CN102393965A - Method for correcting colour of colour difference meter by utilizing tetrahedron interpolation method - Google Patents

Abstract

The invention relates to a method for correcting colour of a colour difference meter by utilizing a tetrahedron interpolation method. Firstly, the traditional interpolation algorithm is used for measuring base colour points in required quantity, then a three-dimensional Delaunay triangulation algorithm is used for carrying out tetrahedron subdivision on base colours, and creating a lookup table by utilizing a tetrahedron set obtained by subdivision; after the lookup table is generated, supposing an input point to be P, after A is obtained, and further judging that which tetrahedron the input point P is located in A by utilizing a volume relation between the point p and each tetrahedron in A, wherein if more than two tetrahedrons are contained in B, the point p is a vertex of some tetrahedron, namely the point p is a point belonging to an interpolation point set, no interpolation is required, and a target RGB (red, green and blue) value can be directly output; and mapping of an imaging system is supposed to be in a linear relation, output standard colour value is pn=(Rn, Gn, Bn), and T can be shown by the following formula: pn-p=lambda*n*sigma. Compared with a common colour measuring method based on trichromatic analysis, the method provided by the invention has the characteristics of simplicity, speediness and accuracy.

Description

A kind of method of utilizing tetrahedron interpolation method to realize the colour examining colour-difference-metre color correction

Technical field

A kind of method of utilizing tetrahedron interpolation method to realize the colour examining colour-difference-metre color correction

Background technology

Industries such as plastic cement, spraying, design, printing, clothes, printing and dyeing need be measured color as far as possible accurately, to satisfy the high-quality demand of precisely selecting look, color matching and fixation.

Though existing colour difference meter can satisfy the requirement that above-mentioned industry is measured color basically basically in the society; But; It is accurate inadequately that prior art is measured method of correcting to the colour difference meter intrinsic colour; Speed is also slow, causes colour difference meter itself to have fiducial error, can not satisfy relevant industries and carry out the high-quality demand of precisely selecting look, color matching and fixation with it.

Summary of the invention

The objective of the invention is on the basis of common tetrahedral interpolation value-based algorithm; Design a kind of new tetrahedral interpolation value-based algorithm; And utilize this algorithm that the colour examining colour-difference-metre based on the RGB trichromatic analysis is carried out color correction; Effectively improve precision and computing velocity, to satisfy the high-quality demands of precisely selecting look, color matching and fixation of industry such as plastic cement, spraying, design, printing, clothes, printing and dyeing to the colour difference meter color correction.

In colour examining colour-difference-metre based on the RGB trichromatic analysis, exchange in order to realize color, must be mapped to the color value that records under the instrument condition in a kind of and device-independent color space, this process is referred to as color correction.

In order to solve the accurate inadequately and slow problem of computing velocity based on the color correction in the colour examining colour-difference-metre of RGB trichromatic analysis; Method of the present invention is: utilize three-dimensional Delaunay algorithm that the primary color space that instrument records is carried out the tetrahedron subdivision; According to the tetrahedral position in input point and place relation; Realize interpolation calculation, carry out fast and accurate color correction.

Concrete computation process of the present invention is following: the primary color points that at first records requirement through traditional interpolation algorithm; Then, utilize three-dimensional Delaunay triangulation, the primary colours collection is carried out the tetrahedron subdivision; Look-up table is set up in the tetrahedron set that utilizes subdivision to obtain; The structure of look-up table is following:

Wherein, given tetrahedron T and summit p thereof ₀p ₁p ₂p ₃After, utilize following system of equations to find the solution to obtain its circumsphere centre of sphere O,

$\left\{\begin{array}{c}\stackrel{\→}{q{m}_1}\·\stackrel{\→}{p_0{p}_1}=0;\\ \stackrel{\→}{q{m}_2}\·\stackrel{\→}{p_1{p}_2}=0;\\ \stackrel{\→}{q{m}_3}\·\stackrel{\→}{p_2{p}_3}=0;\end{array}\right.$

Here suppose m ₁Be p ₀p ₁The mid point of line segment, m ₂Be p ₂p ₃The mid point of line segment, m ₃Be p ₃p ₀The mid point of line segment, some q are that plan is anticipated a bit, that is:

$x_{m_i}=\frac{x_{i-1}+x_i}{2};$

$y_{m_i}=\frac{y_{i-1}+y_i}{2};i=\mathrm{1,2,3}.$

$z_{m_i}=\frac{z_{i-1}+z_i}{2};$

Expansion can obtain its algebraic expression:

$\left\{\begin{array}{c}(x_0-x_1)\·(x-x_{m_1})+(y_0-y_1)\·(y-y_{m_1})+(z_0-z_1)\·(z-z_{m_1})=0\\ (x_1-x_2)\·\left({x-x_m}_2\right)+(y_1-y_2)\·(y-y_{m_2})+(z_1-z_2)\·(z-z_{m_2})=0\\ (x_2-x_3)\·(x-x_{m_3})+(y_2-y_3)\·(y-y_{m_3})+(z_2-z_3)\·(z-z_{m_3})=0\end{array}\right.$

Its expression matrix form is:

$\left[\begin{array}{ccc}{x}_0-x_1& y_0-y_1& z_0-z_1\\ x_1-x_2& y_1-y_2& z_1-z_2\\ x_2-x_3& y_2-y_3& z_2-z_3\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}(x_0-x_1)x_{m_1}+(y_0-y_1)y_{m_1}+(z_0-z_1)z_{m_1}\\ (x_1-x_2)x_{m_2}+(y_1-y_2)y_{m_2}+(z_1-z_2)z_{m_2}\\ (x_2-x_3)x_{m_3}+(y_2-y_3)y_{m_3}+(z_2-z_3)z_{m_3}\end{array}\right]$

Thereby the circumsphere centre of sphere expression formula that can obtain tetrahedron T is:

$\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}(x_0-x_1)x_{m_1}+(y_0-y_1)y_{m_1}+(z_0-z_1)z_{m_1}\\ (x_1-x_2)x_{m_2}+(y_1-y_2)y_{m_2}+(z_1-z_2)z_{m_2}\\ (x_2-x_3)x_{m_3}+(y_2-y_3)y_{m_3}+(z_2-z_3)z_{m_3}\end{array}\right]/\left[\begin{array}{ccc}{x}_0-x_1& y_0-y_1& z_0-z_1\\ x_1-x_2& y_1-y_2& z_1-z_2\\ x_2-x_3& y_2-y_3& z_2-z_3\end{array}\right]$

After generating look-up table, suppose that input point is P, workflow is following:

Utilize the relation apart from the radius r of d and tetrahedron circumsphere of input point p and each tetrahedral circumsphere centre of sphere O, judge whether input point p falls in the tetrahedral circumsphere, promptly p all tetrahedrons of falling into its circumsphere constitute set A; Concrete determination methods is following:

$p\left\{\begin{array}{cc}\∈T& d\≤r\\ \∉T& d>r\end{array}\right.$

After obtaining A, can utilize each tetrahedral volume relationship among a p and the A, judge further input point p is arranged in which tetrahedron of A, having only when a p falls into the summit is p ₀, p ₁, p ₂, p ₃Tetrahedron T in the time, some p and p ₀, p ₁, p ₂The tetrahedron T that constitutes ₁, with p ₀, p ₁, p ₃The tetrahedron T that constitutes ₂, with p ₀, p ₂, p ₃The tetrahedron T that constitutes ₃, with p ₁, p ₂, p ₃The tetrahedron T that constitutes ₄, reach the relation down that is enough to:

V(T ₁)+V(T ₂)+V(T ₃)+V(T ₄)＝V(T)

Wherein, the calculating of tetrahedron volume can obtain through following, when four summits of tetrahedron T are p ₀(x ₀, y ₀, z ₀), p ₁(x ₁, y ₁, z ₁), p ₂(x ₂, y ₂, z ₂), p ₃(x ₃, y ₃, z ₃) time, the computing formula of this tetrahedral volume V (T) is:

So when whether judging point p belongs to certain tetrahedron T, can use following formula to judge:

$p\left\{\begin{array}{cc}\∈T& V\left(T_0\right)+V\left(T_1\right)+V\left(T_2\right)+V\left(T_3\right)=V\left(T\right)\\ \∉T& V\left(T_0\right)+V\left(T_1\right)+V\left(T_2\right)+V\left(T_3\right)\≠V\left(T\right)\end{array}\right.$

All bodies at RP p place are in set B, if B is empty, the p point exceeds the scope that can proofread and correct so, not within the limit of consideration of this algorithm; If two tetrahedrons are arranged among the B, then select any one, utilize the linear regression method interpolation calculation to obtain the target rgb value; If the tetrahedron more than two is arranged among the B, explain that the p point is certain tessarace, that is to say to belong to the point that interpolation point is concentrated, need not interpolation so, directly the export target rgb value;

Can obtain equation of linear regression in the following manner:

The mapping of supposing imaging system is linear, and then the Standard Colors value of output is p _n=(R _n, G _n, B _n) ^TCan be expressed as:

p _n-p＝Λ _nσ

Wherein, p ₀Be the coordinate at zero point, Λ is the 3 * n dimension matrix that has comprised the illumination factor and the corresponding factor of sensor, and σ is the weight coefficient of body surface reflectivity basis function;

The same color value p that under non-standard illumination condition, obtains _a=(R _a, G _a, B _a) ^TSatisfy:

p _a-p＝Λ _aσ

Two formulas can obtain above the simultaneous

$p_n={\mathrm{\Λ}}_n{\mathrm{\Λ}}_a^{-1}{p}_a+(I-{\mathrm{\Λ}}_n{\mathrm{\Λ}}_a^{-1})p$

Order

then the above equation becomes

In order to calculate

and B; At least need know the standard value and the non-standard value of 4 non-coplanar sample points; Through linear regression analysis, adopt least square method to find the solution the corresponding coefficient of each component; Getting in the tetrahedron interpolation process of these four points searched four summits of tetrahedron that obtain.

The Delaunay algorithm claims the Delaunay triangulation quick point location algorithm again, is a kind of algorithm of widespread use, is mainly used in tetrahedron location Calculation aspect.Domestic have translate into " De Laonai ", what have is translated into " De Laonai ", does not still have standard and unifies translation.

The color calibration method that the present invention proposes carries out non-homogeneous division and sets up look-up table the input color space on this basis based on existing even or non-homogeneous primary colours storehouse.For new input point; Utilize volume relationship to judge the tetrahedron at its place, according to the position relation of input point, select to utilize the interpolation calculation formula then with the place tetrahedron top; Obtain output valve, thereby realize of the conversion of instrument color space to the Standard Colors space.Compare with common method for measuring color based on trichromatic analysis, the present invention has simply, quick, characteristic of accurate.

Description of drawings

Accompanying drawing is a calculation process block diagram of the present invention, also is that specification digest is with figure.Each label is respectively among the figure: (1) primary colours are measured; (2) utilize three-dimensional algorithm that primary color space is carried out subdivision, look-up table is set up in (3), and (4) input color value is measured; (5) utilize volume relationship to judge input point place tetrahedron; (6) input point is positioned at tetrahedron top, and (7) linearity is judged to the ownership of method, and (8) go out to proofread and correct the back color value.

Embodiment

The present invention is further specified now in conjunction with the accompanying drawings an instance.

Embodiment:

With the R component is example,

R _n＝b ₁+a ₁₁R _a+a ₁₂G _a+a ₁₃B _a

Suppose the input and output value on known 4 summits, then have:

$\left\{\begin{array}{c}{R}_{n1}=b_1+a_{11}{R}_{a1}+a_{12}{G}_{a1}+a_{13}{B}_{a1}\\ R_{n2}=b_1+a_{11}{R}_{a2}+a_{12}{G}_{a2}+a_{13}{B}_{a2}\\ R_{n3}=b_1+a_{11}{R}_{a3}+a_{12}{G}_{a3}+a_{13}{B}_{a3}\\ R_{n4}=b_1+a_{11}{R}_{a4}+a_{12}{G}_{a4}+a_{13}{B}_{a4}\end{array}\right.$

Order

$Y=\left(\begin{array}{c}{R}_{n1}\\ R_{n2}\\ R_{n3}\\ R_{n4}\end{array}\right),$ $X=\left(\begin{array}{cccc}1& R_{a1}& G_{a1}& B_{a1}\\ 1& R_{a2}& G_{a2}& B_{a2}\\ 1& R_{a3}& G_{a3}& B_{a3}\\ 1& R_{a4}& G_{a4}& B_{a4}\end{array}\right),$ $Z=\left(\begin{array}{c}{b}_1\\ a_{11}\\ a_{12}\\ a_{13}\end{array}\right)$

Can calculate

Z＝(X ^TX) ^-1X ^TY

The component corresponding coefficient that uses the same method and can obtain G and B, thus finally confirm A and B.Thereby obtain input point p to output point p _nComputing formula:

p _n＝AP+B

Claims (3)

1. method of utilizing tetrahedron interpolation method to realize the colour examining colour-difference-metre color correction; It is characterized in that: at first record the primary color points of requirement, then, utilize three-dimensional Delaunay triangulation through traditional interpolation algorithm; The primary colours collection is carried out the tetrahedron subdivision

Look-up table is set up in the tetrahedron set that utilizes subdivision to obtain;

After generating look-up table, suppose that input point is p, workflow is following:

Utilize the relation of input point p and each tetrahedral circumsphere centre of sphere O, judge whether input point p falls in the tetrahedral circumsphere apart from the radius r of d and tetrahedron circumsphere.All tetrahedrons that p falls into its circumsphere constitute set A; Concrete determination methods is following:

$p\left\{\begin{array}{cc}\∈T& d\≤r\\ \∉T& d>r\end{array}\right.$

After obtaining A, can utilize each tetrahedral volume relationship among a p and the A, judge further input point p is arranged in which tetrahedron of A, having only when a p falls into the summit is p ₀, p ₁, p ₂, p ₃Tetrahedron T in the time, some p and p ₀, p ₁, p ₂The tetrahedron T that constitutes ₁, with p ₀, p ₁, p ₃The tetrahedron T that constitutes ₂, with p ₀, p ₂, p ₃The tetrahedron T that constitutes ₃, with p ₁, p ₂, p ₃The tetrahedron T that constitutes ₄, reach the relation down that is enough to:

V(T ₁)+V(T ₂)+V(T ₃)+V(T ₄)＝V(T)

Wherein, the calculating of tetrahedron volume can obtain through following, when four summits of tetrahedron T are p ₀(x ₀, y ₀, z ₀), p ₁(x ₁, y ₁, z ₁), p ₂(x ₂, y ₂, z ₂), p ₃(x ₃, y ₃, z ₃) time, the computing formula of this tetrahedral volume V (T) is:

So when whether judging point p belongs to certain tetrahedron T, can use following formula to judge:

$p\left\{\begin{array}{cc}\∈T& V\left(T_0\right)+V\left(T_1\right)+V\left(T_2\right)+V\left(T_3\right)=V\left(T\right)\\ \∉T& V\left(T_0\right)+V\left(T_1\right)+V\left(T_2\right)+V\left(T_3\right)\≠V\left(T\right)\end{array}\right.$

All bodies at RP p place are in set B, if B is empty, the p point exceeds the scope that can proofread and correct so, not within the limit of consideration of this algorithm; If two tetrahedrons are arranged among the B, then select any one, utilize the linear regression method interpolation calculation to obtain desired value; If the tetrahedron more than two is arranged among the B, explain that the p point is certain tessarace, that is to say to belong to the point that interpolation point is concentrated, need not interpolation so, directly the export target value;

Can obtain equation of linear regression in the following manner:

The mapping of supposing imaging system is linear, and then the Standard Colors value of output is p _n=(R _n, G _n, B _n) ^TCan be expressed as:

p _n-p＝Λ _nσ

Wherein, p ₀Be the coordinate at zero point, Λ is the 3 * n dimension matrix that has comprised the illumination factor and the corresponding factor of sensor, and σ is the weight coefficient of body surface reflectivity basis function;

The same color value p that under non-standard illumination condition, obtains _a=(R _a, G _a, B _a) ^TSatisfy:

p _a-p＝Λ _aσ

Two formulas can obtain above the simultaneous

$p_n={\mathrm{\Λ}}_n{\mathrm{\Λ}}_a^{-1}{p}_a+(I-{\mathrm{\Λ}}_n{\mathrm{\Λ}}_a^{-1})p$

Order

then the above equation becomes

2. method of utilizing tetrahedron interpolation method to realize the colour examining colour-difference-metre color correction as claimed in claim 1, it is characterized in that: the structure of look-up table is following:

Wherein, given tetrahedron T and summit p thereof ₀p ₁p ₂p ₃After, utilize following system of equations to find the solution to obtain its circumsphere centre of sphere O,

$\left\{\begin{array}{c}\stackrel{\→}{q{m}_1}\·\stackrel{\→}{p_0{p}_1}=0;\\ \stackrel{\→}{q{m}_2}\·\stackrel{\→}{p_1{p}_2}=0;\\ \stackrel{\→}{q{m}_3}\·\stackrel{\→}{p_2{p}_3}=0;\end{array}\right.$

Here suppose m ₁Be p ₀p ₁The mid point of line segment, m ₂Be p ₂p ₃The mid point of line segment, m ₃Be p ₃p ₀The mid point of line segment, some q are that plan is anticipated a bit, that is:

$x_{m_i}=\frac{x_{i-1}+x_i}{2};$

$y_{m_i}=\frac{y_{i-1}+y_i}{2};i=\mathrm{1,2,3}.$

$z_{m_i}=\frac{z_{i-1}+z_i}{2};$

Expansion can obtain its algebraic expression:

$\left\{\begin{array}{c}(x_0-x_1)\·(x-x_{m_1})+(y_0-y_1)\·(y-y_{m_1})+(z_0-z_1)\·(z-z_{m_1})=0\\ (x_1-x_2)\·\left({x-x_m}_2\right)+(y_1-y_2)\·(y-y_{m_2})+(z_1-z_2)\·(z-z_{m_2})=0\\ (x_2-x_3)\·(x-x_{m_3})+(y_2-y_3)\·(y-y_{m_3})+(z_2-z_3)\·(z-z_{m_3})=0\end{array}\right.$

Its expression matrix form is:

$\left[\begin{array}{ccc}{x}_0-x_1& y_0-y_1& z_0-z_1\\ x_1-x_2& y_1-y_2& z_1-z_2\\ x_2-x_3& y_2-y_3& z_2-z_3\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}(x_0-x_1)x_{m_1}+(y_0-y_1)y_{m_1}+(z_0-z_1)z_{m_1}\\ (x_1-x_2)x_{m_2}+(y_1-y_2)y_{m_2}+(z_1-z_2)z_{m_2}\\ (x_2-x_3)x_{m_3}+(y_2-y_3)y_{m_3}+(z_2-z_3)z_{m_3}\end{array}\right]$

Thereby the circumsphere centre of sphere expression formula that can obtain tetrahedron T is:

$\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}(x_0-x_1)x_{m_1}+(y_0-y_1)y_{m_1}+(z_0-z_1)z_{m_1}\\ (x_1-x_2)x_{m_2}+(y_1-y_2)y_{m_2}+(z_1-z_2)z_{m_2}\\ (x_2-x_3)x_{m_3}+(y_2-y_3)y_{m_3}+(z_2-z_3)z_{m_3}\end{array}\right]/\left[\begin{array}{ccc}{x}_0-x_1& y_0-y_1& z_0-z_1\\ x_1-x_2& y_1-y_2& z_1-z_2\\ x_2-x_3& y_2-y_3& z_2-z_3\end{array}\right]$

3. method of utilizing tetrahedron interpolation method to realize the colour examining colour-difference-metre color correction as claimed in claim 1, it is characterized in that: the calculating of tetrahedron volume can obtain through following, when four summits of tetrahedron T are p ₀(x ₀, y ₀, z ₀), p ₁(x ₁, y ₁, z ₁), p ₂(x ₂, y ₂, z ₂), p ₃(x ₃, y ₃, z ₃) time, the computing formula of this tetrahedral volume V (T) is:

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