Digital Image Processing: Some Special Techniques Dithering - Duong Anh Duc

Dithering, also called Halftoning or Color Reduction, is the process of rendering an image on a display device with fewer colors than are in the image. Digital Image Processing: Some Special Techniques Dithering presents about it.

Digital Image Processing

Some Special Techniques

Dithering

 Dithering, also called Halftoning or Color

Reduction, is the process of rendering an

image on a display device with fewer colors

than are in the image (Mateus Pins and

Hermann Hild)

 The number of different colors in an image or

on a device is used called its Color Resolution

 If the display device has a higher spatial resolution

than the image that you are trying to reproduce, it can show a very good image even if its color resolution is less This is what we will call 'dithering' and is the

subject of this work

 Dithering is a one-way operation

 Once an image has been dithered, although it may look like

a good reproduction of the original, information is

permanently lost

 Many image processing functions fail on dithered images

Dithering

Dithering Grey-scale and colour simulation

 Dithering on a screen or printer is analogous to the half-toning techniques used in the print

industry

 A CRT can be considered to be a complex

colour “dithering” device with variable colour

intensity

Dithering Grey-scale and colour simulation

 We need to display colour and grey-scale

images on output devices that have a lower information-carrying capacity

 Cheap printers are bi-level or CMYK - clearly

we need to add colours/intensities to

approximate an image

Dithering Methods (Digital Halftoning)

 Floyd-Steinberg

 Burkes

 Stucki

 Sierra

 Jarvis, Judice and Ninke

 Stevenson and Arce

 …

Dithering in Printing Industry

 every primary color is rasterized

separately,different printing angles ensure

unbiased results

Simple shading techniques

A series of examples

 Original picture, half-toning

simulation by a non-PostScript

laser printer.

 The original image has an

8-bit grey scale palette.

 The laser printer has only got

a 1-bit palette (ie bi-level,

black and white) and must

simulate the original shading.

Simple shading techniques

An example

 Bayer - Ordered Dithering

 This method uses a set of

regular arrays of values,

leading to a regular (and

visually poor) output.

 This method creates abrupt

changes between areas,

changes that do not exist on

the original Such artefacts

Simple shading techniques

An example

 Burkes

 This method uses an

error-distribution algorithm to

minimise percieved errors.

 Changes in the average

intensity vary quite smoothly,

resolution permitting, leading

to a more acceptable image.

Simple shading techniques

An example

 Floyd-Steinberg

 FS dithering is popular and

commonly used It is

robust and quite general

 FS dithering works best on

images with few

high-contrast transitions

Threshold Dithering

 every pixel is compared to a threshold t:

t can be:

 equal everywhere (e.g (b–a)/2,arbitrary value,

mean value, median, )

 location dependent (defined locally or globally)

p t a

p > t b

Constant Threshold Dithering

sample image threshold values result

(values between 0 and 9) corresponds to rounding

Principle of Dithering

 Available values a, b

 Missing value x between a and b shall

besimulated by mixing a-pixels and b-pixels

Principle of Dithering

Dithering a Uniform Area

 for a uniform area regular application of

Dithering a Uniform Area

 This can be done by using a different threshold for every pixel (using the interval borders)

Threshold Matrix

 Distances between interval borders are equal,

therefore it suffices to define the sequence of the

pixel values in the matrix:

 instead of only

 i.e for an nxn matrix: values [0,n 2–1]

 Value k corresponds to threshold value: 2k+1/2n2

Dither Matrix Example

dither matrix threshold matrix

Value k corresponds to threshold value: 2k+1/2n2

Threshold Matrix Dithering Example

sample image threshold values result

(values between 0 and 9)

Generation of Threshold Matrices

 recursive method: 4 copies of smaller matrices

Generation of Threshold Matrices

 Direct method: use of magic squares

example

magic squares produce fewer diagonal stripes

Dithering between Grey Levels

 threshold values have to lie between a and b:

calculation is done separately for every pixel

(not once for a dithering matrix)

Grey Level Dithering Example

Dot Diffusion Dithering

Stochastic Dithering?

values

expectation value of total error = 0

no regular artificial patterns possible

(due to bad distribution of random

numbers)

Forced Random Matrix Dithering

 Improved "random" matrices very good results

 Method: insert threshold values one by one into

matrix, always use the position farthest away from all previous points

 Repulsive force field:

 precalculate large threshold matrices: 300x300

very good results!

Error distribution algorithms

Floyd-Steinberg (1975)

 If an image has a pixel with a normalised value

of 0.5, ie half intensity, we cannot accurately

represent it with a black or white dot

 However, we can remember the error and feed

it into the approximation calculation for the

surrounding pixels

 The error value gets distributed locally and the eye reintegrates the values, “recreating” the

grey scale

Floyd-Steinberg Distribution Weighting

3/8 error

Current Pixel

1/4 error

3/8 error

Dithering Some drawbacks

 A dithered image is an image with less information in

it than the original.

 Resolution and apparent colour content are a off, particularly with thermal wax transfer printers etc.

trade- Accurate conversion between original images and

dithered images is generally one-way.

 Some dithering methods cause ugly banding on some images Careful choice of dithering methods can

minimise this problem.

Diffusion Direction Variations

 to gain better results, the error is distributed

toseveral neighbors (with weights)

Error Diffusion Dithering Example

sample image threshold values result

(values between 0 and 9) corresponds to rounding

Serpentine Method

 Artificial stripes can be reduced drastically

byprocessing the scanlines in serpentine order

no additional memory necessary

 Diffuse reflection of white light gives an object its colour.

 Perception of colour is, therefore, dependent upon lighting

 Specular reflection has the colour content of

the light source - what is the colour of a mirror?

 Colour is an everyday experience

Colour Systems Colour in the environment

 Colour can be measured in terms of the

frequency or wavelength of electromagnetic radiation (light)

 Some light sources have a narrow band of

frequencies, eg lasers, but this is rare

 Incandescent lighting has a broad range of

frequencies

 Sodium lamps have two bright frequencies

Colour Systems Colour in the environment

Colour Systems Measuring Colour

 Wavelength and intensity are measurable

quantities - intensity expresses the energy per unit area carried by the radiation

 This is not an intuitive way of specifying

colours!

Light Wavelength (nanometres)

Colour Systems Colour Matching

 The eye cannot discern between a colour

made of a single wavelength and a “visually identical” colour made of a mixture of

wavelengths

 This allows monitors (RGB) and magazines (CMYK) to show the “same” pictures

 The eye is very sensitive to colour and can

distinguish between approximately 300 000

Colour Systems Colour Matching

 For practical purposes, the physical

descrip-tion of colour is abandoned in favour of a more natural way of describing what we see

 Any colour shade can be matched by mixing three monochromatic primary colours, by

definition

 Colour matching is an important problem for

commercial users of print and video

Colour Systems Primary Colours

 In the real world we do not have pure, wavelength colour sources to add - this means that some colour shades are impossible to

Colour Systems The CIE Chromaticity Diagram

The CIE diagram represents all hue and saturation values, with normalised intensity

The outer curve represents all the visible 100% saturated

or pure colours.

Cyan

Blue

Red White

Yellow Green

Magenta

Colour Systems The RGB colour cube

 A system with three

independent variables

can be represented by

a three-dimensional

position.

 The RGB colour cube

represents all of the

colours that an RGB

monitor can create, in a

Yellow Green

White

Black Cyan

Blue Magenta

Red (Greys)

Colour Systems The RGB colour cube

 A system with three

independent variables

can be represented by

a three-dimensional

position.

 The RGB colour cube

represents all of the

colours that an RGB

monitor can create, in a

non-normalized form.

Yellow Green

White Cyan

Blue

Magenta

Red

Colour Systems The HSV model

 Hue, Saturation, Value is

a more intuitive model.

 “Value” is brightness,

constant value hexagons

lie parallel to the top

surface.

 Grey shades run up the

vertical axis, black at the

bottom and white at the V=0

Colour Systems The HLS model

 The Hue, Lightness, Saturation

model was developed by

Tektronix.

 HLS is similar to HSV but with a

double cone.

 This and other models are

combinations of the CIE, RGB

and HSV models.

 Translations are always possible. L=0

Green 120 Yellow 180

Cyan 60

Red 240

L=1

Blue 0 Magenta 300

 http://www.efg2.com/Lab/Library/ImageProcessing/DHALF.TXT

- dither.txt – everything you ever wanted to

know about dithering!

 Computer Graphics, (C version) by D Hearn

Digital Image Processing

Some Special Techniques Thinning (Lọc xương)

Ở đây ta chỉ quan tâm đến loại sau.

làm 2 loại:

còn các điểm biên và nền.

 Thinning là quá trình loại bỏ các pixel phụ

(dư thừa) để làm đối tượng trở nên đơn giản hơn, chỉ gồm các thành phần mảnh, không

có diện tích

 Thinning rất giống với phép co: xóa liên tiếp

các pixel dư thừa cho đến khi chỉ còn khung xương đối tượng

 Thinning phải thỏa các tính chất cơ bản sau:

 Đối tượng kết quả phải mảnh, có độ rộng 1 pixel

 Các pixel tạo nên khung xương phải định vị gần tâm của mặt cắt đối tượng.

 Đảm bảo tính liên thông giống như đối tượng ban đầu.

Thuật toán Zhang – Suen

 Việc giải quyết có xóa hay không xóa 1 pixel sẽ

chỉ phụ thuộc vào 8 pixel lân cận với nó.

xóa 1 pixel:

Quy tắc 1

 Pixel p có thể được xóa nếu 1 < N8(p) < 7 với

N8(p) là số lân cận 8 của p.

 Điều kiện N8(p) > 1 đảm bảo điểm đầu mút của đối

tượng không bị xóa, không bị bào mòn

 Điều kiện N8(p)<7 đảm bảo đối tượng không bị đục

lỗ (trong trường hợp N8(p)=8) hoặc bào mòn quá mức (trong trường hợp N8(p)=7).

Quy tắc 2:

 Pixel p được xóa nếu chỉ số đếm (counting

index hay crossing index - CI) của nó bằng 1

 Định nghĩa: Chỉ số đếm là số ngã rẽ từ pixel

đang xét

Quy tắc 3:

 Trong pha thứ nhất, ảnh sẽ được quét từ

trên xuống dưới và từ trái sang phải Một

pixel chỉ được xóa nếu thỏa cả 2 điều kiện:

 Có ít nhất 1 trong các lân cận 1, 3, 5 là pixel nền.

 Có ít nhất 1 trong các lân cận 3, 5, 7 là pixel nền.

1

7 p 3

5

Quy tắc 4:

 Trong pha thứ nhất, ảnh sẽ được quét từ

dưới lên trên và từ phải sang trái Một pixel chỉ được xóa nếu thỏa cả 2 điều kiện:

 Có ít nhất 1 trong các lân cận 1, 3, 7 là pixel nền.

 Có ít nhất 1 trong các lân cần 1, 5, 7 là pixel nền.

1

7 p 3