数字图像处理色彩空间转换文档与代码

Colors

Colormodels, Conversions and Color Difference in Formulas and Code

Johannes Bildstein

November 24, 2013

Contents

I. Introduction 4

II. Chromatic Adaption 5

III. Colormodels 7

1. XYZ 7

4. Luv 12

4.1. XYZ to Luv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.2. Luv to XYZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5. RGB 14

5.1. XYZ to RGB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5.2. RGB to XYZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

6. HSV 17

6.1. RGB to HSV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

6.2. HSV to RGB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

7. HSL 20

9. LCHab 25

9.1. Lab to LCHab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

9.2. LCHab to Lab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

10.LCHuv 26

10.1. Luv to LCHuv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

10.2. LCHuv to Luv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

11.DIN99 28

11.1. Lab to DIN99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

11.2. DIN99 to Lab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

12.DIN99b 30

12.1. Lab to DIN99b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

14.2. DIN99d to Lab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

15.DEF 36

15.1. XYZ to DEF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

15.2. DEF to XYZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

16.Bef 37

16.1. DEF to Bef . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

16.2. Bef to DEF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

17.BCH 39

17.1. DEF to BCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

17.2. BCH to DEF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

19.1. Delta E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

20.CIE 94 42

20.1. Delta E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

20.2. Delta C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

20.3. Delta H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

21.CIE DE 2000 44

21.1. Delta E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

22.CMC 46

22.1. Delta E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

22.2. Delta C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

22.3. Delta H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

V. Data 49

Part I.

Introduction

This article contains a large amount of color conversion formulas and code. You are free to use the code

in this article. First the colormodels and conversions are listed, then color difference calculations are

listed and at the end there are a few tables with useful data.

You can find a C# library (GPL3 license) with all of the listed colors and some more here:

www.codeproject.com/Articles/613798/Colorspaces-and-Conversions

A general note to the code snipplets:

They are written in C#, but since I didn’t use any fancy language specific stuff, it should be easily

portable to other languages. The code is partially optimized already but still kept readable. Therefore

that returns x ∗ x ∗ x)

• If possible, make constants for calculations that won’t change. Like

• If a part of a formula is used more than one time, only calculate this part once and use the result

for all formulas.

• Pass as few variables as possible when calling methods

• Precalculate what’s possible to precalculate. Chromatic adaption matrices for example.

You also might want to make a border check after the calculation, e.g. if a number is bigger than 1 or

Part II.

Chromatic Adaption

If you convert between colors with a different reference white you have to perform chromatic adaption

as follows:

• X

, Z

are the values from the source whitepoint, which you can find at section 23

• X

, Y

, Z

are the values from the destination whitepoint, which you can find at section 23

X

X

Y

M

γ

γ

0 0

β

β

(2)

And: