CN107067444A - A kind of spectral gamut mapping method of optimization - Google Patents
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Abstract
The present invention provides a kind of spectral gamut mapping method of optimization, comprises the steps of：One：According to human-eye visual characteristic, choose suitable LMS and bore response spectrum sensitivity curve as weighting function, processing is weighted to higher-dimension spectroscopic data；Two：First three principal component of spectrum after weighting processing, construction LMS PCA spectrum links space are extracted using PCA；Three：The maximum spectral boundaries of output equipment are described in LMS PCA spaces；Four：The specific spectral boundaries of output equipment are described in LMS PCA spaces；Five：Judge whether image spectrum color point to be mapped needs to make mapping processing；Six：Mapping processing is carried out using LSLINceLmax gamut compression algorithms to the image spectrum color point beyond output equipment spectral gamut；Seven：The color data handled based on mapping in obtained LMS PCA spaces carries out Spectral Reconstruction.The spectral gamut mapping method of the present invention has higher spectral accuracy and colourity precision, and possesses stable aberration precision under change environment of observation.
Description
Technical field
Show, replicate and multispectral color management field the present invention relates to color, and in particular to multispectral Color Replication
Spectral gamut mapping method in field of reproduction.
Background technology
Research at present both at home and abroad on spectral gamut mapping is still less, and the method for main flow is all based on principal component analysis
(PCA) spectral gamut description side then or LabPQR dimension reduction methods construct low-dimensional ICS spaces, is designed in the low-dimensional ICS spaces
Method, finally completes image to the mapping process of equipment using mapping algorithm.But the spectral gamut mapping model based on PCA space
In, due to not accounting for visual characteristics of human eyes, cause to map that front and rear spectral error is larger, mapping effect is also not ideal；And
Spectral gamut mapping model based on LabPQR spaces is more complicated due to computational methods, causes mapping efficiency to reduce.Energy of the present invention
Problem above is effectively solved, the spectral accuracy and colourity precision of mapping on the basis of mapping efficiency is ensured, can be improved, and
The image obtained after mapping possesses preferable subjective vision impression.
The content of the invention
Overcome above-mentioned the deficiencies in the prior art, a kind of present invention spectral gamut mapping method of optimization of offer.
Present invention employs following technical scheme：
The present invention provides a kind of spectral gamut mapping method of optimization, it is characterised in that：Comprise the steps of：
Step one：According to human-eye visual characteristic, choose suitable LMS and bore response spectrum sensitivity curve as weighting function,
Processing is weighted to higher-dimension spectroscopic data；
Step 2：First three principal component of spectrum after weighting processing is extracted using PCA PCA, LMS- is constructed
PCA spectrum link space ICS；
Step 3：The maximum spectral boundaries GBD of output equipment is described in LMS-PCA spaces；
Step 4：The specific spectral boundaries LBD of output equipment is described in LMS-PCA spaces；
Step 5：Judge whether image spectrum color point to be mapped needs to make mapping processing；
Step 6：LSLINceLmax gamut compressions are used to the image spectrum color point beyond output equipment spectral gamut
Algorithm carries out mapping processing；
Step 7：The color data handled based on mapping in obtained LMS-PCA spaces carries out Spectral Reconstruction.
Further, a kind of spectral gamut mapping method of optimization of the invention, can also have the feature that, step one
In, comprise the following steps：
Step 1-1：According to human-eye visual characteristic, choose suitable LMS and bore response spectrum sensitivity curve as weighting function,
Processing is weighted to higher-dimension spectroscopic data.When spectral tristimulus value is converted to the response of the LMS cones, selection Bradford becomes
Matrix is changed as transformation matrix：
Step 1-2：LMS weighting functions are constructed by formula 2：
In formula, p is variable coefficient, its span between -0.5 to 50, k values be 1~10 between.
Step 1-3：Processing is weighted to higher-dimension spectroscopic data using LMS weighting functions.
Further, a kind of spectral gamut mapping method of optimization of the invention, can also have the feature that, step 2
In：First three principal component of spectrum after weighting processing, construction LMS-PCA spectrum links space are extracted using PCA.
Further, a kind of spectral gamut mapping method of optimization of the invention, can also have the feature that, step 2
In specifically include following steps：
Step 2-1：Singular value decomposition is carried out to the spectroscopic data after weighting；
Step 2-2：Dimensionality reduction is carried out to the spectroscopic data after weighting by the characteristic vector of singular value decomposition, first three is extracted
Principal component builds LMS-PCA rectangular coordinate systems as spectrum and links space.
Further, a kind of spectral gamut mapping method of optimization of the invention, can also have the feature that, step 3
Include step：
Step 3-1：By the rectangular coordinate system P in LMS-PCA spaces1, P2, P3Spherical coordinate system α, θ, r are transformed into, output is calculated
Spherical coordinates value corresponding to the spectral color point of equipment.
Step 3-2：LMS-PCA space uniforms are divided into n × n deciles along α and θ directions respectively, each output is calculated
The spherical coordinates of equipment spectral color sample point, determines that each spectral color sample point is located at LMS-PCA empty according to its α and θ value
Between in which sub-regions；Compare in every sub-regions all spectral color sample points to central point apart from r, retain wherein
The maximum spectral color sample point of r values is as the boundary point of the subregion, all boundary points one square of deposit most obtained at last
Battle array obtains maximum spectral boundaries GBD.
Further, a kind of spectral gamut mapping method of optimization of the invention, can also have the feature that, step 4
Include step：
Step 4-1：Calculate the spherical coordinates α corresponding to the hue angle of image spectrum color point to be mapped, and according to its α value and
Spectroscopic plane coordinate (Co,p1) and central point E, that finds the spectral color point waits α faces.Wherein, coordinate
Step 4-2：According to hue angle α, a pair of adjacent spectrum face are found out from the GBD submatrixs of first horizontal segmentation layer
Color dot, hue angle wherein is more than α, and the hue angle of another point is less than α.Then the two adjacent spectrum color points are connected
In line, the straight line is sought with waiting intersection point in α faces.Due to a shared n horizontal slice, therefore n intersection point finally is can obtain, this
A little intersection points are linear barrier of the output equipment spectral gamut on α faces are waited,
Step 4-3：According to the spectral color in maximum spectral boundaries GBD matrixes with maximum brightness value and minimum brightness value
Sample point, obtains minimum and maximum linear barrier's point in the spectral color sample point of output equipment, obtained by step 4-2
Linear barrier combines the specific spectral boundaries LBD to form output equipment.
Further, a kind of spectral gamut mapping method of optimization of the invention, can also have the feature that, step 5
In comprise the following steps that：
Judge the relation of the mapped color point and output equipment spectral gamut.If the mapped color point is located at output equipment light
Outside spectrum color domain, it need to be handled by the 6th step；If the mapped color point is located within output equipment spectral gamut, does not just do and locate
Reason, is directly entered the 7th step.
Further, a kind of spectral gamut mapping method of optimization of the invention, can also have the feature that, step 5
It is middle judge mapped color point be located within output equipment spectral gamut or outside method it is as follows：
By the spectroscopic plane coordinate points M (C of M pointso,p1) and p1The central point E connections of axle, and extend in line, the straight line
Point H (C' are intersected at LBD linear barrierso,p'1), if Co＜ C'oAnd pmin＜ p'1＜ pmax, then M points are positioned at printer spectrum colour
Within domain, otherwise it is located in outside printer spectral gamut.
Further, a kind of spectral gamut mapping method of optimization of the invention, can also have the feature that, step 6
In, comprise the following steps：
Step 6-1：Using based on LSLINceLmax gamut compressions in LMS-PCA spaces, by super output equipment spectral gamut
Spectrum picture color point to be mapped be mapped in output equipment spectral domain.Based on LSLINceLmax colour gamuts in LMS-PCA spaces
Compression is on the basis of traditional LSLIN algorithms, to add the influence of output equipment spectral gamut lightness intermediate value and spectrum to be mapped
Image brightness maximum influences, while the spectrum chroma and spectrum lightness to spectrum picture spectral color point to be mapped are pressed
Contracting, so as to complete the mapping process of degree of precision.Its spectrum maps expression formula：
In formula, CrFor the spectrum chroma value of output image after mapping, Cr(max)For the maximum spectrum of output equipment spectral gamut
Chroma value, CoFor the spectral color stippling angle value of spectrum picture to be mapped, Co(max)For the maximum light of spectrum picture colour gamut to be mapped
Compose chroma value.prFor the spectrum brightness value of output image after mapping, p1For the spectral color point brightness value of spectrum picture to be mapped,
Center is the brightness value for the form and aspect face spectrum lightness axis central points such as spectrum picture spectral color point to be mapped is corresponding, ceLmax
For the maximum brightness value Lmax and center of spectrum picture to be mapped weighting function.
Step 6-2：CeLmax expression formulas are as follows：
In formula, Lmax is the maximum brightness value of spectrum picture to be mapped, and cc, dd and hh are constant, cc span
It is 0 to 10 for -15 to 15, dd span, and the span that hh takes is 1 to 3.
The beneficial effect of invention
The present invention is weighted processing using suitable LMS weighting functions to higher-dimension spectroscopic data, using principal component analysis
Method extracts first three principal component of weighted spectral, to build LMS-PCA spectrum link space.Introduced in LMS-PCA spaces
The spectral gamut of subregion maturation SMGBD arthmetic statement output equipments, to the spectrum picture color beyond output equipment spectral gamut
Point is mapped in output equipment spectral gamut using LSLINceLmax gamut compressions.The present invention has taken into full account that human eye vision is special
Property, and spectral gamut mapping model is built on the basis of optimization tradition LSLIN algorithms, with higher spectral accuracy and colourity
Precision, and possess stable aberration precision under change environment of observation, new model possesses preferable aberration stability, is suitable for simultaneously
Various types of spectrum pictures, practicality is preferable.
Brief description of the drawings
Fig. 1 is segmentation schematic diagram.
Fig. 2 is the C of linear barrieroP1Plane simulation figure.
Fig. 3 is that mapping judges schematic diagram.
Embodiment
Illustrate the embodiment of the present invention below in conjunction with accompanying drawing.
In this example, the source colour gamut of spectral gamut mapping is the spectral gamut of standard spectrum image, and target color gamut is HP
The spectral gamut of Design Z3200 multichannel printers, mapping light source is set as D50.HP is obtained by making training color target by oneself
The Detailed spectrum colouring information of Design Z3200 printers.A kind of specific steps of the spectral gamut mapping method of optimization are such as
Under：
Step one, according to human-eye visual characteristic, choose suitable LMS and bore response spectrum sensitivity curve as weighting function,
Processing is weighted to higher-dimension spectroscopic data.Following steps are specifically included in step one：
Step 1-1：Bradford's transformation matrix (MBFD) is selected as transformation matrix, by formula 1 by spectral tristimulus value
Be converted to the response of the LMS cones.
Step 1-2：LMS weighting functions are constructed by formula 2：
Step 1-3：It is many to be mapped standard spectrum image and HP Design Z3200 respectively using LMS weighting functions
The higher-dimension spectroscopic data of pass print machine is weighted processing.If the spectral information of printer is R, dimension is N, then after weighting
Spectrum expression formula is as follows：
In formula,It is LMS weighting functionsThe diagonal matrix of conversion.
Step 2：Spectrum after being handled using PCA PCA weighting makees dimension-reduction treatment, extract it is therein first three
Individual principal component, construction LMS-PCA spaces.Following steps are specifically included in step 2：
Step 2-1：Singular value decomposition is carried out to weighted spectral,Obtain characteristic vector U={ U1,U2,
...Un, first three characteristic vector is extracted, is denoted as
Step 2-2：UtilizeDimensionality reduction is carried out to weighted spectral, the three-dimensional weighted spectral after dimensionality reduction is obtained
First three principal component obtained using dimensionality reduction builds LMS-PCA rectangular coordinate systems space, if first three principal component is
P1, P2, P3。
Step 3：The maximum spectral boundaries GBD of output equipment is described in LMS-PCA spaces.Specifically included in step 3
Following steps：
Step 3-1：By LMS-PCA spaces from rectangular coordinate system P1, P2, P3It is transformed into spherical coordinate system α, θ, r.
R and θ calculation is as follows：
The calculating of α values quadrant according to where its angle is different, is calculated by different formulas：
Step 3-2：LMS-PCA space uniforms are divided into n × n deciles along α and θ directions respectively, each printing is calculated
The spherical coordinates of machine spectral color sample point, determines that each spectral color sample point is located at LMS-PCA spaces according to its α and θ value
In which sub-regions；Compare in every sub-regions all spectral color sample points to central point apart from r, retain wherein r
It is worth maximum spectral color sample point as the boundary point of the subregion, all boundary points most obtained at last are stored in a matrix
Obtain maximum spectral boundaries GBD.
Step 4, describes the specific spectral boundaries LBD of output equipment in LMS-PCA spaces.Specifically included in step 4
Following steps：
Step 4-1：Checked object is used as using some spectral color point M in spectrum picture.By the inspection spectral color point
Dimensionality reduction is in LMS-PCA spaces, obtaining its coordinate value for (p1,p2,p3)。
Step 4-2：The spherical coordinates α corresponding to the hue angle of M points is calculated, and according to its α value and spectroscopic plane coordinate (Co,
p1) and central point E find the inspection spectral color point etc. α faces.
Step 4-3：According to the hue angle α of M points, from the maximum spectral boundaries GBD submatrixs of first horizontal segmentation layer
A pair of adjacent spectrum color points are found out, hue angle wherein is more than α, and the hue angle of another point is less than α.Then by the two
Adjacent spectrum color point is connected in line, seeks the straight line with waiting intersection point in α faces.Due to a shared n horizontal slice, therefore most
N intersection point is can obtain eventually, and these intersection points are linear barrier of the printer spectral gamut on α faces are waited.
Step 4-4：Calculate p1Maximum, minimal linear boundary point on axle.In all GBD submatrixs, selection has most
Big p1The spectral color point of value is used as maximum linear boundary point pmax, similarly selection is with minimum p1The spectral color point of value is as most
Small linear barrier's point pmin.The specific spectral boundaries LBD to form printer is combined with the linear barrier obtained by step 4-3.
Step 5：Judge whether image spectrum color point to be mapped needs to make mapping processing.
Judge the relation of the mapped color point and output equipment spectral gamut.If the mapped color point is located at output equipment light
Outside spectrum color domain, it need to be handled by the 6th step；If the mapped color point is located within output equipment spectral gamut, does not just do and locate
Reason, is directly entered the 7th step.
Method outside judging mapped color point within output equipment spectral gamut still in step 5 is as follows：By M
The spectroscopic plane coordinate points M (C of pointo,p1) and p1The central point E connections of axle, and extend in line, the straight line and LBD linear edges
Boundary is intersected at a littleH(C'o,p'1), if Co＜ C'oAnd pmin＜ p'1＜ pmax, then M points are within printer spectral gamut, otherwise
It is located in outside printer spectral gamut, next step LSLINceLmax gamut compressions need to be carried out, Fig. 3 judges schematic diagram for mapping.
Step 6：To the image spectrum color point beyond printer spectral gamut according to formula 3 and formula 4 using based on LMS-
LSLINceLmax gamut compression algorithms in PCA space carry out mapping processing.Following steps are specifically included in step 6：
Step 6-1：Using based on LSLINceLmax gamut compressions in LMS-PCA spaces, by super output equipment spectral gamut
Spectrum picture color point to be mapped be mapped in output equipment spectral domain.Based on LSLINceLmax colour gamuts in LMS-PCA spaces
Compression is on the basis of traditional LSLIN algorithms, to add the influence of output equipment spectral gamut lightness intermediate value and spectrum to be mapped
Image brightness maximum influences, while the spectrum chroma and spectrum lightness to spectrum picture spectral color point to be mapped are pressed
Contracting, so as to complete the mapping process of degree of precision.Its spectrum maps expression formula：
In formula, CrFor the spectrum chroma value of output image after mapping, Cr(max)For the maximum spectrum of output equipment spectral gamut
Chroma value, CoFor the spectral color stippling angle value of spectrum picture to be mapped, Co(max)For the maximum light of spectrum picture colour gamut to be mapped
Compose chroma value.prFor the spectrum brightness value of output image after mapping, p1For the spectral color point brightness value of spectrum picture to be mapped,
Center is the brightness value for the form and aspect face spectrum lightness axis central points such as spectrum picture spectral color point to be mapped is corresponding, ceLmax
For the maximum brightness value Lmax and center of spectrum picture to be mapped weighting function.
Step 6-2：CeLmax expression formulas are as follows：
In formula, Lmax is the maximum brightness value of spectrum picture to be mapped, and cc, dd and hh are constant, cc span
It is 0 to 10 for -15 to 15, dd span, and hh typically takes 1 to 3.
Step 7：Color data in the LMS-PCA spaces obtained after mapping is handled is carried out Spectral Reconstruction, obtained
Image spectrum information after mapping.
Step 8：Terminate.
Certainly, the present embodiment is merely to illustrate a kind of spectral gamut mapping method of optimization of the present invention, is not used to limit
Protection scope of the present invention processed.
Claims (9)
1. a kind of spectral gamut mapping method of optimization, it is characterised in that：Comprise the steps of：
Step one：According to human-eye visual characteristic, choose suitable LMS and bore response spectrum sensitivity curve as weighting function, to height
Dimension spectroscopic data is weighted processing；
Step 2：First three principal component of spectrum after weighting processing is extracted using PCA PCA, LMS-PCA light is constructed
Spectrum link space ICS；
Step 3：The maximum spectral boundaries GBD of output equipment is described in LMS-PCA spaces；
Step 4：The specific spectral boundaries LBD of output equipment is described in LMS-PCA spaces；
Step 5：Judge whether image spectrum color point to be mapped needs to make mapping processing；
Step 6：LSLINceLmax gamut compression algorithms are used to the image spectrum color point beyond output equipment spectral gamut
Carry out mapping processing；
Step 7：The color data handled based on mapping in obtained LMS-PCA spaces carries out Spectral Reconstruction.
2. the spectral gamut mapping method of a kind of optimization according to claim 1, it is characterised in that in step one, including
Following steps：
Step 1-1：According to human-eye visual characteristic, choose LMS and bore response spectrum sensitivity curve as weighting function, to higher-dimension spectrum
Data are weighted processing, when spectral tristimulus value is converted to the response of the LMS cones, select Bradford's transformation matrix conduct
Transformation matrix：
Step 1-2：LMS weighting functions are constructed by formula 2：
In formula, p is variable coefficient, its span between -0.5 to 50, k values be 1~10 between,
Step 1-3：Processing is weighted to higher-dimension spectroscopic data using LMS weighting functions.
3. the spectral gamut mapping method of a kind of optimization according to claim 1, it is characterised in that in step 2：Using
PCA extracts first three principal component of spectrum after weighting processing, construction LMS-PCA spectrum links space.
4. the spectral gamut mapping method of a kind of optimization according to claim 3, it is characterised in that specifically wrapped in step 2
Include following steps：
Step 2-1：Singular value decomposition is carried out to the spectroscopic data after weighting；
Step 2-2：Dimensionality reduction is carried out to the spectroscopic data after weighting by the characteristic vector of singular value decomposition, extract first three it is main into
Structure LMS-PCA rectangular coordinate systems are divided to be used as spectrum to link space.
5. the spectral gamut mapping method of a kind of optimization according to claim 1, it is characterised in that step 3 includes step
Suddenly：
Step 3-1：By the rectangular coordinate system P in LMS-PCA spaces1, P2, P3Spherical coordinate system α, θ, r are transformed into, output equipment is calculated
Spectral color point corresponding to spherical coordinates value,
Step 3-2：LMS-PCA space uniforms are divided into n × n deciles along α and θ directions respectively, each output equipment is calculated
The spherical coordinates of spectral color sample point, determines that each spectral color sample point is located in LMS-PCA spaces according to its α and θ value
Which sub-regions；Compare in every sub-regions all spectral color sample points to central point apart from r, retain wherein r values
Maximum spectral color sample point is as the boundary point of the subregion, and all boundary points most obtained at last are stored in a matrix and obtain
To maximum spectral boundaries GBD.
6. the spectral gamut mapping method of a kind of optimization according to claim 1, it is characterised in that step 4 includes step
Suddenly：
Step 4-1：The spherical coordinates α corresponding to the hue angle of image spectrum color point to be mapped is calculated, and according to its α value and spectrum
Plane coordinates (Co,p1) and central point E, that finds the spectral color point waits α faces, wherein, coordinate
Step 4-2：According to hue angle α, a pair of adjacent spectrum colors are found out from the GBD submatrixs of first horizontal segmentation layer
Point, hue angle wherein is more than α, and the hue angle of another point is less than α, then connects into the two adjacent spectrum color points
One straight line, seeks the straight line with waiting intersection point in α faces, due to a shared n horizontal slice, therefore finally can obtain n intersection point, these
Intersection point is linear barrier of the output equipment spectral gamut on α faces are waited,
Step 4-3：According to the spectral color sample in maximum spectral boundaries GBD matrixes with maximum brightness value and minimum brightness value
Point, obtains minimum and maximum linear barrier's point in the spectral color sample point of output equipment, and linear obtained by step 4-2
The specific spectral boundaries LBD of boundary combinations formation output equipment.
7. the spectral gamut mapping method of a kind of optimization according to claim 1, it is characterised in that specific in step 5
Step is as follows：
The relation of the mapped color point and output equipment spectral gamut is judged, if the mapped color point is located at output equipment spectrum colour
Outside domain, then handled by step 6；If the mapped color point is located within output equipment spectral gamut, do not process,
It is directly entered step 7.
8. the spectral gamut mapping method of a kind of optimization as claimed in claim 1, it is characterised in that mapping is judged in step 5
Color point be located at output equipment spectral gamut within or outside method it is as follows：
By the spectroscopic plane coordinate points M (C of M pointso,p1) and p1The central point E connections of axle, and extend in line, the straight line with
LBD linear barriers intersect at point H (C'o,p'1), if Co＜ C'oAnd pmin＜ p'1＜ pmax, then M points are positioned at printer spectral gamut
Within, otherwise it is located in outside printer spectral gamut.
9. the spectral gamut mapping method of a kind of optimization according to claim 1, it is characterised in that in step 6, including
Following steps：
Step 6-1：Using based on LSLINceLmax gamut compressions in LMS-PCA spaces, by treating for super output equipment spectral gamut
Mapping spectrum picture color point is mapped in output equipment spectral domain, based on LSLINceLmax gamut compressions in LMS-PCA spaces
It is on the basis of traditional LSLIN algorithms, to add the influence of output equipment spectral gamut lightness intermediate value and spectrum picture to be mapped
Lightness maximum influences, while the spectrum chroma and spectrum lightness to spectrum picture spectral color point to be mapped are compressed, from
And the mapping process of degree of precision is completed, its spectrum mapping expression formula is：
In formula, CrFor the spectrum chroma value of output image after mapping, Cr(max)For the maximum spectrum chroma of output equipment spectral gamut
Value, CoFor the spectral color stippling angle value of spectrum picture to be mapped, Co(max)It is color for the maximum spectrum of spectrum picture colour gamut to be mapped
Angle value, prFor the spectrum brightness value of output image after mapping, p1For the spectral color point brightness value of spectrum picture to be mapped,
Center is the brightness value for the form and aspect face spectrum lightness axis central points such as spectrum picture spectral color point to be mapped is corresponding, ceLmax
For the maximum brightness value Lmax and center of spectrum picture to be mapped weighting function,
Step 6-2：CeLmax expression formulas are as follows：
In formula, Lmax is the maximum brightness value of spectrum picture to be mapped, and cc, dd and hh are constant, and cc span is -15
Span to 15, dd is 0 to 10, and the span that hh takes is 1 to 3.
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| CN115546323A (en) * | 2022-08-31 | 2022-12-30 | 广东工业大学 | Image compression reconstruction method based on spherical coordinate principal component analysis |
| CN115546323B (en) * | 2022-08-31 | 2023-06-09 | 广东工业大学 | Image compression reconstruction method based on spherical coordinate principal component analysis |
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