Chapter 6 Color Image Processing

Chapter 6Color Image Processing

國立雲林科技大學電子工程系張傳育 (Chuan-Yu Chang ) 博士Office: ES 709TEL: 05-5342601 ext. 4337E-mail: [email protected]

2

Color Fundamentals In 1666, Sir Isaac Newton

He discovered that when a beam of sunlight passes through a glass prism, the emerging beam of light is consists of a continuous spectrum of colors ranging from violet to red.

3

Color Fundamentals (cont.) Basically, humans and some other animals perceive in

an object are determined by the nature of the light reflected from the object.

Visible light is composed of a relatively narrow band of frequencies in the electromagnetic spectrum.

For humans, colors are seen as variable combinations of the primary colors: red, green, and blue.

4

Color Fundamentals (cont.)

人眼椎狀體吸收之紅、綠、藍光的波長函數

65% 的椎狀體可感應到紅光， 33% 可感應到綠光，只有 2% 感應到藍光

1931 年國際照明組織(CIE) 指定三原色的波長 :Blue:435.8nmGreen:546.1nmRed:700nm

5


For the purpose of standardization, the CIE (the international Commission on Illumination) designated in 1931 the following specific wavelength values to the three primary colors: Blue=435.8 nm, Green=546.1 nm, and Red=700 nm. From Fig. 6.2 and 6.3 that no single color may be called

red, green , or blue. Having three specific primary color wavelengths for the

purpose of standardization does not mean that these three fixed RGB components acting alone can generate all spectrum colors.

6


光的混合式採用加成的方式

In colorants, a primary color is defined as one that subtracts or absorbs a primary color of light and reflects or transmits the other two.

Primary and secondary colors of light and pigments The primary colors can be added to produce the secondary

colors of light: magenta (R+B), cyan (G+B), yellow (R+G)

The primary colors of pigments are magenta, cyan, and yellow

7


The characteristics generally used to distinguish one color from another are Brightness embodies the chromatic notion of intensity. Hue represents dominant color as perceived by an

observer. Saturation is an attribute associated with the dominant

wavelength in a mixture of light waves. Saturation refers to the relative purity or the amount of white

light mixed with a hue. Hue and saturation taken together are called chromaticity,

therefore, a color may be characterized by its brightness and chromaticity.

8

Color Fundamentals (cont.) The amounts of red, green, and blue needed to form any

particular color are called the tri-stimulus values and are denoted, X, Y, and Z.

A color is then specified by its tri-chromatic coefficients, defined as

It is noted from these equations that x + y + z = 1

ZYX

Zz

ZYX

Yy

ZYX

Xx

(6.1-1)

(6.1-2)

(6.1-3)

(6.1-4)

9

The CIE chromaticity diagram Which shows color composition as a function of x (red) and y

(green). For any value of x and y, the corresponding value of z (blue) is

obtained from Eq.(6.1-4). z = 1- ( x + y )

approximately 62% green, 25% red , and 13% blue content. The positions of the various spectrum colors from violet at

380 nm to red at 780 nm are indicated around the boundary of the tongue-shaped chromaticity diagram.

These are the pure colors shown in the spectrum of Fig. 6.2.


10

Color Fundamentals (cont.) CIE 色度圖

綠色點佔62%

藍色點佔13%

紅色點佔25%

11


12

Color Models The RGB Color Model

Each color appears in its primary spectral components of red, green, and blue.

Images represented in the RGB color model consist of three component images, one for each primary color.

When fed into an RGB monitor, these three images combine on the phosphor screen to produce a composite color image.

The number of bits used to represent each pixel in RGB space is called the pixel depth. Full-color denote a 24-bit RGB color image

13

Color Models (cont.) Example 6.1

Generating the hidden face planes and a cross section of the RGB color cube. Fig. 6.8 is a solid, composed of the 224=16777216

colors..

14

Color Models (cont.) Example 6.1 (cont.)

Acquiring a color image is basically the process shown in Fig. 6.9 in reverse.

A color image can be acquired by using three filters, sensitive to red, green, and blue.

When we view a color scene with a monochrome camera equipped with one of these filters, the result is a monochrome image whose intensity is proportional to the response of that filter.

Repeating this process with each filter produces three monochrome images that are RGB component images of the color scene.

15

Color Models (cont.) Safe RGB color, All-system-safe color, Safe Web

color, Safe browser color Given the variety of systems in current use, it is of

considerable interest to have a subset of colors that are likely to be reproduced faithfully, reasonably independently of viewer hardware capabilities.

216 colors are common to most systems, these colors have become the standard for safe colors.

Each of the 216 safe colors is formed from three RGB values, each value can only be 0, 51, 102, 153, 204, or 255.

The values 000000 and FFFFFF represent black and white, respectively.

16

Color Models (cont.)

17

Color Models (cont.) The CMY color model

Cyan, magenta, and yellow are the secondary colors of light Most devices that deposit colored pigments on paper, such as

color printers and copiers, require CMY data input or perform an RGB to CMY conversion internally.

The assumptions is that all color values have been normalized to range [0,1].

The CMYK color model In order to produce true black, a fourth color black is added

B

G

R

Y

M

C

1

1

1

Y

M

C

B

G

R

1

1

1

(6.2-1)

18

Color Models (cont.) The HSI Color Model

When humans view a color object, we describe it by its hue, saturation, and brightness.

Hue is a color attribute that describes a pure color. Saturation gives a measure of the degree to which a pure

color is diluted by white light. Brightness is a subjective descriptor that is practically

impossible to measure. ( 所以用 intensity 來取代brightness)

HSI color model decouples the intensity component from the color-carrying information (hue and saturation) in a color image.

19

Color Models (cont.) Conceptual relationships between the RGB and HIS

color models The intensity is along the line joining the vertices (0,0,0)

and (1,1,1). If we wanted to determine the intensity component of any

color point, we would simply pass a plane perpendicular to the intensity axis and containing the point.

The intersection of the plane with the intensity axis would give us a point with intensity value in the range [0,1].

The intensity axis joining the black and white vertices is vertical

20


Fig. 12(b) shows a plane defined by three points (black, white, and cyan)

All points contained in the plane segment defined by the intensity axis and the boundaries of the cube have the same hue. All colors generated by three colors lie in the triangle

defined by those colors. If two of those points are black and white and the third is a

color point, all points on the triangle would have the same hue.

By rotating the shaded plane about the vertical intensity axis, we would obtain different hues.

21


The HIS space is represented by a vertical intensity axis and the locus of color points that lie on planes perpendicular

Looking at the cube (Fig. 12) down its gray-scale axis, as shown in Fig. 6.13(a).

In this plane we see that the primary colors are separated by 120°.

The hue of the point is determined by an angle from some reference point. Usually an angle of 0° from the red

axis designates 0 hue, and the hue increases countercolockwise from there.

The saturation is the length of the vector from the origin to the point.

22

GBif

GBifH

360

),,min(3

1 BGRBGR

S

)(3

1BGRI

2/12

1_

2

1

cosBGBRGR

GRGR

Color Models (cont.): Converting colors from RGB to HSI The H component of each RGB

pixel is obtained by

with

The saturation component is given by

The intensity component is given by The RGB values have been normalized to

range [0,1] and that angle is measured withrespect to the red axis of the HSI space.

23

Color Models (cont.): Converting colors from HIS to RGB Given values of HIS in the interval [0,1], we can

find the corresponding RGB values in the same range.

The applicable equations depend on the values of H.

There are three sectors of interest, corresponding to the 120 。 intervals in the separation of primaries

24

Color Models (cont.) RG sector

When H is in this sector, the RGB components are given by

GB sector If the given value of H is in this sector, we first subtract

120° from it.

Then the RGB components are

BR sector If the given value of H is in this sector, we first subtract

240° from it.

)1( SIB

1200 H

240120 H

360240 H

)60cos(

cos1

H

HSIR )(3 BRIG

120HH

)1( SIR

240HH

)1( SIG

)60cos(

cos1

H

HSIG

)60cos(

cos1

H

HSIB

)(3 GRIB

)(3 BGIR

25


Fig. 6.8 影像的 Hue

Fig. 6.8 影像的 saturation

Fig. 6.8 影像的 intensity

Its most distinguishing feature is the discontinuity in value along 45 line in the front (red) plane of the cube.

26


Hue 的成分影像

saturation 的成分影像

intensity 的成分影像

RGB 影像

27


修改過的 hue成分影像修改過的 saturation

成分影像

修改過的 intensity成分影像

重建的 RGB 影像

28

Pseudocolor Image Processing Pseudocolor image processing consists of assigning

colors to gray values based on a specified criterion. The principal use of pseudocolor is for human

visualization and interpretation of gray-scale events in an images or sequence of images.

Intensity Slicing If an image is interpreted as a 3D function, the method can

be viewed as one of placing planes parallel to the coordinate plane of the image;

Each plan then “slices” the function in the area of intersection.

29

Pseudocolor Image Processing (cont.) Let [0, L-1] represent the gray scale Let level l0 represent black [f(x,y)=0] Level lL-1 represent white [f(x,y)=L-1] Suppose that P planes perpendicular to the intensity axis are

defined at levels l1, l2,…, lp

Assuming that 0<P<L-1 The P planes partition the gray scale into P+1 intervals, V1, V2,

…, VP+1

Gray-level to color assignments are made according to the relation

where ck is the color associated with the k-th intensity interval Vk.

kk Vf(x,y)cyxf if),(

30

Pseudocolor Image Processing (cont.) Fig. 6.18 shows an example of using a plane at f(x,y)=li to slice

the image function into two levels. If a different color is assigned to each side of the plane, any pixel

whose gray level is above the plane will be coded with one color, and any pixel below the plane will be coded with the other.

Levels that lie on the plane itself may be arbitrarily assigned one of the two colors.

The result is a two-color image whose relative appearance can be controlled by moving the slicing plane up and down the gray-level axis.

31

Pseudocolor Image Processing (cont.)Any input gray level is

assigned one of two colors, depending on whether it is above or below the value of li.

When more levels are used, the mapping function takes on a staircase form.

32

Pseudocolor Image Processing (cont.) Example 6.3 Intensity Slicing

單色的甲狀腺影像(monochrome image of the Picker Thyroid Phantom )

The result of intensity slicing this image into eight color regions.

33

Pseudocolor Image Processing (cont.) Example 6.3 Intensity Slicing (cont.)

Intensity slicing assumes a much more meaningful and useful role when subdivision of the gray scale is based on physical characteristics of the image.

Fig. 6.21(a) shows an X-ray image of a weld containing several cracks and porosities with graylevel of 255.

If the exact values of gray levels one is looking for are known, intensity slicing is a simple but powerful aid in visualization.

Cracks/porosities

34

Pseudocolor Image Processing (cont.) Example 6.4 Use of color to highlight rainfall levels

影像灰階對應平均月降雨量

指定色彩給灰階

色彩編碼後的影像放大南美洲

的色彩編碼影像

35

Pseudocolor Image Processing (cont.) Gray Level to Color Transformations

To perform three independent transformations on the gray level of any input pixel.

The three results are then fed separately into the red, green, and blue channels of a color television monitor.

These are transformations on the gray level values of an image and are not functions of position.

36

Pseudocolor Image Processing (cont.) Example 6.5 Fig. 6.24(a) shows two

monochrome images of luggage obtained from an airport X-ray scanning system.

The purpose of this example is to illustrate the use of gray level to color transformations to obtain various degrees of enhancement.

塑膠炸藥 (plastic explosive)

Ordinary materials

37

Pseudocolor Image Processing (cont.)

Fig 6.25 shows the transformation functions used.

These sinusoidal functions contain regions of relatively constant value around the peaks and regions that change rapidly near the valleys.

Changing the phase and frequency of each sinusoid can emphasize (in color) ranged in the gray scale.

If all three transformations have the same phase and frequency, the output image will be monochrome.

Fig. 6.24(b) was obtained with the transformation functions in Fig. 6.25 (a).

Fig. 6.24(c) was obtained with the transformation functions in Fig. 6.25 (b).

38

Pseudocolor Image Processing (cont.) Combine several monochrome images into a

single color composite. Usually used in Multispectral image processing Different sensors produce individual monochrome

images, each in a different spectral band.

39


Red component of an RGB image

Green component of an RGB image

Blue component of an RGB image

Near-infrared image

Green+Blue+Near-infrared image

Red+Green+Blue

40


Jupiter moon Io木星 Io 衛星影像

Bright red depicts material newly ejected from an active volcano

紅色的區域表示活火山新噴出的物質

Surrounding yellow materials are older

sulfur deposits黃色的區域表示硫磺

的沉積物質

41

Basic of Full-Color Image Processing Full-color image processing approached fall into two

major categories ： Process each component image individually and then form

a composite processed color image from the individually processed components.

Work with color pixels directly. Let c represent an arbitrary vector in RGB color

space:

B

G

R

c

c

c

c

B

G

R

),(

),(

),(

),(

),(

),(

),(

yxB

yxG

yxR

yxc

yxc

yxc

yxc

B

G

R

(6.4-1)

(6.4-2)

42

Basic of Full-Color Image Processing The results of individual color component processing are not

always equivalent to direct processing in color vector space. In order for per-color-component and vector-based processing

to be equivalent, two conditions have to be satisfied: The process has to be applicable to both vectors and scalars. The operations on each component of a vector must be independent

of the other components.

43

Color Transformation Color transformation deal with processing the components of a color

image within the context of a single color model. We model color transformations using the expression

where f(x,y) is a color input image, g(x,y) is the transformed color output image, and T is an operator on f over a spatial neighborhood of (x,y).

The pixel values here are triplets or quartets from the color space chosen to represent the images.

Color transformations

ri and si are variables denoting the color components of f(x,y)and g(x,y) at any point (x,y). n is the number of color components.{T1, T2, …, Tn} is a set of color mapping function that operate on ri to produce si.

n transformations, Ti, combine to implement the single transformation function, T, in Eq(6.5-1).

),(),( yxfTyxg

nirrrTs nii ,...,2,1),,...,,( 21

(6.5-1)

(6.5-2)

44

CMYK 成分，黑色代表 0 ，白色代表 1 。

Strawberries are composed of large amounts of magenta and yellow.

草莓由大量的紅色成分所組成。

Intensity 成分原始影像的單色呈現

Color Transformation (cont.)A bowl of strawberries and cup of coffee

45

Color Transformation (cont.) Suppose that we wish to modify the intensity of the image in

Fig. 6.30(a) using

where 0<k<1. In the HIS color space, this can be down with the simple

transformation

where s1=r1, s2=r2 。 Only HIS intensity component r3 is modified. In the RGB color space, three components must be

transformed:

The CMY space requires a similar set of linear transformations

),(),( yxkfyxg

33 krs

3,2,1 ikrs ii

3,2,11 ikkrs ii

46

Color Transformation (cont.) The result of applying any of the transformations

in Eq.(6.5-4)~ (6.5-6), using k=0.7

47

Color Complements The hues directly opposite one another on

the color circle of Fig. 6.32 are called complements.

Color complements are useful for enhancing detail that is embedded in dark regions of a color image.

48

Example 6.7 補色的轉換函數，其中飽和度 S的成分不變。

RGB 的補色轉換HSI 的補色轉換

Identical to the gray-scale negative transformation.

49

Color Slicing Color slicing

Highlighting a specific range of colors in an image is useful for separating objects from their surroundings.

The basic idea is either to ( 將 ROI 以外的色彩，映射到不重要的中性色彩。 ) Display the colors of interest so that they stand out from the

background Use the region defined by the colors as a mask for further processing

To map the colors outside some range of interest to a nonprominent neutral color. If the colors of interest are enclosed by a cube of width W and centered at a prototypical color with components (a1, a2, …, an) the necessary set of transformations is

Color Cube (hypercube)

otherwiser

Warif

s

i

ninjjj

i ,...,2,1,125.0

W 是立方體寬度，中心成分在(a1,a2,…,an)

50

Color Slicing (cont.)

If a sphere is used to specify the colors of interest, Eq. (6.5-7) becomes

otherwiser

niRarifs

i

n

jjj

i,..,2,1,5.0 2

0

2

1R0 是球體的半徑，中心成分在(a1,a2,…,an)

51

Example 6.8 An illustration of color slicingW=0.2549 ，中心在(0.6863, 0.1608, 0.1922)的 RGB cube

Radius=0.1765 ，中心在(0.6863, 0.1608, 0.1922)的 RGB sphere

52

Tone and Color Corrections

色調與色彩之修正 (Tone and color corrections) Device-independent color model

建立螢幕和輸出裝置以及其裝置之間的色彩範圍 Color management system (CMS)

選擇採用 CIE L*a*b* 模型，或是 CIELAB CIE L*a*b* 具有下列特性：

Colormetric Perceptually uniform Device independent

53

Tone and Color Corrections (cont.) L*a*b* color model

008856.0116/16787.7

008856.0

200*

500*

16116*

3

qq

qqqh

where

Z

Zh

Y

Yhb

Y

Yh

X

Xha

Y

YhL

WW

WW

W

Xw, YW, Zw 是白色的三色激勵值 ( 由圖 6.5 的 CIE 色調圖上 x=0.3127, y=0.3290 所定義 )

54

Tone and Color Corrections (cont.) 色調範圍 (tonal range) ，亦稱為 (key type)是指影像色彩強度的一般分布。 High-key

影像的大部分資訊集中於高 ( 或亮 ) 的強度 Low-key

影像的大部分資訊集中於低 ( 或暗 ) 的強度 Middle-key

影像的大部分資訊介於 high-key 和 low-key 之間

55

Example 6.9 Tonal transformations

56

Example 6.10 Color balancing

57

Histogram Processing

58

Smoothing and Sharpening Color Image Smoothing

The average of the RGB component vectors in the neighborhood is

對每個顏色分量進行 smooth

Smoothing by neighborhood averaging can be carried out on a per-color-plane basis.

xySyx

yxcK

yxc),(

,1

),(

xy

xy

xy

Syx

Syx

Syx

yxBK

yxGK

yxRK

yxc

,

,

,

,1

,1

,1

,

59

Example 6.12 Color image smoothing by neighborhood averaging

Original RGB image

Red component

image

Green component

image

Blue component

image

60

Example 6.12 Color image smoothing by neighborhood averaging (cont.)

Hue component

image

Saturation component

image

Intensity component

image

61

Example 6.12 Color image smoothing by neighborhood averaging (cont.)

Result of processing each RGB component

image

Image smoothing with 5x5 averaging mask

Result of processing Intensity

component image

Difference between the two results

62

Smoothing and Sharpening (cont.) Color Image Sharpening

Computing the Laplacian of each component image separately.

yxB

yxG

yxR

yxc

,

,

,

,2

2

2

2

63

Color Segmentation

Segmentation in HIS color Space Color is represented in the hue image. Saturation is used as a masking image to isolate

further regions of interest in the hue image. Intensity image is used less frequency for

segmentation of color image because it carries no color information.

64

Example 6.14 Segmentation in HIS spaceOriginal

imageHue image

Intensity image

Saturation image

對飽和影像取臨界值 ( 最大值的

10%) 所得的遮罩影像，將大於臨界值的像素點設為 1 ，其餘設為黑色。

遮罩影像和 Hue影像的乘積。

乘積影像的histogram 。

對乘積影像取臨界值 (90%) ，後所得之影像。

65

Color Segmentation (cont.) Segmentation in RGB Vector Space

The objective is to segment objects of a specified color range in an RGB image.

Let the average color be denoted by the RGB vector a. The objective of segmentation is to classify each RGB pixel

in a given image as having a color in the specified range or not.

222

2

1

,

BBGGRR

T

azazaz

azaz

azazD

66

Example 6.15 Color image segmentation in RGB space

67

Color Segmentation (cont.)

Color Edge Detection

68



69

Example 6.16 Edge detection in vector space

70

Example 6.16 Edge detection in vector space (cont.)

Red component 的gradient

Green component的 gradient

Blue component 的gradient

71

Noise in Color Image

72

Example 6.17 Illustration of the effects of converting noisy RGB images to HSI

73

Example 6.17 Illustration of the effects of converting noisy RGB images to HIS (cont.)

74

Example 6.17 Illustration of the effects of converting noisy RGB images to HIS (cont.)

75

Example 6.18 A color image compression example

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Chapter 6 Color Image Processing