CN107067444B - Optimized spectrum color gamut mapping method - Google Patents
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Abstract
The invention provides an optimized spectral gamut mapping method, which comprises the following steps: firstly, the method comprises the following steps: according to the visual characteristics of human eyes, selecting a proper LMS cone response spectrum sensitivity curve as a weighting function to perform weighting processing on high-dimensional spectrum data; II, secondly: extracting the first three principal components of the spectrum after weighting processing by adopting a principal component analysis method, and constructing an LMS-PCA spectrum link space; thirdly, the method comprises the following steps: describing the maximum spectral boundaries of the output device in LMS-PCA space; fourthly, the method comprises the following steps: describing specific spectral boundaries of the output device in LMS-PCA space; fifthly: judging whether the color point of the spectrum of the image to be mapped needs to be mapped or not; sixthly, the method comprises the following steps: mapping the image spectral color points beyond the spectral color gamut of the output equipment by adopting an LSLINceLmax color gamut compression algorithm; seventhly, the method comprises the following steps: and performing spectral reconstruction based on the color data in the LMS-PCA space obtained by mapping processing. The spectral color gamut mapping method has high spectral precision and chromaticity precision, and has stable color difference precision under variable observation environments.
Description
Technical Field
The invention relates to the fields of color display, reproduction and multispectral color management, in particular to a spectral gamut mapping method in the field of multispectral color reproduction and reproduction.
Background
At present, researches on spectral color gamut mapping at home and abroad are still few, and the mainstream method is to construct a low-dimensional ICS space based on Principal Component Analysis (PCA) or LabPQR dimension reduction method, then design a spectral color gamut description method in the low-dimensional ICS space, and finally complete the mapping process from an image to equipment by using a mapping algorithm. However, in the spectrum color gamut mapping model based on the PCA space, because the visual characteristics of human eyes are not considered, the spectrum error before and after mapping is larger, and the mapping effect is not ideal; the spectral gamut mapping model based on the LabPQR space has a relatively complex calculation method, so that the mapping efficiency is reduced. The invention can effectively solve the problems, improve the spectral accuracy and the chromaticity accuracy of mapping on the basis of ensuring the mapping efficiency, and obtain an image with better subjective visual perception after mapping.
Disclosure of Invention
The present invention overcomes the above-mentioned deficiencies of the prior art and provides an optimized spectral gamut mapping method.
The invention adopts the following technical scheme:
the invention provides an optimized spectral gamut mapping method, which is characterized by comprising the following steps: comprises the following steps:
the method comprises the following steps: according to the visual characteristics of human eyes, selecting a proper LMS cone response spectrum sensitivity curve as a weighting function to perform weighting processing on high-dimensional spectrum data;
step two: extracting the first three principal components of the spectrum after weighting treatment by adopting a Principal Component Analysis (PCA) method, and constructing an LMS-PCA spectrum link space (ICS);
step three: describing the maximum spectral boundary GBD of the output device in LMS-PCA space;
step four: describing the specific spectral boundaries LBD of the output device in LMS-PCA space;
step five: judging whether the color point of the spectrum of the image to be mapped needs to be mapped or not;
step six: mapping the image spectral color points beyond the spectral color gamut of the output equipment by adopting an LSLINceLmax color gamut compression algorithm;
step seven: and performing spectral reconstruction based on the color data in the LMS-PCA space obtained by mapping processing.
Further, an optimized spectral gamut mapping method according to the present invention may further have the following features, wherein the first step includes the steps of:
step 1-1: and according to the visual characteristics of human eyes, selecting a proper LMS cone response spectrum sensitivity curve as a weighting function to perform weighting processing on the high-dimensional spectrum data. When the spectrum tristimulus values are converted into LMS cone responses, selecting a Bradford transformation matrix as a transformation matrix:
step 1-2: the LMS weighting function is constructed as equation 2:
in the formula, p is a variable coefficient and ranges from-0.5 to 50, and k is 1-10.
Step 1-3: and carrying out weighting processing on the high-dimensional spectral data by utilizing an LMS weighting function.
Further, an optimized spectral gamut mapping method according to the present invention may further have the following features, in step two: and extracting the first three principal components of the spectrum after weighting processing by adopting a principal component analysis method, and constructing an LMS-PCA spectrum link space.
Further, the optimized spectral gamut mapping method of the present invention may further have the following characteristics, and the step two specifically includes the following steps:
step 2-1: performing singular value decomposition on the weighted spectrum data;
step 2-2: and reducing the dimension of the weighted spectral data through the eigenvector of singular value decomposition, and extracting the first three principal components to construct an LMS-PCA rectangular coordinate system as a spectral link space.
Further, an optimized spectral gamut mapping method according to the present invention may further have the following features, where the step three includes the steps of:
step 3-1: using a rectangular coordinate system P of LMS-PCA space1，P2，P3And converting the coordinate system into a spherical coordinate system α, theta and r, and calculating spherical coordinate values corresponding to the spectral color points of the output device.
And 3-2, uniformly dividing the LMS-PCA space into n multiplied by n equal parts along α and theta directions respectively, calculating the spherical coordinates of each output device spectral color sample point, determining which sub-region of the LMS-PCA space each spectral color sample point is located in according to the values of α and theta, comparing the distances r from all spectral color sample points in each sub-region to the central point, keeping the spectral color sample point with the maximum r value as the boundary point of the sub-region, and finally storing all the obtained boundary points into a matrix to obtain the maximum spectral boundary GBD.
Further, an optimized spectral gamut mapping method according to the present invention may further have the following features, where the step four includes the steps of:
step 4-1, calculating a spherical coordinate α corresponding to the hue angle of the spectrum color point of the image to be mapped, and calculating the color point according to the value α and the spectrum plane coordinate (C)o,p1) And a center point E, finding α planes that are equal to the spectral color point, wherein the coordinates
Step 4-2, finding out a pair of adjacent spectral color points from the GBD submatrix of the first horizontal division layer according to the hue angle α, wherein the hue angle of one point is more than α, and the hue angle of the other point is less than α, then connecting the two adjacent spectral color points into a straight line, and calculating the intersection points of the straight line and the equal α plane, because one horizontal division layer has n total, n intersection points can be finally obtained, the intersection points are the linear boundaries of the spectral color gamut of the output device on the equal α plane,
step 4-3: and obtaining the maximum and minimum linear boundary points in the spectral color sample points of the output device according to the spectral color sample points with the maximum lightness value and the minimum lightness value in the maximum spectral boundary GBD matrix, and combining the maximum and minimum linear boundary points with the linear boundary obtained in the step 4-2 to form a specific spectral boundary LBD of the output device.
Further, the optimized spectral gamut mapping method of the present invention may also have the following characteristics, and the specific steps in step five are as follows:
and judging the relation between the mapping color point and the spectral color gamut of the output device. If the mapped color point is outside the spectral color gamut of the output device, processing according to a sixth step; if the mapped color point is within the spectral gamut of the output device, no processing is performed and the seventh step is entered directly.
Further, an optimized spectral gamut mapping method according to the present invention may further have such a feature that the method for determining whether the mapped color point is located inside or outside the spectral gamut of the output device in step five is as follows:
coordinate point M (C) of spectral plane of point Mo,p1) And p1The center point E of the shaft is connected to and extends to a straight line intersecting the LBD linear boundary at point H (C'o,p'1) If C iso＜C'oAnd p ismin＜p'1＜pmaxThen the M points are within the printer spectral gamut, otherwise they are outside the printer spectral gamut.
Further, an optimized spectral gamut mapping method according to the present invention may further have the following feature, in step six, including the steps of:
step 6-1: and mapping the color points of the spectral image to be mapped of the spectral color gamut of the super-output device into the spectral domain of the output device by utilizing the LSLINCELmax color gamut compression in the LMS-PCA-based space. Based on LSLINceLmax color gamut compression in LMS-PCA space, on the basis of a traditional LSLIN algorithm, the influence of a spectral color gamut median value of output equipment and the influence of a spectral image brightness maximum value to be mapped are added, and meanwhile, the spectral chroma and the spectral brightness of a spectral color point of a spectral image to be mapped are compressed, so that a mapping process with higher precision is completed. The spectrum mapping expression is as follows:
in the formula, CrFor the spectral chroma value, C, of the mapped output imager(max)Maximum spectral chroma value, C, of the spectral gamut of the output deviceoAs a spectral color point chroma value, C, of the spectral image to be mappedo(max)Is the maximum spectral chroma value of the spectral image gamut to be mapped. p is a radical ofrFor the spectral brightness value, p, of the mapped output image1The spectral image brightness value is the spectral color point brightness value of the spectral image to be mapped, the center is the brightness value of the central point of the equal hue surface spectral brightness axis corresponding to the spectral color point of the spectral image to be mapped, and the cemmax is the weighting function of the maximum brightness value Lmax and the center of the spectral image to be mapped.
Step 6-2: the cemmax expression is as follows:
in the formula, Lmax is the maximum brightness value of the spectral image to be mapped, cc, dd and hh are constants, the value range of cc is-15 to 15, the value range of dd is 0 to 10, and the value range of hh is 1 to 3.
Advantageous effects of the invention
According to the invention, the high-dimensional spectral data is weighted by using a proper LMS weighting function, and the first three principal components of the weighted spectrum are extracted by using a principal component analysis method so as to construct an LMS-PCA spectral link space. And introducing a partition mature SMGBD algorithm into an LMS-PCA space to describe the spectral color gamut of the output device, and mapping the spectral image color point beyond the spectral color gamut of the output device into the spectral color gamut of the output device by adopting LSLINceLmax color gamut compression. The invention fully considers the visual characteristics of human eyes, constructs a spectral color gamut mapping model on the basis of optimizing the traditional LSLIN algorithm, has higher spectral precision and chromaticity precision, has stable color difference precision under variable observation environment, has better color difference stability simultaneously, is suitable for various types of spectral images, and has better practicability.
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Fig. 1 is a schematic diagram of segmentation.
FIG. 2 is C of a linear boundaryoP1Plane dieDrawing.
Fig. 3 is a diagram illustrating mapping determination.
Detailed Description
The following describes embodiments of the present invention with reference to the drawings.
In this example, the source gamut of the spectral gamut mapping is the spectral gamut of the standard spectral image, the target gamut is the spectral gamut of the HPDesign Z3200 multi-channel printer, and the mapping light source is set to D50. And obtaining detailed spectral color information of the HPdesign Z3200 printer through a self-made training color target. The optimized spectral gamut mapping method comprises the following specific steps:
firstly, according to the visual characteristics of human eyes, a proper LMS cone response spectrum sensitivity curve is selected as a weighting function, and weighting processing is carried out on high-dimensional spectrum data. The first step specifically comprises the following steps:
step 1-1: the bradford transformation Matrix (MBFD) is selected as the transformation matrix, and the spectral tristimulus values are converted into LMS cone responses according to equation 1.
Step 1-2: the LMS weighting function is constructed as equation 2:
step 1-3: and respectively carrying out weighting processing on the standard spectral image to be mapped and the high-dimensional spectral data of the HP Design Z3200 multi-channel printer by utilizing the LMS weighting function. If the spectral information of the printer is R and the dimension is N, the weighted spectral expression is as follows:
in the formula (I), the compound is shown in the specification,
is the LMS weighting function
A diagonal matrix of transitions.
Step two: and performing dimensionality reduction on the spectrum after weighting treatment by adopting a Principal Component Analysis (PCA), extracting the first three principal components, and constructing an LMS-PCA space. The second step specifically comprises the following steps:
step 2-1: the weighted spectrum is subjected to a singular value decomposition,
obtaining a characteristic vector U ═ U1,U2,...UnExtracting the first three feature vectors, and recording the vectors as
Step 2-2: by using
Reducing the dimension of the weighted spectrum to obtain a three-dimensional weighted spectrum after dimension reduction
Constructing an LMS-PCA rectangular coordinate system space by using the first three principal components obtained by dimensionality reduction, and setting the first three principal components as P1，P2，P3。
Step three: the maximum spectral boundary GBD of the output device is described in LMS-PCA space. The third step specifically comprises the following steps:
step 3-1: the LMS-PCA space is transformed from a rectangular coordinate system P1，P2，P3And converted to a spherical coordinate system α, theta, r.
r and θ are calculated as follows:
α, the calculation of the value is calculated according to different formulas according to different quadrants of the included angle:
and 3-2, uniformly dividing the LMS-PCA space into n multiplied by n equal parts along α and theta directions respectively, calculating the spherical coordinates of each printer spectral color sample point, determining which sub-region of the LMS-PCA space each spectral color sample point is located in according to the values of α and theta, comparing the distances r from all spectral color sample points in each sub-region to the central point, reserving the spectral color sample point with the maximum r value as the boundary point of the sub-region, and finally storing all the obtained boundary points into a matrix to obtain the maximum spectral boundary GBD.
And step four, describing the specific spectral boundary LBD of the output device in the LMS-PCA space. The fourth step specifically comprises the following steps:
step 4-1: a certain spectral color point M in the spectral image is taken as a checking object. Reducing the dimension of the color point of the test spectrum to the LMS-PCA space to obtain the coordinate value of (p)1,p2,p3)。
Step 4-2, calculating a spherical coordinate α corresponding to the hue angle of the M point, and calculating a α value and a spectrum plane coordinate (C)o,p1) And the center point E finds the equal α planes of the inspection spectral color point.
And 4-3, finding out a pair of adjacent spectral color points from the maximum spectral boundary GBD sub-matrix of the first horizontal segmentation layer according to the hue angle α of the M points, wherein the hue angle of one point is more than α, and the hue angle of the other point is less than α, connecting the two adjacent spectral color points into a straight line, and solving the intersection point of the straight line and the equal α plane, wherein n intersection points are finally obtained as n horizontal layers are total, and the intersection points are linear boundaries of the printer spectral color gamut on the equal α plane.
Step 4-4: calculating p1Maximum and minimum linear boundary points on the axis. Among all GBD sub-matrices, the one with the largest is selectedp1Spectral color point of value as maximum linear boundary point pmaxSimilarly, choose to have the minimum p1Spectral color point of value as minimum linear boundary point pmin. Combined with the linear boundaries obtained in step 4-3 to form the printer specific spectral boundaries LBD.
Step five: and judging whether the color point of the spectrum of the image to be mapped needs to be mapped or not.
And judging the relation between the mapping color point and the spectral color gamut of the output device. If the mapped color point is outside the spectral color gamut of the output device, processing according to a sixth step; if the mapped color point is within the spectral gamut of the output device, no processing is performed and the seventh step is entered directly.
The method for judging whether the mapping color point is positioned in the spectral color gamut of the output device or not in the step five is as follows: coordinate point M (C) of spectral plane of point Mo,p1) And p1The center points E of the axes are connected and extend to a line intersecting the linear boundary of LBD at a pointH(C'o,p'1) If C iso＜C'oAnd p ismin＜p'1＜pmaxIf the M points are located within the printer spectral color gamut, otherwise, the M points are located outside the printer spectral color gamut, and the next lslincellmax color gamut compression is performed, where fig. 3 is a mapping determination diagram.
Step six: the image spectral color points that exceed the printer spectral gamut are mapped according to equations 3 and 4 using the lslincellmax gamut compression algorithm in the LMS-PCA based space. The sixth step specifically comprises the following steps:
step 6-1: and mapping the color points of the spectral image to be mapped of the spectral color gamut of the super-output device into the spectral domain of the output device by utilizing the LSLINCELmax color gamut compression in the LMS-PCA-based space. Based on LSLINceLmax color gamut compression in LMS-PCA space, on the basis of a traditional LSLIN algorithm, the influence of a spectral color gamut median value of output equipment and the influence of a spectral image brightness maximum value to be mapped are added, and meanwhile, the spectral chroma and the spectral brightness of a spectral color point of a spectral image to be mapped are compressed, so that a mapping process with higher precision is completed. The spectrum mapping expression is as follows:
in the formula, CrFor the spectral chroma value, C, of the mapped output imager(max)Maximum spectral chroma value, C, of the spectral gamut of the output deviceoAs a spectral color point chroma value, C, of the spectral image to be mappedo(max)Is the maximum spectral chroma value of the spectral image gamut to be mapped. p is a radical ofrFor the spectral brightness value, p, of the mapped output image1The spectral image brightness value is the spectral color point brightness value of the spectral image to be mapped, the center is the brightness value of the central point of the equal hue surface spectral brightness axis corresponding to the spectral color point of the spectral image to be mapped, and the cemmax is the weighting function of the maximum brightness value Lmax and the center of the spectral image to be mapped.
Step 6-2: the cemmax expression is as follows:
where Lmax is the maximum brightness value of the spectral image to be mapped, cc, dd, and hh are constants, cc ranges from-15 to 15, dd ranges from 0 to 10, and hh generally ranges from 1 to 3.
Step seven: and carrying out spectral reconstruction on the color data in the LMS-PCA space obtained after mapping processing to obtain the mapped image spectral information.
Step eight: and (6) ending.
Of course, this embodiment is only used for illustrating an optimized spectral gamut mapping method of the present invention, and is not used to limit the scope of the present invention.
Claims (1)
1. An optimized spectral gamut mapping method, characterized by: comprises the following steps:
the method comprises the following steps:
step 1-1: according to the visual characteristics of human eyes, an LMS cone response spectral sensitivity curve is selected as a weighting function, high-dimensional spectral data are weighted, and when a spectral tristimulus value is converted into an LMS cone response, a Bradford transformation matrix is selected as a transformation matrix:
step 1-2: the LMS weighting function is constructed as equation 2:
wherein p is a variable coefficient and has a value ranging from-0.5 to 50, k is 1 to 10,
step 1-3: the high-dimensional spectral data is weighted by using an LMS weighting function,
step two: extracting the first three principal components of the spectrum after weighting treatment by adopting a Principal Component Analysis (PCA) method, and constructing an LMS-PCA spectrum link space (ICS);
the second step specifically comprises the following steps:
step 2-1: performing singular value decomposition on the weighted spectrum data;
step 2-2: reducing the dimension of the weighted spectral data through the eigenvector of singular value decomposition, extracting the first three principal components to construct an LMS-PCA rectangular coordinate system as a spectral link space, constructing the LMS-PCA rectangular coordinate system space by using the first three principal components obtained by dimension reduction, and setting the first three principal components as P1，P2，P3,
Step three: describing the maximum spectral boundary GBD of the output device in LMS-PCA space;
step 3-1: using a rectangular coordinate system P of LMS-PCA space1，P2，P3Converting into a spherical coordinate system α, theta, r, calculating the spherical coordinate value corresponding to the spectral color point of the output device,
step 3-2, evenly dividing the LMS-PCA space into n multiplied by n equal parts along α and theta directions, respectively, calculating the spherical coordinates of each output device spectrum color sample point, determining which sub-region of the LMS-PCA space each spectrum color sample point is located in according to the values of α and theta, comparing the distances r from all spectrum color sample points in each sub-region to the central point, reserving the spectrum color sample point with the maximum r value as the boundary point of the sub-region, finally storing all the obtained boundary points into a matrix to obtain the maximum spectrum boundary GBD,
step four: describing the specific spectral boundaries LBD of the output device in LMS-PCA space;
the fourth step comprises the following steps:
step 4-1, calculating a spherical coordinate α corresponding to the hue angle of the spectrum color point of the image to be mapped, and calculating the color point according to the value α and the spectrum plane coordinate (C)o,p1) And a center point E, finding α planes that are equal to the spectral color point, wherein the coordinates are
p1、p2、p3Is a rectangular coordinate system P1、P2、P3The coordinate values of (a) and (b),
step 4-2, finding out a pair of adjacent spectrum color points from the GBD submatrix of the first horizontal division layer according to the hue angle α, wherein the hue angle of one point is more than α, the hue angle of the other point is less than α, then connecting the two adjacent spectrum color points into a straight line, solving the intersection points of the straight line and the equal α plane, and finally obtaining n intersection points which are linear boundaries of the output device spectrum color gamut on the equal α plane as a total of n horizontal layers,
step 4-3: according to maximum spectral margin GBD matrix with maximum p1Value and minimum p1Spectral color sample points of values, resulting in a maximum linear boundary point p among the spectral color sample points of the output devicemaxAnd a minimum linear boundary point pminCombined with the linear boundaries obtained in step 4-2 to form specific spectral boundaries LBD of the output device,
step five: judging whether the color point of the spectrum of the image to be mapped needs to be mapped or not;
judging the relation between the mapping color point and the spectral color gamut of the output device, and if the mapping color point is positioned outside the spectral color gamut of the output device, processing according to the sixth step; if the mapped color point is within the spectral gamut of the output device, then proceed directly to step seven without processing,
the method for judging whether the mapping color point is positioned in the spectral color gamut of the output device or not in the step five is as follows:
coordinate point M (C) of spectral plane of point Mo,p1) And p1The center point E of the shaft is connected to and extends to a straight line intersecting the LBD linear boundary at point H (C'o,p'1) If C iso＜C'oAnd p ismin＜p'1＜pmaxThen the M points are within the printer spectral gamut, otherwise they are outside the printer spectral gamut,
step six: mapping the image spectral color points beyond the spectral color gamut of the output equipment by adopting an LSLINceLmax color gamut compression algorithm;
in the sixth step, the method comprises the following steps:
step 6-1: the method comprises the following steps of utilizing LSLINCELmax color gamut compression in an LMS-PCA space to map color points of a spectral image to be mapped of a spectral color gamut of super-output equipment into a spectral domain of the output equipment, adding the influence of a median value of spectral color gamut brightness of the output equipment and the influence of a maximum value of the brightness of the spectral image to be mapped on the basis of a traditional LSLIN algorithm and simultaneously compressing the spectral chroma and the spectral brightness of the spectral color points of the spectral image to be mapped, thereby completing the mapping process with higher precision, wherein the spectral mapping expression is as follows:
in the formula, CrFor the spectral chroma value, C, of the mapped output imager(max)Maximum spectral chroma value, C, of the spectral gamut of the output deviceoAs a spectral color point chroma value, C, of the spectral image to be mappedo(max)Is the maximum spectral chroma value, p, of the spectral image gamut to be mappedrFor the spectral brightness value, p, of the mapped output image1Spectral color point brightness for spectral images to be mappedThe center is the brightness value of the central point of the isochromatic plane spectral brightness axis corresponding to the spectral color point of the spectral image to be mapped, the cemmax is the weighting function of the maximum brightness value Lmax and the center of the spectral image to be mapped,
step 6-2: the cemmax expression is as follows:
wherein Lmax is the maximum brightness value of the spectral image to be mapped, cc, dd and hh are constants, cc ranges from-15 to 15, dd ranges from 0 to 10, hh ranges from 1 to 3,
step seven: and performing spectral reconstruction based on the color data in the LMS-PCA space obtained by mapping processing.
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