N of (i ═ 1,2, …, C)fiAnd metameric black Ki(i ═ 1,2, …, C) and the metameric black K was verifiediWhether the tristimulus values of the spectrum are all 0 or not, and when XYZ is not all 0, deleting the metameric black;
step 3, calculating a metamerism set Nm corresponding to any target sample set N0;
step 4, eliminating metamerism spectra of which the magnitude values of all wave bands in the metamerism set Nm corresponding to any sample set N0 do not belong to the range of [0,1] to form a new metamerism set M;
and 5, for the metamerism set M generated in the step 4, adopting a common metamerism index GM under a single light source E0 to maximize the metamerism index GM according to the metamerism degree of the evaluation spectrum, and selecting the most representative metamerism spectrum.
Further, step 2 is realized as follows,
step 2.1, calculating an object color matching function A based on a standard light source, as shown in formula (1), wherein the standard illuminant is E0, cmf is the spectral tristimulus value of a standard observer,
A＝cmf×E0 (1)
step 2.2, calculating an orthogonal projection operator of the color matching function, as shown in formula (2),
R＝A(ATA)-1AT (2)
step 2.3, respectively calculating C groups of basic color stimulus N of C color samplesfiAnd metameric black KiAs shown in the formulas (3) and (4),
Nfi＝R×Ni (3)
Ki＝Ni–Nfi (4)
step 2.4, metamerism black K calculated in step 2.3iSpectrum, verifying whether its tristimulus values XYZ are all 0, and deleting the metameric black when none of XYZ is 0, wherein the tristimulus values are calculated from the spectrum as formula (5),
where x (λ) y (λ) z (λ) represents the human eye visual matching function, E0(λ) represents the selected standard illumination source, K (λ) represents the metameric black spectral reflectance information, and λ represents a range of visible wavelengths.
Further, step 3 is realized as follows,
calculating the basic color spectrum stimulus N of each spectrum of the arbitrary target sample set N0 by using the formula (3)ffAnd the metamerism set Nm corresponding to the sample set is solved by using a formula (6),
Nm＝Nff+Ki (6)
wherein, KiAnd (3) obtaining metamerism black spectrums of the color spectrum library of the C standard objects obtained in the step (2).
Further, step 5 is realized as follows,
step 5.1, respectively calculating the difference value of the spectral reflectivity of any pair of metamerism colors M and N0 under each wave band with the lambda being in a certain range by using a formula (7),
Δβ(λ)＝||M(λ)-N0(λ)|| (7)
step 5.2, calculating the general metamerism index GM by using a formula (8), wherein the calculation method of w (lambda) is shown in a formula (9),
GM＝∑λw(λ)×Δβ(λ) (8)
wherein,the derivatives of L, a and b, representing any pair of metameric colors, with respect to β (λ) were calculated according to the chain rule.
Furthermore, the present invention provides a metamerism spectrum generation and evaluation system for light source detection, comprising the following modules:
a representative color sample collection module for performing representative sample sampling in a large number of spectral data sets that can be collected, obtaining C representative color samples,
a color decomposition module for decomposing in color space to obtain C color samples NiBasic color stimulus N of (i ═ 1,2, …, C)fiAnd metameric black Ki(i ═ 1,2, …, C) and the metameric black K was verifiediWhether the tristimulus values of the spectrum are all 0 or not, and when XYZ is not all 0, deleting the metameric black;
the metamerism set calculation module is used for calculating a metamerism set Nm corresponding to any target sample set N0;
the special spectrum eliminating module is used for eliminating metamerism spectrums, of which the magnitude values of all wave bands in the metamerism set Nm corresponding to any sample set N0 do not belong to the range of [0,1], to form a new metamerism set M;
and the representative metamerism spectrum selection module is used for selecting the most representative metamerism spectrum according to the metamerism degree of the evaluation spectrum by maximizing a common metamerism index GM under a single light source E0 for the metamerism set M generated in the special spectrum rejection module.
Further, the color separation module is a module having a function for further processing,
an object color matching function a based on a standard illuminant is calculated as shown in equation (1), where the standard illuminant is E0, cmf is the standard observer spectral tristimulus value,
A＝cmf×E0 (1)
the orthogonal projection operator for calculating the color matching function, as shown in equation (2),
R＝A(ATA)-1AT (2)
respectively calculating C groups of basic color stimulus N of C color samplesfiAnd metameric black KiAs shown in the formulas (3) and (4),
Nfi＝R×Ni (3)
Ki＝Ni–Nfi (4)
for the calculated metamerism black KiSpectrum, verifying whether its tristimulus values XYZ are all 0, and deleting the metameric black when none of XYZ is 0, wherein the tristimulus values are calculated from the spectrum as formula (5),
X＝∫λx(λ)E0(λ)K(λ)dλ
Y＝∫λy(λ)E0(λ)K(λ)dλ
Z＝∫λz(λ)E0(λ)K(λ)dλ (5)
where x (λ) y (λ) z (λ) represents the human eye visual matching function, E0(λ) represents the selected standard illumination source, K (λ) represents the metameric black spectral reflectance information, and λ represents a range of visible wavelengths.
Further, the metamerism set calculation module is a module having functions for further processing,
calculating the basic color spectrum stimulus N of each spectrum of the arbitrary target sample set N0 by using the formula (3)ffAnd the metamerism set Nm corresponding to the sample set is solved by using a formula (6),
Nm＝Nff+Ki (6)
wherein, KiThe metamerism black spectrum of the color spectrum library of the C standard objects is obtained in the color decomposition module.
Further, the representative metamerism spectrum selection module is a module having the following functions, further used for,
the difference value of the spectral reflectance of any pair of metamerism colors M and N0 at each wavelength band with lambda in a certain range is calculated by formula (7),
Δβ(λ)＝||M(λ)-N0(λ)|| (7)
calculating general metamerism index GM by using formula (8), wherein the calculation method of w (lambda) is shown in formula (9),
GM＝∑λw(λ)×Δβ(λ) (8)
wherein,the derivatives of L, a and b, representing any pair of metameric colors, with respect to β (λ) were calculated according to the chain rule.
According to the metamerism spectrum generation and evaluation method for light source detection, the metamerism spectrum is generated by sampling and screening in a huge spectrum library, utilizing a color science related calculation formula and combining a method for evaluating the metamerism degree based on a single light source. Sampling is carried out based on a standard object color spectrum library, and metamerism colors with high reference values can be obtained by screening due to large data volume, so that the accuracy of a metamerism set is improved. In the aspect of generation, the implementation is convenient. Metamerism evaluation is performed based on a single light source, so that higher independence is achieved, dependence on a test light source is reduced, the requirements for evaluation of various light sources are met, and the efficiency of light source evaluation is increased.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
FIG. 2 is an example of a spectral reflectance curve of a metameric sample prepared in accordance with the present invention.
Detailed Description
When the technical scheme of the invention is implemented, the technical scheme can be automatically operated by a person skilled in the art by adopting a computer software technology. In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The metamerism spectrum generation and evaluation method for light source detection provided by the embodiment shown in fig. 1 improves the metamerism generation precision and evaluation effect to a certain extent, and obtains a relatively ideal spectrum prediction result.
In the embodiment, a computer is adopted to finish the generation of a large amount of metamerism colors which accord with the reality of a specific color sample in MATLAB based on a specific algorithm, and the metamerism evaluation is carried out. It should be noted that the present invention is not limited to the SOCS standard object color spectrum library and the specific original spectrum of the color, and is also applicable to any other metamerism generation algorithm and evaluation method proposed by the present invention.
The embodiment comprises the following steps:
1) typical sample sampling was performed on a large socs (standard Object Color Spectra database) standard Object Color spectrum library, yielding a total of 53486 typical Color samples.
2) Decomposing into basic color stimulus NfiAnd metameric black KiFor 53486 color samples Ni(i ═ 1,2, …,53486), group C, basic color stimuli N were obtained in this example as followsfiAnd metameric black Ki(i ═ 1,2, …,53486) values:
2.1) calculating an object color matching function A based on a standard illuminant D65, as shown in equation (1), wherein illuminant D65 is E0, cmf is the CIE1964 standard observer 10 ° field spectrum tristimulus value,
A＝cmf×E0 (1)
2.2) the orthogonal projection operator for calculating the color matching function, as shown in equation (2),
R＝A(ATA)-1AT (2)
2.3) calculating C group metamerism black K of C color samples respectivelyiIn which N isfFor its basic color stimulus, as shown in formulas (3) and (4),
Nfi＝R×Ni (3)
Ki＝Ni–Nfi (4)
2.4) for the calculated spectrum of the metameric black K in example 2.3), it is verified whether the tristimulus values XYZ are all 0, when none of XYZ is 0, the metameric black is deleted, otherwise step 3 is performed, in which the spectrum calculates the tristimulus values as in equation (5),
wherein x (λ) y (λ) z (λ) represents a human eye visual matching function, E0(λ) represents an illumination light source D65, K (λ) represents spectral reflectance information of metameric black, and λ represents a visible light wavelength in a range of 400nm to 700 nm.
3) Calculating the basic color spectrum stimulus N of any target sample set N0 by using formula (3)ffAnd solving metamerism set Nm, K corresponding to the sample set by using formula (6)iMetameric black for the library of standard object color spectra as found in example 2),
Nm＝Nff+Ki (6)
according to the calculation process described in formulas (1) (2) (3) (4) (5) (6), the metamerism set N1 corresponding to each of the 24 standard color samples defined by the Colorchecker24 color standard color chart and containing 53486 spectra is calculated in the final embodiment.
4) Eliminating metamerism spectrums, of which the magnitude values of all wave bands in the metamerism set Nm corresponding to any sample set N0 do not belong to the range of [0,1] (namely do not accord with the physical significance of the reflection spectrum), and forming a new metamerism set M;
in this embodiment, taking the first color sample in the Colorchecker24 color standard color card as an example, based on 53486 spectra in the corresponding metamerism set obtained in 2)3)4), 28948 spectra exist, and the magnitude of each waveband does not belong to the range of [0,1], so the spectra are removed, and the rest samples are analogized.
5) For the metamerism set M generated in example 4), the metamerism spectrum with the most representative is selected by maximizing the common metamerism index GM under the single light source D65 according to the metamerism degree of the evaluation spectrum.
5.1) calculating the difference value of the spectral reflectivity of any pair of metamerism colors M and N0 under each wave band with the lambda of 400 nm-700 nm respectively according to the formula (7),
Δβ(λ)＝||M(λ)-N0(λ)|| (7)
5.2) calculating the general metamerism index GM by using the formula (8), wherein the calculation method of w (lambda) is shown in the formula (9),
GM＝∑λw(λ)×Δβ(λ) (8)
wherein the derivatives of L, a and b for any pair of metameric colors with respect to β (λ) are calculated according to the chain ruleThe chain rule is the conventional calculation rule, and the present invention is not repeated.
In the embodiment, firstly, based on the maximization of the general metamerism index, the metamerism spectrum with the most obvious metamerism effect in the respective metamerism set of 24 typical color samples is selected. Fig. 2 shows a reflectance curve of the first color sample of the Colorchecker24 color standard color chart and the corresponding optimal metamerism sample. The two color data are as follows:
original sample:
XYZ values under D65 illuminant (10.6691, 9.4280, 5.9746);
metameric samples shown in fig. 2:
XYZ values under D65 illuminant (10.6691, 9.4280, 5.9746);
the general metamerism indices of both under D65 illuminant are: 67.7655
Therefore, the degree of metamerism is very high, and the difference is obvious. Then, according to the same standard, 10 most obvious metameric spectrum pairs are selected from the 2438 metameric spectrum pair samples, so that the preparation of the metameric samples is completed, and the corresponding samples and the metameric spectrum values are finally obtained in the embodiment.
In addition, the embodiment of the invention also provides a metamerism spectrum generation and evaluation system for light source detection, which comprises the following modules:
a representative color sample collection module for performing representative sample sampling in a large number of spectral data sets that can be collected, obtaining C representative color samples,
a color decomposition module for decomposing in color space to obtain C color samples NiBasic color stimulus N of (i ═ 1,2, …, C)fiAnd metameric black Ki(i ═ 1,2, …, C) and the metameric black K was verifiediWhether the tristimulus values of the spectrum are all 0 or not, and when XYZ is not all 0, deleting the metameric black;
the metamerism set calculation module is used for calculating a metamerism set Nm corresponding to any target sample set N0;
the special spectrum eliminating module is used for eliminating metamerism spectrums, of which the magnitude values of all wave bands in the metamerism set Nm corresponding to any sample set N0 do not belong to the range of [0,1], to form a new metamerism set M;
and the representative metamerism spectrum selection module is used for selecting the most representative metamerism spectrum according to the metamerism degree of the evaluation spectrum by maximizing a common metamerism index GM under a single light source E0 for the metamerism set M generated in the special spectrum rejection module.
Wherein the color decomposition module is a module having the following functions, further for,
an object color matching function a based on a standard illuminant is calculated as shown in equation (1), where the standard illuminant is E0, cmf is the standard observer spectral tristimulus value,
A＝cmf×E0 (1)
the orthogonal projection operator for calculating the color matching function, as shown in equation (2),
R＝A(ATA)-1AT (2)
respectively calculating C groups of basic color stimulus N of C color samplesfiAnd metameric black KiAs shown in the formulas (3) and (4),
Nfi＝R×Ni (3)
Ki＝Ni–Nfi (4)
for the calculated metamerism black KiSpectrum, verifying whether its tristimulus values XYZ are all 0, and deleting the metameric black when none of XYZ is 0, wherein the tristimulus values are calculated from the spectrum as formula (5),
X＝∫λx(λ)E0(λ)K(λ)dλ
Y＝∫λy(λ)E0(λ)K(λ)dλ
Z＝∫λz(λ)E0(λ)K(λ)dλ (5)
where x (λ) y (λ) z (λ) represents the human eye visual matching function, E0(λ) represents the selected standard illumination source, K (λ) represents the metameric black spectral reflectance information, and λ represents a range of visible wavelengths.
Wherein the metamerism set calculation module is a module having the following functions, further for,
calculating the basic color spectrum stimulus N of each spectrum of the arbitrary target sample set N0 by using the formula (3)ffAnd the metamerism set Nm corresponding to the sample set is solved by using a formula (6),
Nm＝Nff+Ki (6)
wherein, KiThe metamerism black spectrum of the color spectrum library of the C standard objects is obtained in the color decomposition module.
Wherein the representative metamerism spectrum selection module is a module having the following functions for further processing,
the difference value of the spectral reflectance of any pair of metamerism colors M and N0 at each wavelength band with lambda in a certain range is calculated by formula (7),
Δβ(λ)＝||M(λ)-N0(λ)|| (7)
calculating general metamerism index GM by using formula (8), wherein the calculation method of w (lambda) is shown in formula (9),
GM＝∑λw(λ)×Δβ(λ) (8)
wherein,the derivatives of L, a and b, representing any pair of metameric colors, with respect to β (λ) were calculated according to the chain rule.
The specific implementation of each module corresponds to each step, and the detailed description of the invention is omitted.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.
Claims (6)
1. A metamerism spectrum generation and evaluation method for light source detection, comprising the steps of:
step 1, performing typical sample sampling in a large amount of collected spectral data sets to obtain C typical color samples,
step 2, decomposing in the color space to obtain C color samples NiBasic color stimulus N of (i ═ 1,2, …, C)fiAnd metameric black Ki(i ═ 1,2, …, C) and the metameric black K was verifiediWhether or not the tristimulus values of the spectrum are all0, when neither XYZ is 0, deleting the metameric black;
step 3, calculating a metamerism set Nm corresponding to any target sample set N0;
step 4, eliminating metamerism spectra of which the magnitude values of all wave bands in the metamerism set Nm corresponding to any sample set N0 do not belong to the range of [0,1] to form a new metamerism set M;
step 5, regarding the metamerism set M generated in the step 4, adopting the common metamerism index GM under a single light source E0 to maximize the metamerism index into a metamerism spectrum according to the evaluation spectrum, selecting the most representative metamerism spectrum,
the implementation of step 5 is as follows,
step 5.1, respectively calculating the difference value of the spectral reflectivity of any pair of metamerism colors M and N0 under each wave band with the lambda being in a certain range by using a formula (7),
Δβ(λ)＝||M(λ)-N0(λ)|| (7)
step 5.2, calculating the general metamerism index GM by using a formula (8), wherein the calculation method of w (lambda) is shown in a formula (9),
GM＝∑λw(λ)×Δβ(λ) (8)
wherein,the derivatives of L, a and b, representing any pair of metameric colors, with respect to β (λ) were calculated according to the chain rule.
2. The metameric spectral generation and evaluation method for light source detection according to claim 1, characterized in that: the implementation of step 2 is as follows,
step 2.1, calculating an object color matching function A based on a standard light source, as shown in formula (1), wherein the standard illuminant is E0, cmf is the spectral tristimulus value of a standard observer,
A＝cmf×E0 (1)
step 2.2, calculating an orthogonal projection operator of the color matching function, as shown in formula (2),
R＝A(ATA)-1AT (2)
step 2.3, respectively calculating C groups of basic color stimulus N of C color samplesfiAnd metameric black KiAs shown in the formulas (3) and (4),
Nfi＝R×Ni (3)
Ki＝Ni–Nfi (4)
step 2.4, metamerism black K calculated in step 2.3iSpectrum, verifying whether its tristimulus values XYZ are all 0, and deleting the metameric black when none of XYZ is 0, wherein the tristimulus values are calculated from the spectrum as formula (5),
where x (λ) y (λ) z (λ) represents the human eye visual matching function, E0(λ) represents the selected standard illumination source, K (λ) represents the metameric black spectral reflectance information, and λ represents a range of visible wavelengths.
3. The metameric spectral generation and evaluation method for light source detection according to claim 2, characterized in that: the implementation of step 3 is as follows,
calculating the basic color spectrum stimulus N of each spectrum of the arbitrary target sample set N0 by using the formula (3)ffAnd the metamerism set Nm corresponding to the sample set is solved by using a formula (6),
Nm＝Nff+Ki (6)
wherein, KiAnd (3) obtaining metamerism black spectrums of the color spectrum library of the C standard objects obtained in the step (2).
4. A metamerism spectrum generation and evaluation system for light source detection, comprising the following modules:
a representative color sample collection module for performing representative sample sampling in a large number of spectral data sets that can be collected, obtaining C representative color samples,
a color decomposition module for decomposing in color space to obtain C color samples NiBasic color stimulus N of (i ═ 1,2, …, C)fiAnd metameric black Ki(i ═ 1,2, …, C) and the metameric black K was verifiediWhether the tristimulus values of the spectrum are all 0 or not, and when XYZ is not all 0, deleting the metameric black;
the metamerism set calculation module is used for calculating a metamerism set Nm corresponding to any target sample set N0;
the special spectrum eliminating module is used for eliminating metamerism spectrums, of which the magnitude values of all wave bands in the metamerism set Nm corresponding to any sample set N0 do not belong to the range of [0,1], to form a new metamerism set M;
the representative metamerism spectrum selection module is used for selecting the most representative metamerism spectrum according to the metamerism degree of the evaluation spectrum by maximizing a common metamerism index GM under a single light source E0 for the metamerism set M generated in the special spectrum rejection module, and has the following functions:
the difference value of the spectral reflectance of any pair of metamerism colors M and N0 at each wavelength band with lambda in a certain range is calculated by formula (7),
Δβ(λ)＝||M(λ)-N0(λ)|| (7)
calculating general metamerism index GM by using formula (8), wherein the calculation method of w (lambda) is shown in formula (9),
GM＝∑λw(λ)×Δβ(λ) (8)
wherein,the derivatives of L, a and b, representing any pair of metameric colors, with respect to β (λ) were calculated according to the chain rule.
5. The metameric spectral generation and evaluation system for light source detection of claim 4, wherein: the color decomposition module is a module having a function for further processing,
an object color matching function a based on a standard illuminant is calculated as shown in equation (1), where the standard illuminant is E0, cmf is the standard observer spectral tristimulus value,
A＝cmf×E0 (1)
the orthogonal projection operator for calculating the color matching function, as shown in equation (2),
R＝A(ATA)-1AT (2)
respectively calculating C groups of basic color stimulus N of C color samplesfiAnd metameric black KiAs shown in the formulas (3) and (4),
Nfi＝R×Ni (3)
Ki＝Ni–Nfi (4)
for the calculated metamerism black KiSpectrum, verifying whether its tristimulus values XYZ are all 0, and deleting the metameric black when none of XYZ is 0, wherein the tristimulus values are calculated from the spectrum as formula (5),
where x (λ) y (λ) z (λ) represents the human eye visual matching function, E0(λ) represents the selected standard illumination source, K (λ) represents the metameric black spectral reflectance information, and λ represents a range of visible wavelengths.
6. The metameric spectral generation and evaluation system for light source detection of claim 5, wherein: the metamerism set calculation module is a module having the following functions, further for,
calculating the basic color spectrum stimulus N of each spectrum of the arbitrary target sample set N0 by using the formula (3)ffAnd the metamerism set Nm corresponding to the sample set is solved by using a formula (6),
Nm＝Nff+Ki (6)
wherein, KiThe metamerism black spectrum of the color spectrum library of the C standard objects is obtained in the color decomposition module.
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