CN102393965B

CN102393965B - A method for color correction of colorimeter by using tetrahedron interpolation method

Info

Publication number: CN102393965B
Application number: CN201110156725.6A
Authority: CN
Inventors: 林金龙; 欧阳泳春; 王果
Original assignee: BOYA ZHIHUI INTERNATIONAL CO LTD
Current assignee: BOYA ZHIHUI INTERNATIONAL CO LTD
Priority date: 2011-06-01
Filing date: 2011-06-01
Publication date: 2014-01-29
Anticipated expiration: 2031-06-01
Also published as: CN102393965A

Abstract

A method for realizing color correction of a color measurement colorimeter by utilizing a tetrahedral interpolation method comprises the steps of firstly measuring a required number of primary color points through a traditional interpolation algorithm, then carrying out tetrahedral subdivision on a primary color set by utilizing a three-dimensional Delaunay triangulation algorithm, and establishing a lookup table by utilizing a tetrahedral set obtained by the tetrahedral subdivision; after a lookup table is generated, assuming that an input point is P, after A is obtained, further judging which tetrahedron the input point P is located in A by using the volume relationship between the point P and each tetrahedron in A, if more than two tetrahedrons exist in B, the point P is the vertex of a certain tetrahedron, namely belongs to a point in an interpolation point set, and a target RGB value can be directly output without interpolation; assuming that the mapping of the imaging system is linear, the output standard color value is p_n＝(R_n，G_n，B_n)^TCan be expressed as: p is a radical of_n-p＝Λ_nCompared with the common color measurement method based on three-color analysis, the method has the characteristics of simplicity, rapidness and accuracy.

Description

A method for color correction of colorimeter by using tetrahedron interpolation method

技术领域 technical field

一种利用四面体插值法实现测色色差计颜色校正的方法A method for color correction of colorimeter by using tetrahedron interpolation method

背景技术 Background technique

塑胶、喷涂、设计、印刷、服装、印染等行业需要对颜色进行尽可能精准的测量，以满足高品质精准选色、配色和定色的需求。Industries such as plastics, spraying, design, printing, clothing, and printing and dyeing need to measure colors as accurately as possible to meet the needs of high-quality and accurate color selection, color matching and color fixing.

社会上现有的色差计虽然可以基本上满足上述行业对颜色进行基本测定的要求，但是，现有技术对色差计本身颜色测定校正的方法不够精准，速度也比较慢，导致色差计本身存有基准误差，不能满足相关行业用其进行高品质精准选色、配色和定色的需求。Although the existing color difference meters in the society can basically meet the requirements of the above-mentioned industries for basic color measurement, the existing technology is not accurate enough to measure and correct the color of the color difference meter itself, and the speed is relatively slow, resulting in the color difference meter itself. The benchmark error cannot meet the needs of related industries for high-quality and accurate color selection, color matching and color fixing.

发明内容 Contents of the invention

本发明的目的是在普通四面体插值算法的基础上，设计一种新的四面体插值算法，并利用该算法对基于RGB三色分析的测色色差计进行颜色校正，有效提高对色差计颜色校正的精度与计算速度，以满足塑胶、喷涂、设计、印刷、服装、印染等行业高品质精准选色、配色和定色的需求。The purpose of the present invention is to design a new tetrahedron interpolation algorithm on the basis of the common tetrahedron interpolation algorithm, and use this algorithm to carry out color correction to the color measuring color difference meter based on the RGB three-color analysis, effectively improve the accuracy of the color difference meter. Calibration accuracy and calculation speed to meet the needs of high-quality and accurate color selection, color matching and color fixing in industries such as plastics, spraying, design, printing, clothing, and printing and dyeing.

在基于RGB三色分析的测色色差计中，为了实现颜色交流，必须把仪器条件下测得的颜色值，映射到一种与设备无关的颜色空间内，这一过程称之为颜色校正。In the color difference meter based on RGB three-color analysis, in order to realize color communication, the color values measured under the instrument conditions must be mapped to a device-independent color space. This process is called color correction.

为了解决基于RGB三色分析的测色色差计中的颜色校正不够精准和计算速度慢的问题，本发明的方法是：利用三维Delaunay算法对仪器测得的基色空间进行四面体剖分，根据输入点与所在四面体的位置关系，实现插值计算，进行快速、精准的颜色校正。In order to solve the problem of inaccurate color correction and slow calculation speed in the color difference meter based on RGB three-color analysis, the method of the present invention is: use the three-dimensional Delaunay algorithm to tetrahedralize the primary color space measured by the instrument, according to the input The position relationship between the point and the tetrahedron where it is located realizes the interpolation calculation and performs fast and accurate color correction.

本发明的具体计算过程如下：首先通过传统的插值算法测得所需数量的基色点，然后，利用三维Delaunay三角剖分算法，对基色集进行四面体剖分，利用剖分得到的四面体集合，建立查找表；查找表的结构如下：The concrete calculation process of the present invention is as follows: at first measure the basic color point of required quantity by traditional interpolation algorithm, then, utilize three-dimensional Delaunay triangulation algorithm, carry out tetrahedral subsection to basic color set, utilize the tetrahedron set that subdivision obtains , to establish a lookup table; the structure of the lookup table is as follows:

其中，给定四面体T及其顶点p₀ p₁ p₂ p₃后，利用如下方程组求解得到其外接球球心O，Among them, given the tetrahedron T and its vertices p ₀ p ₁ p ₂ p ₃ , use the following equations to solve to obtain its circumscribed sphere center O,

$\{\begin{matrix} \overset{&RightArrow; &Right Arrow;}{q q {m m}_{11}} \cdot \cdot \overset{&RightArrow; &Right Arrow;}{{p p}_{00} {p p}_{11}} = = 00;; \\ \overset{&RightArrow; &Right Arrow;}{q q {m m}_{22}} \cdot \cdot \overset{&RightArrow; &Right Arrow;}{{p p}_{11} {p p}_{22}} = = 00;; \\ \overset{&RightArrow; &Right Arrow;}{q q {m m}_{33}} \cdot \cdot \overset{&RightArrow; &Right Arrow;}{{p p}_{22} {p p}_{33}} = = 00;; \end{matrix}$

这里假定m₁是p₀p₁线段的中点，m₂是p₂p₃线段的中点，m₃是p₃p₀线段的中点，点q是平面上任意一点，即：It is assumed here that m ₁ is the midpoint of the line segment p ₀ p ₁ , m ₂ is the midpoint of the line segment p ₂ p ₃ , m ₃ is the midpoint of the line segment p ₃ p ₀ , and point q is any point on the plane, namely:

${x x}_{{m m}_{i i}} = = \frac{{x x}_{i i - - 11} + + {x x}_{i i}}{22};;$

${y the y}_{{m m}_{i i}} = = \frac{{y the y}_{i i - - 11} + + {y the y}_{i i}}{22};; i i = = 1,2,3 1,2,3 . .$

${z z}_{{m m}_{i i}} = = \frac{{z z}_{i i - - 11} + + {z z}_{i i}}{22};;$

展开即可得到其代数表达式为：Expand to get its algebraic expression:

$\{\begin{matrix} (({x x}_{00} - - {x x}_{11})) \cdot &Center Dot; ((x x - - {x x}_{{m m}_{11}})) + + (({y the y}_{00} - - {y the y}_{11})) \cdot &Center Dot; ((y the y - - {y the y}_{{m m}_{11}})) + + (({z z}_{00} - - {z z}_{11})) \cdot \cdot ((z z - - {z z}_{{m m}_{11}})) = = 00 \\ (({x x}_{11} - - {x x}_{22})) \cdot \cdot (({x x - - {x x}_{m m}}_{22})) + + (({y the y}_{11} - - {y the y}_{22})) \cdot \cdot ((y the y - - {y the y}_{{m m}_{22}})) + + (({z z}_{11} - - {z z}_{22})) \cdot \cdot ((z z - - {z z}_{{m m}_{22}})) = = 00 \\ (({x x}_{22} - - {x x}_{33})) \cdot \cdot ((x x - - {x x}_{{m m}_{33}})) + + (({y the y}_{22} - - {y the y}_{33})) \cdot &Center Dot; ((y the y - - {y the y}_{{m m}_{33}})) + + (({z z}_{22} - - {z z}_{33})) \cdot &Center Dot; ((z z - - {z z}_{{m m}_{33}})) = = 00 \end{matrix}$

其矩阵表达形式为：Its matrix expression is:

$[\begin{matrix} {x x}_{00} - - {x x}_{11} & {y the y}_{00} - - {y the y}_{11} & {z z}_{00} - - {z z}_{11} \\ {x x}_{11} - - {x x}_{22} & {y the y}_{11} - - {y the y}_{22} & {z z}_{11} - - {z z}_{22} \\ {x x}_{22} - - {x x}_{33} & {y the y}_{22} - - {y the y}_{33} & {z z}_{22} - - {z z}_{33} \end{matrix}] [\begin{matrix} x x \\ y the y \\ z z \end{matrix}] = = [\begin{matrix} (({x x}_{00} - - {x x}_{11})) {x x}_{{m m}_{11}} + + (({y the y}_{00} - - {y the y}_{11})) {y the y}_{{m m}_{11}} + + (({z z}_{00} - - {z z}_{11})) {z z}_{{m m}_{11}} \\ (({x x}_{11} - - {x x}_{22})) {x x}_{{m m}_{22}} + + (({y the y}_{11} - - {y the y}_{22})) {y the y}_{{m m}_{22}} + + (({z z}_{11} - - {z z}_{22})) {z z}_{{m m}_{22}} \\ (({x x}_{22} - - {x x}_{33})) {x x}_{{m m}_{33}} + + (({y the y}_{22} - - {y the y}_{33})) {y the y}_{{m m}_{33}} + + (({z z}_{22} - - {z z}_{33})) {z z}_{{m m}_{33}} \end{matrix}]$

从而可求出四面体T的外接球球心表达式为：Thus, the expression of the center of the circumscribed sphere of the tetrahedron T can be obtained as:

$[\begin{matrix} x x \\ y the y \\ z z \end{matrix}] = = [\begin{matrix} (({x x}_{00} - - {x x}_{11})) {x x}_{{m m}_{11}} + + (({y the y}_{00} - - {y the y}_{11})) {y the y}_{{m m}_{11}} + + (({z z}_{00} - - {z z}_{11})) {z z}_{{m m}_{11}} \\ (({x x}_{11} - - {x x}_{22})) {x x}_{{m m}_{22}} + + (({y the y}_{11} - - {y the y}_{22})) {y the y}_{{m m}_{22}} + + (({z z}_{11} - - {z z}_{22})) {z z}_{{m m}_{22}} \\ (({x x}_{22} - - {x x}_{33})) {x x}_{{m m}_{33}} + + (({y the y}_{22} - - {y the y}_{33})) {y the y}_{{m m}_{33}} + + (({z z}_{22} - - {z z}_{33})) {z z}_{{m m}_{33}} \end{matrix}] / / [\begin{matrix} {x x}_{00} - - {x x}_{11} & {y the y}_{00} - - {y the y}_{11} & {z z}_{00} - - {z z}_{11} \\ {x x}_{11} - - {x x}_{22} & {y the y}_{11} - - {y the y}_{22} & {z z}_{11} - - {z z}_{22} \\ {x x}_{22} - - {x x}_{33} & {y the y}_{22} - - {y the y}_{33} & {z z}_{22} - - {z z}_{33} \end{matrix}]$

生成查找表后，假定输入点为P，工作流程如下：After generating the lookup table, assuming that the input point is P, the workflow is as follows:

利用输入点p与每个四面体的外接球球心O的距离d和四面体外接球的半径r的关系，判断输入点p是否落入四面体的外接球内，即p落入其外接球的所有四面体构成集合A；具体判断方法如下：Use the relationship between the distance d between the input point p and the center O of the circumscribed sphere of each tetrahedron and the radius r of the circumscribed sphere of the tetrahedron to determine whether the input point p falls into the circumscribed sphere of the tetrahedron, that is, p falls into its circumscribed sphere All tetrahedrons of constitute a set A; the specific judgment method is as follows:

$p p \{\begin{matrix} &Element; &Element; T T & d d \leq \leq r r \\ &NotElement; &NotElement; T T & d d > > r r \end{matrix}$

得到A后，可以利用点p与A中每一个四面体的体积关系，进一步判断输入点p位于A中的哪个四面体内，只有当点p落入顶点为p₀，p₁，p₂，p₃的四面体T内时，点p与p₀，p₁，p₂构成的四面体T₁，与p₀，p₁，p₃构成的四面体T₂，与p₀，p₂，p₃构成的四面体T₃，与p₁，p₂，p₃构成的四面体T₄，才满足以下关系：After obtaining A, you can use the volume relationship between the point p and each tetrahedron in A to further judge which tetrahedron the input point p is located in A, only when the point p falls into the vertices p ₀ , p ₁ , p ₂ , p When inside the tetrahedron T of ₃ , the tetrahedron T 1 formed by the point p and p ₀ , p ₁ , p _{2 ,} the tetrahedron T 2 formed by the point p ₀ _, p ₁ , p ₃ , and the tetrahedron T ₂ formed by the point p ₀ , p ₂ , p The tetrahedron T ₃ formed by ₃ and the tetrahedron T ₄ formed by p ₁ , p ₂ , and p ₃ satisfy the following relationship:

V(T₁)+V(T₂)+V(T₃)+V(T₄)＝V(T)V(T ₁ )+V(T ₂ )+V(T ₃ )+V(T ₄ )＝V(T)

其中，四面体体积的计算可以通过下述得到，当四面体T的四个顶点为p₀(x₀，y₀，z₀)，p₁(x₁，y₁，z₁)，p₂(x₂，y₂，z₂)，p₃(x₃，y₃，z₃)时，该四面体的体积V(T)的计算公式为：Among them, the calculation of tetrahedron volume can be obtained as follows, when the four vertices 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 ), the formula for calculating the volume V(T) of the tetrahedron is:

所以判断点p是否属于某个四面体T时，可以用如下公式判断：Therefore, when judging whether a point p belongs to a certain tetrahedron T, the following formula can be used to judge:

$p p \{\begin{matrix} &Element; &Element; T T & V V (({T T}_{00})) + + V V (({T T}_{11})) + + V V (({T T}_{22})) + + V V (({T T}_{33})) = = V V ((T T)) \\ &NotElement; &NotElement; T T & V V (({T T}_{00})) + + V V (({T T}_{11})) + + V V (({T T}_{22})) + + V V (({T T}_{33})) &NotEqual; &NotEqual; V V ((T T)) \end{matrix}$

记录点p所在的所有体于集合B中，如果B为空，那么p点超出能够校正的范围，不在该算法的考虑范围之内；如果B中有两个四面体，则选择任意一个，利用线性回归法插值计算得到目标RGB值；如果B中有多于两个的四面体，说明p点是某个四面体的顶点，也就是说属于插值点集中的点，那么无需插值，可直接输出目标RGB值；Record all volumes where point p is located in set B. If B is empty, point p is beyond the range that can be corrected and is not considered by the algorithm; if there are two tetrahedrons in B, choose any one and use The target RGB value is obtained by linear regression interpolation calculation; if there are more than two tetrahedrons in B, it means that point p is the vertex of a certain tetrahedron, that is to say, it belongs to the point in the interpolation point set, so it can be directly output without interpolation Target RGB value;

可通过以下方式得到线性回归方程：The linear regression equation can be obtained by:

假设成像系统的映射呈线性关系，则输出的标准颜色值为p_n＝(R_n，G_n，B_n)^T可以表示为：Assuming that the mapping of the imaging system is linear, the output standard color value p _n = (R _n , G _n , B _n ) ^T can be expressed as:

p_n-p＝Λ_nσp _n -p = Λ _n σ

其中，p₀为零点坐标，Λ为包含了光照因子和传感器相应因子的3×n维矩阵，σ为物体表面反射率基函数的权重系数；Among them, p ₀ is the coordinate of the zero point, Λ is a 3×n-dimensional matrix including the illumination factor and the corresponding factor of the sensor, and σ is the weight coefficient of the reflectance basis function of the object surface;

同样在非标准光照条件下得到的颜色值p_a＝(R_a，G_a，B_a)^T满足：Similarly, the color value p _a = (R _a , G _a , B _a ) ^T obtained under non-standard lighting conditions satisfies:

p_a-p＝Λ_aσp _a -p = Λ _a σ

联立上面两式即可得到Combine the above two formulas to get

${p p}_{n no} = = {Λ Λ}_{n no} {Λ Λ}_{a a}^{- - 11} {p p}_{a a} + + ((I I - - {Λ Λ}_{n no} {Λ Λ}_{a a}^{- - 11})) p p$

令

则上式变为make

Then the above formula becomes

为了计算

和B，至少需要知道4个非共面的样本点的标准值及非标准值，通过线性回归分析，采用最小二乘法求解各个分量的相应系数；这四个点的取四面体插值过程中，查找得到的四面体四个顶点。to calculate

and B, at least need to know the standard value and non-standard value of 4 non-coplanar sample points, through linear regression analysis, use the least square method to solve the corresponding coefficients of each component; in the tetrahedral interpolation process of these four points, Find the four vertices of the resulting tetrahedron.

Delaunay算法又称Delaunay三角剖分快速点定位算法，是一种广泛应用的算法，主要应用于四面体定位计算方面。国内有的翻译成“德劳奈”，有的译成“德劳耐”，尚无标准统一译法。The Delaunay algorithm, also known as the Delaunay triangulation fast point positioning algorithm, is a widely used algorithm, mainly used in tetrahedron positioning calculations. Some of them are translated into "Delaunay" in China, and some are translated into "Delaunay". There is no standard and unified translation method.

本发明提出的颜色校正方法基于已有均匀或非均匀基色库，在此基础上对输入颜色空间进行非均匀划分并建立查找表。对于新的输入点，利用体积关系判断其所在的四面体，然后根据输入点与所在四面体顶点的位置关系，选择利用插值计算公式，得到输出值，从而实现仪器颜色空间到标准颜色空间的转换。与普通基于三色分析的测色方法相比较，本发明具有简单、快捷、准确的特点。The color correction method proposed by the invention is based on the existing uniform or non-uniform primary color library, and on this basis, the input color space is non-uniformly divided and a look-up table is established. For a new input point, use the volume relationship to judge the tetrahedron it is in, and then according to the positional relationship between the input point and the vertex of the tetrahedron, choose to use the interpolation calculation formula to get the output value, so as to realize the conversion from the instrument color space to the standard color space . Compared with the common color measuring method based on three-color analysis, the present invention has the characteristics of simplicity, quickness and accuracy.

附图说明 Description of drawings

附图是本发明的计算流程方框示意图，也是说明书摘要用图。图中各标号分别是：(1)基色测量，(2)利用三维算法对基色空间进行剖分，(3)建立查找表，(4)输入颜色值测量，(5)利用体积关系判断输入点所在四面体，(6)输入点位于四面体顶点，(7)线性判归法，(8)出校正后颜色值。Accompanying drawing is the block schematic diagram of calculation flow of the present invention, also is the figure with description abstract. The labels in the figure are: (1) base color measurement, (2) use three-dimensional algorithm to divide the base color space, (3) establish a lookup table, (4) input color value measurement, (5) use the volume relationship to judge the input point Where the tetrahedron is located, (6) the input point is located at the vertex of the tetrahedron, (7) the linear regression method, (8) the corrected color value is output.

具体实施方式 Detailed ways

现结合附图给一实例对本发明做进一步说明。Now give an example in conjunction with accompanying drawing and further illustrate the present invention.

实施例：Example:

以R分量为例，Taking the R component as an example,

R_n＝b₁+a₁₁R_a+a₁₂G_a+a₁₃B_a R _n =b ₁ +a ₁₁ R _a +a ₁₂ G _a +a ₁₃ B _a

假设已知4个顶点的输入输出值，则有：Assuming that the input and output values of 4 vertices are known, there are:

$\{\begin{matrix} {R R}_{n no 11} = = {b b}_{11} + + {a a}_{1111} {R R}_{a a 11} + + {a a}_{1212} {G G}_{a a 11} + + {a a}_{1313} {B B}_{a a 11} \\ {R R}_{n no 22} = = {b b}_{11} + + {a a}_{1111} {R R}_{a a 22} + + {a a}_{1212} {G G}_{a a 22} + + {a a}_{1313} {B B}_{a a 22} \\ {R R}_{n no 33} = = {b b}_{11} + + {a a}_{1111} {R R}_{a a 33} + + {a a}_{1212} {G G}_{a a 33} + + {a a}_{1313} {B B}_{a a 33} \\ {R R}_{n no 44} = = {b b}_{11} + + {a a}_{1111} {R R}_{a a 44} + + {a a}_{1212} {G G}_{a a 44} + + {a a}_{1313} {B B}_{a a 44} \end{matrix}$

令make

$Y Y = = (\begin{matrix} {R R}_{n no 11} \\ {R R}_{n no 22} \\ {R R}_{n no 33} \\ {R R}_{n no 44} \end{matrix}),,$ $X x = = (\begin{matrix} 11 & {R R}_{a a 11} & {G G}_{a a 11} & {B B}_{a a 11} \\ 11 & {R R}_{a a 22} & {G G}_{a a 22} & {B B}_{a a 22} \\ 11 & {R R}_{a a 33} & {G G}_{a a 33} & {B B}_{a a 33} \\ 11 & {R R}_{a a 44} & {G G}_{a a 44} & {B B}_{a a 44} \end{matrix}),,$ $Z Z = = (\begin{matrix} {b b}_{11} \\ {a a}_{1111} \\ {a a}_{1212} \\ {a a}_{1313} \end{matrix})$

可以计算得出can be calculated

Z＝(X^TX)^-1X^TYZ＝(X ^T X) ^-1 X ^T Y

用同样的方法可以得到G和B的分量相应系数，从而最终确定A和B。从而得到输入点p到输出点p_n的计算公式：In the same way, the corresponding coefficients of G and B components can be obtained, so as to finally determine A and B. Thus, the calculation formula from the input point p to the output point p _n is obtained:

p_n＝AP+Bp _n =AP+B

Claims

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 \{\begin{matrix} &Element; T & d \leq r \\ &NotElement; T & d > r \end{matrix}

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 (T) = \frac{1}{6} | | \begin{matrix} 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{matrix} | |

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

p \{\begin{matrix} &Element; T & V (T_{0}) + V (T_{1}) + V (T_{2}) + V (T_{3}) = V (T) \\ &NotElement; T & V (T_{0}) + V (T_{1}) + V (T_{2}) + V (T_{3}) &NotEqual; V (T) \end{matrix}

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} = Λ_{n} Λ_{a}^{- 1} p_{a} + (I - Λ_{n} Λ_{a}^{- 1}) p_{0}

Order

Λ = Λ_{n} Λ_{a}^{- 1} = (\begin{matrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{matrix}), B = (I - Λ_{n} Λ_{a}^{- 1}) p_{0} = (\begin{matrix} b_{1} \\ b_{2} \\ b_{3} \end{matrix}),

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,

\{\begin{matrix} \overset{&RightArrow;}{{qm}_{1} \cdot} \overset{&RightArrow;}{p_{0} p_{1}} = 0; \\ \overset{&RightArrow;}{{qm}_{2}} \cdot \overset{&RightArrow;}{p_{1} p_{2}} = 0; \\ \overset{&RightArrow;}{{qm}_{3}} \cdot \overset{&RightArrow;}{p_{2} p_{3}} = 0; \end{matrix}

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 = 1,2,3 .

z_{m_{i}} = \frac{z_{i - 1} + z_{i}}{2};

Expansion can obtain its algebraic expression:

\{\begin{matrix} (x_{0} - x_{1}) \cdot (x - x_{m_{1}}) + (y_{0} - y_{1}) \cdot (y - y_{m_{1}}) + (z_{0} - z_{1}) \cdot (z - z_{m_{1}}) = 0 \\ (x_{1} - x_{2}) \cdot (x - x_{m_{2}}) + (y_{1} - y_{2}) \cdot (y - y_{m_{2}}) + (z_{1} - z_{2}) \cdot (z - z_{m_{2}}) = 0 \\ (x_{2} - x_{3}) \cdot (x - x_{m_{3}}) + (y_{2} - y_{3}) \cdot (y - y_{m_{3}}) + (z_{2} - z_{3}) \cdot (z - z_{m_{3}}) = 0 \end{matrix}

Its expression matrix form is:

[\begin{matrix} 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{matrix}] [\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} (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{matrix}]

Thereby the circumsphere centre of sphere expression formula of obtaining tetrahedron T is:

[\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} (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{matrix}] / [\begin{matrix} 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{matrix}] .