CN108335351B - BRDF color gamut mapping method based on directional statistical analysis - Google Patents

BRDF color gamut mapping method based on directional statistical analysis Download PDF

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CN108335351B
CN108335351B CN201810075452.4A CN201810075452A CN108335351B CN 108335351 B CN108335351 B CN 108335351B CN 201810075452 A CN201810075452 A CN 201810075452A CN 108335351 B CN108335351 B CN 108335351B
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brdf
high light
color gamut
ink
diffuse
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CN108335351A (en
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过洁
潘金贵
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Nanjing University
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Abstract

The invention discloses a BRDF color gamut mapping method based on directional statistical analysis, which comprises the following steps: obtaining BRDF of the ink of the target equipment; extracting diffuse reflectivity, high light reflectivity and a dispersion matrix of the ink of the target equipment; forming a BRDF color gamut of the target device; extracting diffuse reflectance, high light reflectance and dispersion matrix of the source BRDF; according to the set weight, optimizing and mapping the source BRDF to the BRDF color gamut of the target equipment by adopting a quadratic programming method; and obtaining a final BRDF mapping result. The invention has simple calculation and low memory consumption, and allows the user to carry out self-adaptive control by adjusting the weight.

Description

BRDF color gamut mapping method based on directional statistical analysis
Technical Field
The invention relates to the field of material appearance management in computer graphics, in particular to a BRDF color gamut mapping method based on directional statistical analysis.
Background
In the field of computer graphics and computer vision, a Bidirectional Reflectance Distribution Function (BRDF) is generally used to model the reflectance properties of a non-transparent single material. The method is a four-dimensional function depending on the incident light direction and the viewpoint direction, and reflects the ratio relation between the irradiance micro-increment in the incident direction on a certain fixed incident point on the surface of the material and the reflected radiation brightness micro-increment caused by the irradiance micro-increment.
During 3D material printing, the material reflection properties of the target device ink determine the range of reproducible materials, which is called BRDF color gamut. Similar to the conventional color gamut mapping technique, the BRDF gamut mapping technique maps a source material (BRDF) outside the color gamut of the target device BRDF into its color gamut, and finds a target material (BRDF) such that the error between the target material (BRDF) and the source material (BRDF) is minimized under a given distance metric calculation method. The BRDF gamut mapping ensures that the source BRDF and the target BRDF have similar appearance characteristics, such as diffuse reflectance, high light reflectance morphology, and the like.
Currently, BRDF gamut mapping methods can be divided into three categories.
The first type is the texture space method. The method considers the BRDF as a high-dimensional signal, calculates the distance between two BRDFs by adopting a traditional Euclidean distance method, and finds the target BRDF with the minimum distance for the source BRDF within the color gamut range of the BRDF. Such methods can be referred to a.ngan, f.durand, and w.matusik, "experimental analysis of BRDF models," in proc.europatics Conference on RenderingTechniques, ser.egsr' 05,2005, pp.117-126; pellacini and j.lawrence, "applied ware: cutting measured materials using application-drive optimization," acmtrans.graph "(proc.sigwraph 2007), vol.26, No.3, pp.54: 1-54: 9, jul.2007; FORES A., FERWHEAD J., GU J., ZHAO X.: forward a performance based metric for BRDFmolding. in 20th Color and Imaging Conference (2012), CIC' 12, pp.142-148. Since BRDF is a high-dimensional signal, such methods are typically computationally expensive. Meanwhile, the material space cannot intuitively reflect the appearance characteristics of the material, so that the mapped result only has the similarity in the meaning of signal data and does not have the similarity of the appearance characteristics.
The second type is the image space approach. Such methods do not directly calculate the distance between the BRDFs themselves, but rely on the images generated by the BRDFs. Generally, a BRDF is photorealistically rendered using a simple geometric shape (e.g., spherical, etc.) under different lighting conditions (e.g., point light source, ambient light source, etc.). Thereafter, the distance between the BRDFs can be calculated using any image similarity metric method, and BRDF gamut mapping can be performed based on this distance. Such methods can be referred to as a.ngan, f.durand, andw.matusik, "Image-driven navigation of analytical BRDF models," inproc.eurographics Conference on reporting technologies, ser.egsr' 06,2006, pp.399-40; MATUSIK w., AJDIN b., GU j, LAWRENCE j, lens h.p.a., pellicani f., ruskiewicz s: Printing application-varying reflection.acm trans.graph (proc.siggraph Asia)28,5(2009),128: 1-128: 9; PEREIRA T, RUSINKIEWICZ S, Gamma mapping varying reflecting with an improved BRDF similar reflecting device, Comp.graph.Forum 31,4 (2012). Because the generated image has higher visual perception correlation degree to the material, the method can ensure that the result of the color gamut mapping has good visual perception similarity to a certain extent. However, since graphic rendering is involved, the amount of calculation is generally large.
The third type is attribute space methods. The method abstracts the BRDF into a plurality of attributes, and measures the distance between the BRDF by calculating the similarity between the attributes. Compared with the above two methods, this method has the advantage that the control can be adaptively performed by the weight between the attributes. Currently such methods are mainly referenced to t.sun, a.serrano, d.gutierrez, and b.massa, "Attribute preserving mapping of measured brdfs," company.graph.forum, vol.36, No.4, pp.47-54,2017. But this method relies on the image in addition to the use of attributes. Meanwhile, the extraction of the attributes is relatively complex, so that the pre-calculated amount is relatively large.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention provides a BRDF color gamut mapping method based on directional statistical analysis (directional statistical analysis), which can be used for material appearance management in realistic graph drawing and 3D printing. The method also belongs to an attribute space method, but the material appearance attribute of the invention is obtained by utilizing a spherical distance (spherical moment) method in directional statistical analysis, so the calculation speed is higher and the occupied memory is less.
The technical scheme is as follows: the BRDF color gamut mapping method based on the directed statistical analysis comprises the following steps:
(1) collecting BRDF of the ink of the target device, and decomposing the BRDF into a diffuse reflection part and a high light reflection part;
(2) obtaining the material appearance attributes of each ink BRDF, including the diffuse reflectance, the high light reflectance and the scattering matrix, by means of a spherical distance method in directional statistical analysis according to the decomposed diffuse reflectance and high light reflectance;
(3) forming a BRDF color gamut of the target equipment by using the material appearance attribute in the step (2);
(4) performing diffuse reflection and high light reflection decomposition on the source BRDF to be mapped, and acquiring material appearance attributes including diffuse reflection rate, high light reflection rate and a scattering matrix;
(5) defining similarity measurement formulas of two BRDF, and setting the weight of each appearance attribute;
(6) and optimizing and mapping the source BRDF to the BRDF color gamut of the target equipment by adopting a quadratic programming method based on the similarity measurement formula of the BRDF to obtain a final BRDF mapping result.
Further, the step (1) specifically comprises:
(1-1) collecting BRDF set { rho ] of target equipment ink by adopting reflection measuring instrumentk(ωo,ωi) 1, ·, K }; where ρ isk(ωo,ωi) The K-th BRDF of the ink of the target device, K is the total number of BRDF of the ink of the target device, omegaiAnd ωoRespectively representing an incident light direction and a viewpoint direction;
(1-2) decomposing each BRDF into a diffuse reflection part and a high light reflection part according to the following steps:
a: for arbitrary rhok(ωo,ωi) Three sample data are taken from the following: peak top sample ρk,max(ωn,ωn) Peak bottom sample ρk,min(ωn,ωt) And near peak sample ρk,c(ωn,ωc) (ii) a Wherein ω isnThe term (0,0,1) is the normal direction of the material surface, ωtTangential to the material surface, ω (1,0,0)c＝(sinθc,0,cosθc) Is a direction close to the peak, thetac＝π/32；
B: based on the three samples above, a Phong model of the form:
Figure BDA0001559366170000031
in the formula, kdAs the diffuse reflection term of the Phong model,
Figure BDA0001559366170000032
is a high light reflection term, and the parameter p controls the form of the high light reflection, isThe fitted target:
Figure BDA0001559366170000033
c: finding a direction of incident light closest to the normal
Figure BDA0001559366170000034
Satisfy the requirement of
Figure BDA0001559366170000035
Wherein epsilon is a predetermined small quantity, the reflection value of which
Figure BDA0001559366170000036
As a threshold for diffuse-specular decomposition;
d: based on the above threshold value, pk(ωo,ωi) The diffuse reflection part and the high light reflection part are respectively:
diffuse reflection section
Figure BDA0001559366170000037
High light reflection part
Figure BDA0001559366170000038
Further, the step (2) specifically comprises:
(2-1) the diffuse reflectance of the kth BRDF of the target device ink is the 0-order spherical distance of the corresponding diffuse reflection part, and the calculation formula is as follows:
αk,d(ωo)＝∫Ωρk,d(ωo,ωi)cosθidωi
in the formula, ρk,d(ωo,ωi) Denotes the diffuse reflection part, ω, of the kth BRDFiAnd ωoRespectively representing incident light direction and viewpoint direction, thetaiRepresenting the zenith angle of incident light;
(2-2) the high light reflectance of the kth BRDF of the target device ink is the 0th order sphere distance of the corresponding high light reflectance part, and the calculation formula is as follows:
αk,s(ωo)＝∫Ωρk,s(ωo,ωi)cosθidωi
in the formula, ρk,s(ωo,ωi) Represents the high light reflectance portion of the kth BRDF;
(2-3) the dispersion matrix of the kth BRDF of the target device ink is the spherical distance of 2 nd order corresponding to the high light reflection portion, and the calculation formula is:
Figure BDA0001559366170000041
wherein, the scattering matrix is a 3 × 3 semi-positive definite symmetric matrix, and has three non-negative eigenvalues: sk,1、sk,2And sk,3And satisfy sk,1+sk,2+sk,3＝1。
Further, the step (3) specifically comprises:
(3-1) according to the material appearance attribute of the kth BRDF of the ink of the target equipment, acquiring a corresponding attribute vector
Figure BDA0001559366170000042
K1, 2, K, wherein αk,d,αk,sRespectively representing the diffuse reflectance and the high light reflectance of the kth BRDF of the target device ink;
Figure BDA0001559366170000043
sk,1、sk,2and sk,3Three non-negative eigenvalues of the scatter matrix;
(3-2) forming a matrix by using the attribute vectors of all BRDF as the BRDF color gamut of the target device:
Figure BDA0001559366170000044
then Px (Σ x ═ 1) denotes all material in the gamut, where
Figure BDA0001559366170000045
Is a coefficient vector.
Further, the step (5) specifically comprises:
the similarity measure between two BRDFs is defined by the formula:
Figure BDA0001559366170000046
wherein (i) { αd,αs,sg,saIs an attribute vector comprising four attributes, αd,αsRespectively representing the diffuse reflectance and the high light reflectance of the BRDF,
Figure BDA0001559366170000047
s1、s2and s3Three non-negative eigenvalues of the scatter matrix;
Figure BDA0001559366170000048
λca weight for each attribute;
Figure BDA0001559366170000049
c1、c2representation αd,αs,sg,saRespectively elevation angle theta with observation directionoIs measured in a direction perpendicular to the direction of the curve (c),
Figure BDA0001559366170000051
is a group of 0 to
Figure BDA0001559366170000052
The sampling points are distributed at equal intervals, N is the number of the sampling points, αd,αsUsing the CIELAB color space, sg,saThe use of a logarithmic space is used,
Figure BDA0001559366170000053
x is 0 to
Figure BDA0001559366170000054
The sampling points in between.
Further, the step (6) specifically comprises:
the objective function is defined as:
Figure BDA0001559366170000055
Figure BDA0001559366170000056
namely, finding a BRDF in the color gamut of the BRDF of the target device: px, the BRDF being a convex combination of target device ink BRDF and source BRDF
Figure BDA0001559366170000057
The optimal problem is solved by adopting a quadratic programming method under the distance measurement of delta E.
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages: the method has low calculation complexity and low storage overhead, can reduce distortion in the BRDF color gamut mapping process by adjusting the weight, and reserves the appearance characteristics of materials as much as possible.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a graphical representation of the result of the diffuse reflectance-specular reflectance decomposition of the BRDF in accordance with the present invention;
FIG. 3 is a schematic diagram of the relationship between eigenvalues of a dispersion matrix and three-dimensional ellipsoids in the present invention;
FIG. 4 is a graph of the results of diffuse reflectance and specular reflectance calculations for 100 materials in the MERL library according to the present invention;
FIG. 5 is a graph of the results of the gloss and anisotropy calculations for 100 materials in the MERL library;
fig. 6 is a comparison graph of the BRDF gamut mapping results in the present invention versus the effects of other methods.
Detailed Description
The embodiment provides a BRDF color gamut mapping method based on directional statistical analysis, as shown in fig. 1, including the following steps:
(1) the BRDF of the target device ink is collected and decomposed into a diffusely reflective portion and a highly reflective portion.
The BRDF of the target device ink can be collected using a conventional reflectometer (gonioreffelectometer). Assuming that the target device has K inks, K BRDF functions ρ need to be obtainedk(ωo,ωi) K ═ K (1,2,. K). Wherein ω isiAnd ωoRespectively representing the incident light direction and the viewpoint direction.
BRDFs of common materials contain both diffuse and high light reflectance components. To facilitate quantitative statistical analysis, particularly for calculating spherical distance, the present invention first applies any BRDF ρ (ω) too,ωi) Decomposed into diffuse reflectance terms ρd(ωo,ωi) And a high light reflectance term ρs(ωo,ωi). The specific decomposition algorithm is as follows:
① pairs of arbitrary rhok(ωo,ωi) Three sample data are taken from the following: peak top sample ρk,max(ωn,ωn) Peak bottom sample ρk,min(ωn,ωt) And near peak sample ρk,c(ωn,ωc) (ii) a Wherein ω isnThe term (0,0,1) is the normal direction of the material surface, ωtTangential to the material surface, ω (1,0,0)c＝(sinθc,0,cosθc) Is a direction close to the peak, thetac＝π/32；
② based on the three samples above, an approximate Phong model of the form:
Figure BDA0001559366170000061
wherein the plus sign is preceded by the diffuse reflectance term of the Phong model and followed by its high light reflectance term. The parameter p controls the morphology of the high light reflection and is the target of the fitting:
Figure BDA0001559366170000062
③ intuitively, when the index term in equation (1) is small, the Phong model only has the diffuse reflection term left, so we only need to find the incident light direction closest to the normal
Figure BDA0001559366170000063
Satisfy the requirement of
Figure BDA0001559366170000064
Where epsilon is a preset small amount. Its reflection value
Figure BDA0001559366170000065
As a threshold for diffuse-specular decomposition.
④ is based on the above threshold, ρ (ω)o,ωi) The diffuse reflection part and the high light reflection part are respectively:
Figure BDA0001559366170000066
Figure BDA0001559366170000067
FIG. 2 shows the result of the diffuse-specular decomposition of specific-yellow-phenolic materials in the MERL material database.
(2) And acquiring the diffuse reflectance and the high light reflectance of the ink BRDF and the appearance attributes of the materials such as the scattering matrix and the like by a spherical distance method in the directional statistical analysis.
After the diffuse reflection-highlight reflection decomposition of the BRDF is completed, the directional statistical analysis can be carried out on each component, and the spherical distance of each component is respectively calculated. Wherein, the 0-order spherical distance of the diffuse reflection item corresponds to the diffuse reflection rate of the BRDF, the 0-order spherical distance of the high light reflection item corresponds to the high light reflection rate of the BRDF, and the 2-order spherical distance (namely, the scattering matrix) of the high light reflection item corresponds to the high light form of the BRDF. The specific calculation is as follows:
① the formula for calculating the diffuse reflectance (i.e. 0th order spherical distance of diffuse reflection term) is:
αk,d(ωo)＝∫Ωρk,d(ωo,ωi)cosθidωi(5)
② the formula for calculating high light reflectivity (i.e. 0th order sphere distance of high light reflectivity term) is:
αk,s(ωo)＝∫Ωρk,s(ωo,ωi)cosθidωi(6)
③ the calculation formula of the high light reflection scattering matrix (i.e. the 2 nd order spherical distance of the high light reflection term) is:
Figure BDA0001559366170000071
the equations (5) to (7) are all in a fixed viewing direction ωoIn the case of (3), a two-dimensional slice of BRDF is calculated. The scattering matrix S is a 3 × 3 semi-positive definite symmetric matrix, and has three non-negative eigenvalues: s1、s2And s3And satisfy s1+s2+s3＝1。s1、s2And s3In fact reflects when ps(ωo,ωi) Is approximately the size of three axial directions when the shape of the three-dimensional space is an ellipsoid. FIG. 3 shows the shape and approximate ellipsoid of natural-209 in the MERL texture database.
We further define:
Figure BDA0001559366170000072
and
Figure BDA0001559366170000073
wherein s isgHigh light-reflecting glossiness, s, of the drawingaAnisotropy of high light reflectance was measured. Table 1 lists sgAnd saAnd (4) depicting the highlight form of the material by value.
Table 1: sgAnd saRelationship with the highlight form of the material
sg sa High gloss profile
＝∞ Ideal specular reflection
＝2 ＝1 Ideal diffuse reflection
>2 ＝1 Isotropic high light reflection
>2 >1 Anisotropic high light reflection
<2 Annular belt shape
FIG. 4 shows the diffuse reflectance and high light reflectance for all 100 materials in the MERL library. FIG. 5 shows the gloss and anisotropy curves for all 100 materials in the MERL library.
(3) And (3) forming the BRDF color gamut of the target device by using the appearance attribute in the step (2).
After step (2) is completed, each BRDF of target device ink has an attribute vector
Figure BDA0001559366170000081
K ═ 1,2,. K. If these attributes are regarded as one point of the high-dimensional space, the convex hull formed by these points is the BRDF color gamut of the target device. The following matrix is defined:
Figure BDA0001559366170000082
then Px (Σ x ═ 1) indicates all material in the gamut. Wherein
Figure BDA0001559366170000083
Is a coefficient vector.
(4) And (3) performing diffuse reflection and high light reflection decomposition on the source BRDF to be mapped, and acquiring the material appearance attributes such as diffuse reflection, high light reflection and scattering matrix.
Given a source BRDF ρ to be mappedo(ωo,ωi) We can also calculate its diffuse reflectance αd,oHigh light reflectivity αs,oAnd a scatter matrix SoAnd to a gloss value sg,oAnd anisotropy sa,o. The calculation formula is as in step (2).
(5) Defining BRDF distance formula and setting weight of each appearance attribute
Before performing the BRDF color gamut mapping, a distance formula for measuring the BRDF similarity needs to be defined. Since the various attributes of the BRDFs have been obtained, the distance between the computed BRDFs translates into a distance between the computed attribute values. For computational accuracy, we can consider each property as the viewing direction elevation angle θ for isotropic materialoA function of, i.e. αd(θo)、αs(θo)、sg(θo) And sa(θo). Thus, calculating the similarity of a certain attribute translates intoThe similarity between the corresponding curves is calculated. We calculate the distance between the two property curves using the following distance formula:
Figure BDA0001559366170000091
wherein c represents αd(θo)、αs(θo)、sg(θo) Or sa(θo) Curve line.
Figure BDA0001559366170000092
Is a group of 0 to
Figure BDA0001559366170000093
α between the sampling pointsd(θo) And αs(θo) A CIELAB color space is adopted; sg(θo) And sa(θo) A logarithmic space is used. The w function is introduced to reduce the influence of unreliable sampling of the high grazing angle of the material in the MERL material database:
Figure BDA0001559366170000094
based on the above attribute distance calculation formula, the similarity measure formula between two BRDFs can be defined as:
Figure BDA0001559366170000095
Figure BDA0001559366170000096
wherein λcAs a weight for each attribute. The similarity of the BRDF can be adjusted in a self-adaptive mode by setting the relative weight of each attribute. Introducing a weight λcThe advantages of (A) are as follows: when source BRDF ρo(ωo,ωi) When the BRDF color gamut of the target device is far away, the required appearance characteristics can be kept as far as possible by adjusting the weight.For example: when set larger
Figure BDA0001559366170000097
In time, the diffuse reflection effect of the source BRDF can be kept as much as possible in the mapping result.
(6) Optimizing the BRDF color gamut for mapping the source BRDF to the target equipment by adopting a quadratic programming method to obtain a final BRDF mapping result
Finally, the BRDF gamut mapping is the solution of the following optimization problem:
Figure BDA0001559366170000098
namely, finding a BRDF in the color gamut of the BRDF of the target device: px, the BRDF being a convex combination of target device ink BRDF and source BRDF
Figure BDA0001559366170000099
The most similar under the distance measure of Δ E. Wherein
Figure BDA00015593661700000910
The optimization problem can be solved by adopting a quadratic programming method.
The simulation is carried out on the invention, and an implementation example of the invention is realized on a machine which is provided with 3.2 GHz Intel Core i7-6900K CPU and 16G memory. All the pictures in fig. 6 were generated by the open source rendering engine Mitsuba, the scene was a spherical object illuminated by ambient lighting, and the picture resolution was 512 x 512. The bulb surface was covered with the test BRDF used in the present invention. FIG. 6 tests three materials in the MERL material database: tungsten-carbide, green-acrylic and chrome-steel, and compared to prior methods. The leftmost column is the result of the method mapping proposed by Pereira and Rusinkiewicz, the middle left column is the result of the method mapping proposed by Sun et al, the middle right column is the result of the method mapping proposed by the present invention, and the source BRDF which needs to be mapped is the rightmost column. Obviously, the method provided by the invention can keep the visual appearance characteristics of the source BRDF as much as possible, such as diffuse reflection color, highlight form and the like, and reduce distortion by adjusting the weight. Compared with other methods, the method has the advantages of small calculation amount and small memory occupation.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims (6)

1. A BRDF color gamut mapping method based on oriented statistical analysis is characterized by comprising the following steps:
(1) collecting BRDF of the ink of the target device, and decomposing the BRDF into a diffuse reflection part and a high light reflection part;
(2) obtaining the material appearance attributes of each ink BRDF, including the diffuse reflectance, the high light reflectance and the scattering matrix, by means of a spherical distance method in directional statistical analysis according to the decomposed diffuse reflectance and high light reflectance;
(3) forming a BRDF color gamut of the target equipment by using the material appearance attribute in the step (2);
(4) performing diffuse reflection and high light reflection decomposition on the source BRDF to be mapped, and acquiring material appearance attributes including diffuse reflection rate, high light reflection rate and a scattering matrix;
(5) defining similarity measurement formulas of two BRDF, and setting the weight of each appearance attribute;
(6) and optimizing and mapping the source BRDF to the BRDF color gamut of the target equipment by adopting a quadratic programming method based on the similarity measurement formula of the BRDF to obtain a final BRDF mapping result.
2. The BRDF color gamut mapping method based on directed statistical analysis according to claim 1, wherein: the step (1) specifically comprises the following steps:
(1-1) collecting BRDF set { rho ] of target equipment ink by adopting reflection measuring instrumentk(ωo,ωi) 1, ·, K }; where ρ isk(ωo,ωi) The K-th BRDF of the ink of the target device, K is the total number of BRDF of the ink of the target device, omegaiAnd ωoRespectively representing an incident light direction and a viewpoint direction;
(1-2) decomposing each BRDF into a diffuse reflection part and a high light reflection part according to the following steps:
a: for arbitrary rhok(ωo,ωi) Three sample data are taken from the following: peak top sample ρk,max(ωn,ωn) Peak bottom sample ρk,min(ωn,ωt) And near peak sample ρk,c(ωn,ωc) (ii) a Wherein ω isnThe term (0,0,1) is the normal direction of the material surface, ωtTangential to the material surface, ω (1,0,0)c＝(sinθc,0,cosθc) Is a direction close to the peak, thetac＝π/32；
B: based on the three samples above, a Phong model of the form:
Figure FDA0002354950020000011
in the formula, kdAs the diffuse reflection term of the Phong model,
Figure FDA0002354950020000012
is a high light reflection item, and the parameter p controls the form of high light reflection, which is a fitting target:
Figure FDA0002354950020000013
in the formula, ρk,min、ρk,maxRespectively representing the peak top samples ρk,max(ωn,ωn) Peak bottom sample ρk,min(ωn,ωt) Abbreviations of (a);
c: finding a direction of incident light closest to the normal
Figure FDA0002354950020000014
Satisfy the requirement of
Figure FDA0002354950020000015
Wherein epsilon is a predetermined small quantity, the reflection value of which
Figure FDA0002354950020000016
As a threshold for diffuse-specular decomposition;
d: based on the above threshold value, pk(ωo,ωi) The diffuse reflection part and the high light reflection part are respectively:
diffuse reflection section
Figure FDA0002354950020000021
High light reflection part
Figure FDA0002354950020000022
3. The BRDF color gamut mapping method based on directed statistical analysis according to claim 1, wherein: the step (2) specifically comprises the following steps:
(2-1) the diffuse reflectance of the kth BRDF of the target device ink is the 0-order spherical distance of the corresponding diffuse reflection part, and the calculation formula is as follows:
αk,d(ωo)＝∫Ωρk,d(ωo,ωi)cosθidωi
in the formula, ρk,d(ωo,ωi) Denotes the diffuse reflection part, ω, of the kth BRDFiAnd ωoRespectively representing incident light direction and viewpoint direction, thetaiRepresenting the zenith angle of incident light;
(2-2) the high light reflectance of the kth BRDF of the target device ink is the 0th order sphere distance of the corresponding high light reflectance part, and the calculation formula is as follows:
αk,s(ωo)＝∫Ωρk,s(ωo,ωi)cosθidωi
in the formula, ρk,s(ωo,ωi) Represents the high light reflectance portion of the kth BRDF;
(2-3) the dispersion matrix of the kth BRDF of the target device ink is the spherical distance of 2 nd order corresponding to the high light reflection portion, and the calculation formula is:
Figure FDA0002354950020000023
wherein, the scattering matrix is a 3 × 3 semi-positive definite symmetric matrix, and has three non-negative eigenvalues: sk,1、sk,2And sk,3And satisfy sk,1+sk,2+sk,3＝1。
4. The BRDF color gamut mapping method based on directed statistical analysis according to claim 1, wherein: the step (3) specifically comprises the following steps:
(3-1) according to the material appearance attribute of the kth BRDF of the ink of the target equipment, acquiring a corresponding attribute vector
Figure FDA0002354950020000024
K1, 2, K, wherein αk,d,αk,sRespectively representing the diffuse reflectance and the high light reflectance of the kth BRDF of the target device ink;
Figure FDA0002354950020000025
sk,1、sk,2and sk,3Three non-negative eigenvalues of the scatter matrix;
(3-2) forming a matrix by using the attribute vectors of all BRDF as the BRDF color gamut of the target device:
Figure FDA0002354950020000031
then Px (Σ x ═ 1) denotes all material in the gamut, where
Figure FDA0002354950020000032
Is a coefficient vector.
5. The BRDF color gamut mapping method based on directed statistical analysis according to claim 1, wherein: the step (5) specifically comprises the following steps:
the similarity measure between two BRDFs is defined by the formula:
Figure FDA0002354950020000033
wherein (i) { αd,αs,sg,saIs an attribute vector comprising four attributes, αd,αsRespectively representing the diffuse reflectance and the high light reflectance of the BRDF,
Figure FDA0002354950020000034
s1、s2and s3Three non-negative eigenvalues of the scatter matrix;
Figure FDA0002354950020000035
λca weight for each attribute;
Figure FDA0002354950020000036
c1、c2representation αd,αs,sg,saRespectively elevation angle theta with observation directionoIs measured in a direction perpendicular to the direction of the curve (c),
Figure FDA0002354950020000037
is a group of 0 to
Figure FDA0002354950020000038
The sampling points are distributed at equal intervals, N is the number of the sampling points, αd,αsUsing the CIELAB color space, sg,saThe use of a logarithmic space is used,
Figure FDA0002354950020000039
x is 0 to
Figure FDA00023549500200000310
The sampling points in between.
6. The BRDF color gamut mapping method based on directed statistical analysis according to claim 1, wherein: the step (6) specifically comprises the following steps:
the objective function is defined as:
Figure FDA00023549500200000311
Figure FDA00023549500200000312
namely, finding a BRDF in the color gamut of the BRDF of the target device: px, the BRDF being a convex combination of target device ink BRDF and source BRDF
Figure FDA0002354950020000041
The most similar is obtained under the distance measurement of delta E, and the objective function is obtained by solving through a quadratic programming method.
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1909594A (en) * 2005-08-02 2007-02-07 佳能株式会社 Color processing method and apparatus
CN102256044A (en) * 2010-04-02 2011-11-23 佳能株式会社 Color processing method and color processing apparatus
EP2852491B1 (en) * 2012-05-22 2019-01-09 MCOR Technologies Limited Colour 3-dimensional printing with 3d gamut mapping

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US9767599B2 (en) * 2006-12-29 2017-09-19 X-Rite Inc. Surface appearance simulation

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1909594A (en) * 2005-08-02 2007-02-07 佳能株式会社 Color processing method and apparatus
CN102256044A (en) * 2010-04-02 2011-11-23 佳能株式会社 Color processing method and color processing apparatus
EP2852491B1 (en) * 2012-05-22 2019-01-09 MCOR Technologies Limited Colour 3-dimensional printing with 3d gamut mapping

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
"Attribute-preserving gamut mapping of measured BRDFs";Tiancheng Sun;《Wiley Online Library》;20170705;全文 *
"Directional Statistics BRDF Model";Ko Nishino;《2009 IEEE 12th International Conference on Computer Vision》;20100506;全文 *
"Gamut mapping spatially varying reflectance with an improved BRDF similarity metric";Thiago Pereira等;《Wiley Online Library》;20120704;全文 *
"多尺度粗糙表面的实时绘制方法";过洁等;《中国图像图形学报》;20150416;第20卷(第4期);全文 *
"粗糙表面下的实时透明和半透明效果绘制";陆添超等;《系统仿真学报》;20130930;第25卷(第9期);全文 *

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