CN102393965B - 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 colour examining colour-difference-metre color correction

Technical field

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

Background technology

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

Although existing colour difference meter can substantially meet above-mentioned industry color is carried out to the basic requirement of measuring in society, but, it is accurate not that prior art is measured the method for proofreading and correct to colour difference meter intrinsic colour, speed is also slow, cause colour difference meter itself to have fiducial error, can not meet relevant industries and carry out the high-quality demand of precisely selecting look, color matching and fixation with it.

Summary of the invention

The object 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 to carry out color correction to the colour examining colour-difference-metre based on RGB trichromatic analysis, effectively improve to the precision of colour difference meter color correction and computing velocity, to meet 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.

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

In order to solve color correction in the colour examining colour-difference-metre based on RGB trichromatic analysis not precisely and the slow problem of computing velocity, method of the present invention is: the primary color space of utilizing three-dimensional Delaunay algorithm to record instrument is carried out tetrahedron subdivision, according to the tetrahedral position relationship of input point and place, realize interpolation calculation, carry out fast and accurate color correction.

Concrete computation process of the present invention is as follows: the primary color points that first records requirement by traditional interpolation algorithm, then, utilize three-dimensional Delaunay triangulation, primary colours collection is carried out to tetrahedron subdivision, the tetrahedron set that utilizes subdivision to obtain, sets up look-up table; The structure of look-up table is as follows:

Wherein, given tetrahedron T and summit p thereof ₀p ₁p ₂p ₃after, utilize following solving equations 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 ₁p ₀p ₁the mid point of line segment, m ₂p ₂p ₃the mid point of line segment, m ₃p ₃p ₀the mid point of line segment, some q is any point in plane, 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:

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

Generate after look-up table, suppose that input point is P, workflow is as follows:

Utilize the relation of input point p and the distance d of each tetrahedral circumsphere centre of sphere O and the radius r of tetrahedron circumsphere, judge whether input point p falls in tetrahedral circumsphere, p falls into all tetrahedrons formation set A of its circumsphere; Concrete determination methods is as follows:

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

Obtain after A, can utilize each tetrahedral volume relationship in a p and A, further judge input point p is arranged in which tetrahedron of A, only having when a p falls into summit is p ₀, p ₁, p ₂, p ₃tetrahedron T in time, some p and p ₀, p ₁, p ₂the tetrahedron T forming ₁, with p ₀, p ₁, p ₃the tetrahedron T forming ₂, with p ₀, p ₂, p ₃the tetrahedron T forming ₃, with p ₁, p ₂, p ₃the tetrahedron T forming ₄, reach the lower relation 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 by 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 judge with following formula:

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

All bodies at measuring point p place are in set B, if B is empty, p point exceeds the scope that can proofread and correct so, not within the limit of consideration of this algorithm; If there are two tetrahedrons in B, select any one, utilize linear regression method interpolation calculation to obtain target rgb value; If there is the tetrahedron more than two in B, illustrate that p point is certain tessarace, that is to say and belong to the concentrated point of interpolation point, so without interpolation, direct export target rgb value;

Can obtain in the following manner equation of linear regression:

The mapping of supposing imaging system is linear, and 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 ₀for coordinate at zero point, Λ is the 3 * n dimension matrix that has comprised Illumination and the corresponding factor of sensor, and σ is the weight coefficient of body surface reflectivity basis function;

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

p _a-p＝Λ _aσ

Above simultaneous, two formulas can obtain

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

Order

above formula becomes

In order to calculate

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

Delaunay algorithm claims again Delaunay triangulation Quick-Point location algorithm, 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 ", the standard of there is no is unified translation.

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

Accompanying drawing explanation

Accompanying drawing is calculation process block diagram of the present invention, is also figure for specification digest.In figure, each label respectively: (1) primary colours are measured, (2) utilize three-dimensional algorithm to carry out subdivision to primary color space, (3) set up look-up table, (4) input color value is measured, (5) utilize volume relationship judgement 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 rear color value.

Embodiment

The present invention will be further described now to give by reference to the accompanying drawings an example.

Embodiment:

Take R component as example,

R _n＝b ₁+a ₁₁R _a+a ₁₂G _a+a ₁₃B _a

The input and output value of supposing known 4 summits, has:

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

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

Use the same method and can obtain the component corresponding coefficient of G and B, thereby finally determine A and B.Thereby obtain input point p to output point p _ncomputing formula:

p _n＝AP+B

Claims (2)

1. a method of utilizing tetrahedron interpolation method to realize colour examining colour-difference-metre color correction, it is characterized in that: the primary color points that first records requirement by traditional interpolation algorithm, then, utilize three-dimensional Delaunay triangulation, primary colours point set is carried out to tetrahedron subdivision, the tetrahedron set that utilizes subdivision to obtain, sets up the look-up table consisting of each tetrahedral circumscribed circle center of circle, circumradius, the former rgb value of tetrahedron top and target rgb value; Generate after look-up table, suppose that input point is p, workflow is as follows:

Utilize the relation of input point p and the distance d of each tetrahedral circumsphere centre of sphere O and the radius r of tetrahedron circumsphere, judge whether input point p falls in tetrahedral circumsphere, all tetrahedrons that p falls into its circumsphere form set A; Concrete determination methods is as follows:

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

Obtain after A, utilize each tetrahedral volume relationship in some p and A, further judge input point p is arranged in which tetrahedron of A, only having when some p falls into summit is p ₀, p ₁, p ₂, p ₃tetrahedron T in time, some p and p ₀, p ₁, p ₂the tetrahedron T forming ₁, with p ₀, p ₁, p ₃the tetrahedron T forming ₂, with p ₀, p ₂, p ₃the tetrahedron T forming ₃, with p ₁, p ₂, p ₃the tetrahedron T forming ₄, reach the lower relation that is enough to:

V(T ₁)+V(T ₂)+V(T ₃)+V(T ₄)＝V(T)

Wherein, the calculating of tetrahedron volume obtains by 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:

$V\left(T\right)=\frac{1}{6}\left|\right|\begin{array}{cccc}1& 1& 1& 1\\ x_0& x_1& x_2& x_3\\ y_0& y_1& y_2& y_3\\ z_0& z_1& z_2& z_3\end{array}\left|\right|$

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

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

The tetrahedron T at measuring point p place is in set B, if B is empty, p point exceeds the scope that can proofread and correct so, not within the limit of consideration of this algorithm; If there are two tetrahedrons in B, select any one, utilize linear regression method interpolation calculation to obtain desired value; If there is the tetrahedron more than two in B, illustrate that p point is certain tessarace, that is to say and belong to the concentrated point of interpolation point, so without interpolation, direct export target value;

Obtain in the following manner equation of linear regression:

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

p _n-p ₀＝Λ _nσ

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

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

p _a-p ₀＝Λ _aσ

Above simultaneous, two formulas can obtain

$p_n={\mathrm{\Λ}}_n{\mathrm{\Λ}}_a^{-1}{p}_a+(I-{\mathrm{\Λ}}_n{\mathrm{\Λ}}_a^{-1})p_0$

Order $\mathrm{\Λ}={\mathrm{\Λ}}_n{\mathrm{\Λ}}_a^{-1}=\left(\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right),B=(I-{\mathrm{\Λ}}_n{\mathrm{\Λ}}_a^{-1})p_0=\left(\begin{array}{c}{b}_1\\ b_2\\ b_3\end{array}\right),$ Above formula becomes

p _n＝Λp _a+B。

2. a method of utilizing tetrahedron interpolation method to realize colour examining colour-difference-metre color correction as claimed in claim 1, it is characterized in that: the look-up table being formed by the circumscribed circle center of circle, circumradius, the former rgb value in summit and summit target rgb value, given tetrahedron T and summit p thereof ₀p ₁p ₂p ₃after, utilize following solving equations to obtain its circumsphere centre of sphere O,

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

Here suppose m ₁p ₀p ₁the mid point of line segment, m ₂p ₁p ₂the mid point of line segment, m ₃p ₂p ₃the mid point of line segment, some q is any point in plane, 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:

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

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 of obtaining tetrahedron T is:

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

Images