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04/27/2304/27/23 Duong Anh Duc - Digital Image ProcessingDuong Anh Duc - Digital Image Processing 11
Digital Image Processing
Some Special TechniquesSome Special TechniquesDitheringDithering
04/27/2304/27/23 Duong Anh Duc - Digital Image ProcessingDuong Anh Duc - Digital Image Processing 22
DitheringDithering Dithering, also called Halftoning or Color Dithering, also called Halftoning or Color
Reduction, is the process of rendering an Reduction, is the process of rendering an image on a display device with fewer colors image on a display device with fewer colors than are in the image. (than are in the image. (Mateus Pins and Mateus Pins and Hermann HildHermann Hild) )
The number of different colors in an image or The number of different colors in an image or on a device is used called its Color Resolution. on a device is used called its Color Resolution.
04/27/2304/27/23 Duong Anh Duc - Digital Image ProcessingDuong Anh Duc - Digital Image Processing 33
DitheringDithering If the display device has a higher spatial resolution If the display device has a higher spatial resolution
than the image that you are trying to reproduce, it can than the image that you are trying to reproduce, it can show a very good image even if its color resolution is show a very good image even if its color resolution is less. This is what we will call 'dithering' and is the less. This is what we will call 'dithering' and is the subject of this work. subject of this work.
Dithering is a one-way operation. Dithering is a one-way operation. Once an image has been dithered, although it may look like Once an image has been dithered, although it may look like
a good reproduction of the original, information is a good reproduction of the original, information is permanently lost. permanently lost.
Many image processing functions fail on dithered images. Many image processing functions fail on dithered images.
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DitheringDithering
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DitheringDitheringGrey-scale and colour simulationGrey-scale and colour simulation
Dithering on a screen or printer is analogous to Dithering on a screen or printer is analogous to the half-toning techniques used in the print the half-toning techniques used in the print industry.industry.
A CRT can be considered to be a complex A CRT can be considered to be a complex colour “dithering” device with variable colour colour “dithering” device with variable colour intensity.intensity.
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DitheringDitheringGrey-scale and colour simulationGrey-scale and colour simulation
We need to display colour and grey-scale We need to display colour and grey-scale images on output devices that have a lower images on output devices that have a lower information-carrying capacity.information-carrying capacity.
Cheap printers are bi-level or CMYK - clearly Cheap printers are bi-level or CMYK - clearly we need to add colours/intensities to we need to add colours/intensities to approximate an image.approximate an image.
04/27/2304/27/23 Duong Anh Duc - Digital Image ProcessingDuong Anh Duc - Digital Image Processing 77
Dithering MethodsDithering Methods(Digital Halftoning)(Digital Halftoning)
Threshold dithering ordered dither stochastic dither dot diffusion ....
Error diffusion dithering Floyd-Steinberg Burkes Stucki Sierra Jarvis, Judice and Ninke Stevenson and Arce Stevenson and Arce ……
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Dithering in Printing IndustryDithering in Printing Industry
Newspapersblack ink on light paper, rasterization of theimages
enables also grey levels, equal pointdensity everywhere, variable size
Color printingevery primary color is rasterized
separately,different printing angles ensure unbiased results
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Simple shading techniquesSimple shading techniquesA series of examplesA series of examples
Original picture, half-toning Original picture, half-toning simulation by a non-PostScript simulation by a non-PostScript laser printer.laser printer.
The original image has an 8-The original image has an 8-bit grey scale palette.bit grey scale palette.
The laser printer has only got The laser printer has only got a 1-bit palette (ie bi-level, a 1-bit palette (ie bi-level, black and white) and must black and white) and must simulatesimulate the original shading. the original shading.
04/27/2304/27/23 Duong Anh Duc - Digital Image ProcessingDuong Anh Duc - Digital Image Processing 1010
Simple shading techniquesSimple shading techniquesAn exampleAn example
Bayer - Ordered DitheringBayer - Ordered Dithering This method uses a set of This method uses a set of
regular arrays of values, regular arrays of values, leading to a regular (and leading to a regular (and visually poor) output.visually poor) output.
This method creates abrupt This method creates abrupt changes between areas, changes between areas, changes that do not exist on changes that do not exist on the original. Such the original. Such artefactsartefacts are are not desirable.not desirable.
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Simple shading techniquesSimple shading techniquesAn exampleAn example
BurkesBurkes This method uses an error-This method uses an error-
distribution algorithm to distribution algorithm to minimise percieved errors.minimise percieved errors.
Changes in the average Changes in the average intensity vary quite smoothly, intensity vary quite smoothly, resolution permitting, leading resolution permitting, leading to a more acceptable image.to a more acceptable image.
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Simple shading techniquesSimple shading techniquesAn exampleAn example
Floyd-SteinbergFloyd-Steinberg FS dithering is popular and FS dithering is popular and
commonly used. It is commonly used. It is robust and quite general.robust and quite general.
FS dithering works best on FS dithering works best on images with few high-images with few high-contrast transitions.contrast transitions.
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Threshold DitheringThreshold 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
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Constant Threshold DitheringConstant Threshold Dithering
sample image threshold values result
(values between 0 and 9)corresponds to rounding
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Principle of DitheringPrinciple of Dithering
Available values a, b Missing value x between a and b shall
besimulated by mixing a-pixels and b-pixels
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Principle of DitheringPrinciple of Dithering
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Dithering a Uniform AreaDithering a Uniform Area
for a uniform area regular application ofthis patternwill producethis grey toneinterval borders
all grey levels in this intervalwill be mapped to 1/4
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Dithering a Uniform AreaDithering a Uniform Area
This can be done by using a different threshold for every pixel (using the interval borders)
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Threshold MatrixThreshold 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,n2–1] Value k corresponds to threshold value: 2k+1/2n2
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Dither Matrix ExampleDither Matrix Example
dither matrix threshold matrix
Value k corresponds to threshold value: 2k+1/2n2
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Threshold Matrix Dithering ExampleThreshold Matrix Dithering Example
sample image threshold values result
(values between 0 and 9)
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Generation of Threshold MatricesGeneration of Threshold Matrices
recursive method: 4 copies of smaller matrices
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Generation of Threshold MatricesGeneration of Threshold Matrices
Direct method: use of magic squaresexample
magic squares producefewer diagonal stripes
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Dithering between Grey LevelsDithering 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)
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Grey Level Dithering ExampleGrey Level Dithering Example
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Dot Diffusion DitheringDot Diffusion Dithering
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Stochastic Dithering?Stochastic Dithering?
Use of random numbers as threshold valuesexpectation value of total error = 0no regular artificial patterns possible
Unfortunately: very bad results!(due to bad distribution of random numbers)
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Forced Random Matrix DitheringForced 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: 300x300very good results!
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Error distribution algorithmsError distribution algorithmsFloyd-Steinberg (1975)Floyd-Steinberg (1975)
If an image has a pixel with a normalised value of If an image has a pixel with a normalised value of 0.5, ie half intensity, we cannot accurately 0.5, ie half intensity, we cannot accurately represent it with a black or white dot.represent it with a black or white dot.
However, we can However, we can rememberremember the error and feed it the error and feed it into the approximation calculation for the into the approximation calculation for the surrounding pixels.surrounding pixels.
The error value gets distributed locally and the The error value gets distributed locally and the eye reintegrates the values, “recreating” the grey eye reintegrates the values, “recreating” the grey scale.scale.
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Floyd-SteinbergFloyd-SteinbergDistribution WeightingDistribution Weighting
3/8 error
CurrentPixel
1/4 error
3/8 error
Next scan line of image
Current scan line of image
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DitheringDitheringSome drawbacksSome drawbacks
A dithered image is an image with less information in A dithered image is an image with less information in it than the original.it than the original.
Resolution and apparent colour content are a trade-Resolution and apparent colour content are a trade-off, particularly with thermal wax transfer printers etc.off, particularly with thermal wax transfer printers etc.
Accurate conversion between original images and Accurate conversion between original images and dithered images is generally one-way.dithered images is generally one-way.
Some dithering methods cause ugly banding on some Some dithering methods cause ugly banding on some images. Careful choice of dithering methods can images. Careful choice of dithering methods can minimise this problem.minimise this problem.
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Diffusion Direction VariationsDiffusion Direction Variations
to gain better results, the error is distributed toseveral neighbors (with weights)
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Error Diffusion Dithering ExampleError Diffusion Dithering Example
sample image threshold values result
(values between 0 and 9)corresponds to rounding
04/27/2304/27/23 Duong Anh Duc - Digital Image ProcessingDuong Anh Duc - Digital Image Processing 3434
Serpentine MethodSerpentine Method
Artificial stripes can be reduced drastically byprocessing the scanlines in serpentine order
no additional memory necessary
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Diffuse reflection of white light gives an object Diffuse reflection of white light gives an object its colour.its colour.
Perception of colour is, therefore, dependent Perception of colour is, therefore, dependent upon lighting.upon lighting.
Specular reflection has the colour content of Specular reflection has the colour content of the light source - what is the colour of a mirror?the light source - what is the colour of a mirror?
Colour is an everyday experience.Colour is an everyday experience.
Colour SystemsColour SystemsColour in the environmentColour in the environment
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Colour can be measured in terms of the Colour can be measured in terms of the frequency or wavelength of electromagnetic frequency or wavelength of electromagnetic radiation (light).radiation (light).
Some light sources have a narrow band of Some light sources have a narrow band of frequencies, eg lasers, but this is rare.frequencies, eg lasers, but this is rare.
Incandescent lighting has a broad range of Incandescent lighting has a broad range of frequencies.frequencies.
Sodium lamps have two bright frequencies.Sodium lamps have two bright frequencies.
Colour SystemsColour SystemsColour in the environmentColour in the environment
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Colour SystemsColour SystemsMeasuring ColourMeasuring Colour
Wavelength and intensity are measurable Wavelength and intensity are measurable quantities - intensity expresses the energy per quantities - intensity expresses the energy per unit area carried by the radiation.unit area carried by the radiation.
This is not an intuitive way of specifying colours!This is not an intuitive way of specifying colours!
400 480 500 520 580 600 650 700 720Light Wavelength (nanometres)
Violet Blue Cyan Green Yellow Orange Red
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Colour SystemsColour SystemsColour MatchingColour Matching
The eye cannot discern between a colour made The eye cannot discern between a colour made of a single wavelength and a “visually identical” of a single wavelength and a “visually identical” colour made of a mixture of wavelengths.colour made of a mixture of wavelengths.
This allows monitors (RGB) and magazines This allows monitors (RGB) and magazines (CMYK) to show the “same” pictures.(CMYK) to show the “same” pictures.
The eye is very sensitive to colour and can The eye is very sensitive to colour and can distinguish between approximately 300 000 distinguish between approximately 300 000 different different shadesshades of colour. of colour.
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Colour SystemsColour SystemsColour MatchingColour Matching
For practical purposes, the physical descrip-For practical purposes, the physical descrip-tion of colour is abandoned in favour of a more tion of colour is abandoned in favour of a more natural way of describing what we see.natural way of describing what we see.
Any colour shade can be matched by mixing Any colour shade can be matched by mixing three monochromatic primary colours, by three monochromatic primary colours, by definition.definition.
Colour matching is an important problem for Colour matching is an important problem for commercial users of print and video.commercial users of print and video.
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Colour SystemsColour SystemsPrimary ColoursPrimary Colours
In the real world we do not have pure, single-In the real world we do not have pure, single-wavelength colour sources to add - this means wavelength colour sources to add - this means that some colour shades are impossible to that some colour shades are impossible to match.match.
A way of specifying colours in a sensible way A way of specifying colours in a sensible way was developed by the CIE (Comission was developed by the CIE (Comission Internationale de L’Eclairage) in 1931.Internationale de L’Eclairage) in 1931.
The CIE chromaticity diagram is widely used.The CIE chromaticity diagram is widely used.
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Colour SystemsColour SystemsThe CIE Chromaticity DiagramThe CIE Chromaticity Diagram
The CIE diagram represents The CIE diagram represents all hue and saturation values, all hue and saturation values, with normalised intensity. with normalised intensity. The outer curve represents The outer curve represents all the visible 100% saturated all the visible 100% saturated or pure colours.or pure colours.
Cyan
Blue
RedWhite
Yellow
Green
Magenta
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Colour SystemsColour SystemsThe RGB colour cubeThe RGB colour cube
A system with three A system with three independent variables independent variables can be represented by a can be represented by a three-dimensional three-dimensional position.position.
The RGB colour cube The RGB colour cube represents all of the represents all of the colours that an RGB colours that an RGB monitor can create, in a monitor can create, in a non-normalized form.non-normalized form.
YellowGreen
White
Black
Cyan
Blue Magenta
Red(Greys)
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Colour SystemsColour SystemsThe RGB colour cubeThe RGB colour cube
A system with three A system with three independent variables independent variables can be represented by a can be represented by a three-dimensional three-dimensional position.position.
The RGB colour cube The RGB colour cube represents all of the represents all of the colours that an RGB colours that an RGB monitor can create, in a monitor can create, in a non-normalized form.non-normalized form.
Yellow
Green
WhiteCyan
Blue
Magenta
Red
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Colour SystemsColour SystemsThe HSV modelThe HSV model
Hue, Saturation, Value is a Hue, Saturation, Value is a more intuitive model.more intuitive model.
““Value” is brightness, Value” is brightness, constant value hexagons constant value hexagons lie parallel to the top lie parallel to the top surface.surface.
Grey shades run up the Grey shades run up the vertical axis, black at the vertical axis, black at the bottom and white at the bottom and white at the top.top. V=0
Green 120 Yellow 60
Cyan 180Red 0
Blue 240 Magenta 300
V=1
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Colour SystemsColour SystemsThe HLS modelThe HLS model
The Hue, Lightness, Saturation The Hue, Lightness, Saturation model was developed by model was developed by Tektronix.Tektronix.
HLS is similar to HSV but with a HLS is similar to HSV but with a double cone.double cone.
This and other models are This and other models are combinations of the CIE, RGB combinations of the CIE, RGB and HSV models.and HSV models.
Translations are always possible.Translations are always possible. L=0
Green 120
Yellow 180
Cyan 60
Red 240
L=1
Blue 0
Magenta 300
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ReferencesReferences
http://www.efg2.com/Lab/Library/http://www.efg2.com/Lab/Library/ImageProcessingImageProcessing/DHALF.TXT/DHALF.TXT - dither.txt – everything you ever - dither.txt – everything you ever wanted to know about dithering!wanted to know about dithering!
Computer Graphics, (C version) by D. Hearn and Computer Graphics, (C version) by D. Hearn and P. Baker:P. Baker:Section 4 of Chapter 15, Halftone Patterns and Section 4 of Chapter 15, Halftone Patterns and
Dithering TechniquesDithering TechniquesChapter 15, Colour Models and Colour Applications Chapter 15, Colour Models and Colour Applications
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Digital Image Processing
Some Special TechniquesSome Special TechniquesThinning (Lọc xương)Thinning (Lọc xương)
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ThinningThinning
Các pixel trên một ảnh có thể chia làm 2 loại:Các pixel trên một ảnh có thể chia làm 2 loại: Pixel nềnPixel nền Pixel thuộc một đối tượngPixel thuộc một đối tượngỞ đây ta chỉ quan tâm đến loại sau.Ở đây ta chỉ quan tâm đến loại sau.
Các pixel thuộc một đối tượng lại có thể chia Các pixel thuộc một đối tượng lại có thể chia làm 2 loại:làm 2 loại:
Điểm biênĐiểm biên Điểm bên trongĐiểm bên trong
Thinning là quá trình biến đổi để trên ảnh chỉ Thinning là quá trình biến đổi để trên ảnh chỉ còn các điểm biên và nền.còn các điểm biên và nền.
04/27/2304/27/23 Duong Anh Duc - Digital Image ProcessingDuong Anh Duc - Digital Image Processing 4949
ThinningThinning
ThinningThinning là quá trình loại bỏ các pixel phụ là quá trình loại bỏ các pixel phụ (dư thừa) để làm đối tượng trở nên đơn g(dư thừa) để làm đối tượng trở nên đơn giiản ản hơnhơn, ch, chỉỉ g gồmồm c cácác th thànhành ph phầnần m mảnhảnh, kh, khôông ng ccóó di diệnện t tích. ích.
Thinning rất giống với phép co: xóa liên tiếp Thinning rất giống với phép co: xóa liên tiếp các pixel dư thừa cho đến khi chỉ còn khung các pixel dư thừa cho đến khi chỉ còn khung xương đối tượng. xương đối tượng.
04/27/2304/27/23 Duong Anh Duc - Digital Image ProcessingDuong Anh Duc - Digital Image Processing 5050
ThinningThinning
ThinThinnning phải thỏa các tính chất cơ bản sau:ing phải thỏa các tính chất cơ bản sau: Đối tượng kết quả phải mảnh, có độ rộng 1 pixelĐối tượng kết quả phải mảnh, có độ rộng 1 pixel Các pixel tạo nên khung xương phải định vị gần Các pixel tạo nên khung xương phải định vị gần
tâm của mặt cắt đối tượng.tâm của mặt cắt đối tượng. Đảm bảo tính liên thông giống như đối tượng ban Đảm bảo tính liên thông giống như đối tượng ban
đầu.đầu.
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Thuật toán Zhang – SuenThuật toán Zhang – Suen
Tư tưởng cơ bản:Tư tưởng cơ bản: Việc giải quyết có xóa hay không xóa 1 pixel sẽ Việc giải quyết có xóa hay không xóa 1 pixel sẽ
chỉ phụ thuộc vào 8 pixel lân cận với nó.chỉ phụ thuộc vào 8 pixel lân cận với nó. Bốn quy tắc để quyết định xóa hay không Bốn quy tắc để quyết định xóa hay không
xóa 1 pixelxóa 1 pixel::
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Quy tắc 1Quy tắc 1
Pixel Pixel pp có thể được xóa nếu 1 < N8( có thể được xóa nếu 1 < N8(pp) < 7 với ) < 7 với N8(N8(pp) là số lân cận 8 của ) là số lân cận 8 của p.p.
Điều kiện N8(Điều kiện N8(pp) > 1 đảm bảo điểm đầu mút của đối ) > 1 đảm bảo điểm đầu mút của đối tượng không bị xóa, không bị bào mòn. tượng không bị xóa, không bị bào mòn.
Điều kiện N8(Điều kiện N8(pp)<7 đảm bảo đối tượng không bị đục )<7 đảm bảo đối tượng không bị đục lỗ (trong trường hợp N8(lỗ (trong trường hợp N8(pp)=8) hoặc bào mòn quá )=8) hoặc bào mòn quá mức (trong trường hợp N8(mức (trong trường hợp N8(pp)=7).)=7).
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Quy tắc 2:Quy tắc 2:
Pixel Pixel pp được xóa nếu chỉ số đếm (counting được xóa nếu chỉ số đếm (counting index hay crossing index - CI) của nó bằng 1. index hay crossing index - CI) của nó bằng 1.
Định nghĩa:Định nghĩa: Chỉ số đếm là số ngã rẽ từ pixel Chỉ số đếm là số ngã rẽ từ pixel đang xét.đang xét.
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Cách tính Cách tính crossing index - CIcrossing index - CI
Ví dụ:Ví dụ:
pp
CI=0
11
11 pp
11 11CI=1
11 11
11 pp
11 11CI=2
11 pp
11CI=2
11 11
11 pp
11CI=3
11 11
pp
11 11CI=4
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Quy tắc 3:Quy tắc 3:
Trong pha thứ nhất, ảnh sẽ được quét từ Trong pha thứ nhất, ảnh sẽ được quét từ trên xuống dưới và từ trái sang phải. trên xuống dưới và từ trái sang phải. MMột ột pixel chỉ được xóa nếu thỏa cả 2 điều kiệnpixel 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 1, 3, 5 là pixel nền. Có ít nhất 1 trong các lân cận 3, 5, 7 là pixel nền.Có ít nhất 1 trong các lân cận 3, 5, 7 là pixel nền.
11
77 pp 33
55
04/27/2304/27/23 Duong Anh Duc - Digital Image ProcessingDuong Anh Duc - Digital Image Processing 5656
Quy tắc 4:Quy tắc 4:
Trong pha thứ nhất, ảnh sẽ được quét từ Trong pha thứ nhất, ảnh sẽ được quét từ dưới lên trên và từ phải sang trái. dưới lên trên và từ phải sang trái. MMột pixel ột pixel chỉ được xóa nếu thỏa cả 2 điều kiệnchỉ 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 cận 1, 3, 7 là pixel nền. Có ít nhất 1 trong các lân cần 1, 5, 7 là pixel nền.Có ít nhất 1 trong các lân cần 1, 5, 7 là pixel nền.
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