Binary Image

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Binary ImageBinary ImageProcessingProcessing

By:By:AminAmin KhajehKhajeh DjahromiDjahromi

Department of Electrical EngineeringUniversity of Texas at Arlington


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RoadmapRoadmap

Binary Image ProcessingBinary Image Processing

ThresholdingThresholding

Geometric PropertiesGeometric Properties

RunRun--Length EncodingLength Encoding

Binary AlgorithmsBinary Algorithms

Morphological OperatorsMorphological OperatorsApplicationsApplications


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What is Binary Image?What is Binary Image?

Binary images are images whose pixelsBinary images are images whose pixels

have only two possible intensity values.have only two possible intensity values.

Gray Level ImageBinary Image


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Why do we use binary images?Why do we use binary images?

Smaller memory requirementsSmaller memory requirements

Faster execution timeFaster execution time

Many techniques developed for theseMany techniques developed for these

systems are also applicable to visionsystems are also applicable to visionsystems which use gray scale imagessystems which use gray scale images

Less expensiveLess expensive


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Disadvantages of using binaryDisadvantages of using binary

imagesimages Limited applicationLimited application

Can not be extended to 3DCan not be extended to 3D

Losing internal details of objects (i.e. inLosing internal details of objects (i.e. in

inspection tasks)inspection tasks) difficult to control the contrast between thedifficult to control the contrast between the

background and the objects (i.e. inbackground and the objects (i.e. inmaterial handling and assembly tasks)material handling and assembly tasks)


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Some aspects of Binary VisionSome aspects of Binary Vision

SystemsSystems Formation of binary images :Formation of binary images : Binary isBinary is

obtained byobtained by thresholdingthresholding the gray scalethe gray scaleimage. Many cameras are designed toimage. Many cameras are designed to

performperform thresholdingthresholding in hardware.in hardware.

Geometric Properties:Geometric Properties: Size, Position,Size, Position,

Orientation and Projection.Orientation and Projection.

Topological PropertiesTopological Properties

Object recognition in binary imagesObject recognition in binary images


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SegmentationSegmentation

Segmentation:Segmentation: The partitioning of anThe partitioning of an

image into regions is called segmentationimage into regions is called segmentation


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ThresholdingThresholding

ThresholdingThresholding:: Is a method to convert aIs a method to convert a

Gray Scale Image into a Binary Image, soGray Scale Image into a Binary Image, sothat objects of interest are separated fromthat objects of interest are separated from

the background.the background.


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Example ofExample ofThresholdingThresholding

OriginalBinary (Threshold =140)


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Importance of objectImportance of object--backgroundbackground

separationseparationForForthresholdingthresholding to be effective in objectto be effective in object--

background separation, it is necessarybackground separation, it is necessarythat the objects and background havethat the objects and background have

sufficient contrast and that we know thesufficient contrast and that we know the

intensity levels of either the objects or theintensity levels of either the objects or the

background. In a fixedbackground. In a fixed thresholdingthresholding

scheme these intensity characteristicsscheme these intensity characteristicsdetermine the value of threshold.determine the value of threshold.


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Some Types ofSome Types ofThresholdingThresholding

FixedFixed ThresholdingThresholding

HistogramHistogram--derived Thresholdsderived Thresholds

IsodataIsodata algorithmalgorithm

Background Symmetry algorithmBackground Symmetry algorithm Triangular algorithmTriangular algorithm


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Geometric propertiesGeometric properties

SizeSize

PositionPosition

OrientationOrientation

ProjectionProjection


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SizeSize

SizeSize:: summation of allsummation of allpixel valuespixel values or theor the

number of pixels of thenumber of pixels of the

object.object.

00 00 00 0000 11 11 00

00 11 11 00

00 00 00 00

Size = 4


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PositionPosition:: The center of the area of the object. In order toThe center of the area of the object. In order tocalculate the position of the object we need to calculate the ficalculate the position of the object we need to calculate the firstrst--

order moments.order moments.

OrientationOrientation:: The way an object is situated in the image. ForThe way an object is situated in the image. Forsome shapes (such as circle), orientation is not unique and tosome shapes (such as circle), orientation is not unique and todefine unique orientation an object must be elongated.define unique orientation an object must be elongated.

ProjectionProjection::

1.1. Horizontal projectionHorizontal projection2.2. Vertical projectionVertical projection

3.3. Diagonal projectionDiagonal projection


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RunRun--length Encoding (RLE)length Encoding (RLE)

Compact representation of a binary imageCompact representation of a binary image

Used for image transmissionUsed for image transmission Some properties, such as the area,Some properties, such as the area,

projection of the objects, may be directlyprojection of the objects, may be directlycomputed from their runcomputed from their run--length codes.length codes.

Greater compression achieved for longerGreater compression achieved for longerand more frequent runsand more frequent runs

Widely used for binary images.Widely used for binary images.


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General example for RLEGeneral example for RLE

AAAAABBBBBAAAAABBBBB require 10 bytes to storerequire 10 bytes to store

Run Counts :Run Counts : 5 55 5 Run Value :Run Value : A BA B

RLE code,RLE code, 5A5B5A5B RLE require only 4 bytesRLE require only 4 bytes

Compression ratio : 10/4=2.5Compression ratio : 10/4=2.5


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Another example of RLEAnother example of RLE

Input :Input : DDDDBBBBGVVVVVVDDDDBBBBGVVVVVV

RLE codes:RLE codes: 4D4B1G6V4D4B1G6V RLE Packet : 8 bytesRLE Packet : 8 bytes

Compression ratio : 15/8Compression ratio : 15/8


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Two approaches for RLETwo approaches for RLE

1.1. Using start position and length of 1s forUsing start position and length of 1s for

each row.each row.

2.2. Using length of runs, starting with theUsing length of runs, starting with thelength of the 1 run for each row.length of the 1 run for each row.


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Example for approach 1Example for approach 1

11 11 11 11 00 00 00 11 11 11 11 11 11 11 00 00 0000 00 00 11 11 11 11 11 00 00 00 00 00 00 00 11 11

Start position and length of 1 runs: (1,4) (8,7)

(4,5) (16,2)


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Binary AlgorithmsBinary Algorithms

Before discussing Binary Algorithms, we first need to defineBefore discussing Binary Algorithms, we first need to definesome related terms.some related terms.

NeighborsNeighbors PathPath

ForegroundForeground

BackgroundBackground

ConnectivityConnectivity

Connected ComponentsConnected Components

BoundaryBoundary

InteriorInterior

SurroundsSurrounds


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NeighborhoodNeighborhood

A pixel has a common boundary with fourA pixel has a common boundary with four

pixels and shares a corner with fourpixels and shares a corner with fouradditional pixels.additional pixels.

44--neighbors: Two pixels areneighbors: Two pixels are 44--neighborsneighborsififthey share a common boundary.they share a common boundary.

88--neighbors: Two pixels areneighbors: Two pixels are 88--neighborsneighborsifif

they share at least one corner.they share at least one corner.

E l fE l f 44 i hbi hb dd 88 i hbi hb


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Examples ofExamples of44--neighborsneighborsandand 88--neighborsneighbors

(a) 4-neighbors, (b) 8-neighbors


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PathPath

A path from the pixel at [A path from the pixel at [ii0,j00,j0 ] is a] is a

sequence of pixel indicessequence of pixel indices[[ii00,j,j00],[],[ii11,j,j11],],[[iinn,j,jnn] such that the pixel at] such that the pixel at[[iikk,j,jkk] is neighbor of the pixel at [] is neighbor of the pixel at [iik+1k+1,j,jk+1k+1] for] for

allall kkwithwith 00


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Examples of 4Examples of 4--path andpath and

88--pathpath

(a) 4-path (b) 8-path

F d B k d dF d B k d d


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Foreground, Background andForeground, Background and

HolesHoles Foreground: The set of all 1 pixels in anForeground: The set of all 1 pixels in an

image is called theimage is called the foregroundforegroundand isand isdenoted bydenoted by SS

Background: The set of all connectedBackground: The set of all connected

components of complement ofcomponents of complement ofSS thatthathave points on the border of an image ishave points on the border of an image iscalled the background.called the background.

All the other components of complementAll the other components of complementofofSS are calledare called holes.holes.

E l f f d dE l f f d d


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Example of foreground andExample of foreground and

backgroundbackgroundConsider the below picture:

11

11 11

11

If we consider 4-connectedness for both foreground and background, there are four

Objects that are 1 pixel in size and there is no hole.

But,if we use 8-connectedness, then there is one object and no hole.

So

to avoid this awkward situations, if we use 8-connectedness for foreground, then

4-connecteness should be used for background.


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ConnectivityConnectivity

A pixelA pixel pp S is said to beS is said to be connectedconnected toto

qq

S if there is a path fromS if there is a path from pptoto qqconsisting entirely of pixels of S.consisting entirely of pixels of S.

For any three pixelsFor any three pixels p,qp,qand r in S, we have:and r in S, we have:

1.1. PixelPixel ppis connected tois connected to p (p (reflexivity).reflexivity).

2.2. IfIfppis connected tois connected to qq, then q is, then q is

connected to p (connected to p (commutativitycommutativity).).3.3. IfIfppis connected tois connected to qqandand qqis connectedis connected

toto rr, then, then ppis connected tois connected to rr(transitivity).(transitivity).


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Example of connectivityExample of connectivity

Two connected components based on 4-connectivity


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Boundary, Interior and surroundsBoundary, Interior and surrounds

Boundary: The boundary of S is the set ofBoundary: The boundary of S is the set of

pixels of S that have 4pixels of S that have 4--neighbors inneighbors in SbarSbar..The boundary is usually denoted by S` .The boundary is usually denoted by S` .

Interior: The interior is the set of pixels ofInterior: The interior is the set of pixels of

S that are not in itS that are not in its boundary. The interiors boundary. The interiorof S is (Sof S is (S--S`).S`).

Surrounds: T surrounds region S, if any 4Surrounds: T surrounds region S, if any 4--path from any points of S to the border ofpath from any points of S to the border ofpicture must intersect T.picture must intersect T.

Example of Boundary Interior andExample of Boundary Interior and


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Example of Boundary, Interior andExample of Boundary, Interior and

surroundssurrounds

Black: boundary pixels

Gray: interior pixelsWhite: surrounds pixels

Original image


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Components LabelingComponents Labeling

To find connected components in anTo find connected components in an

image. The points in a connectedimage. The points in a connectedcomponents form a region that representcomponents form a region that represent

an object.an object.

Require the characteristics of theRequire the characteristics of the

components (size, position, orientationcomponents (size, position, orientation

andand ))


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Example of Component LabelingExample of Component Labeling

Original image Its connected components

Two algorithm for ComponentTwo algorithm for Component


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Two algorithm for ComponentTwo algorithm for Component

LabelingLabeling11-- Recursive algorithmRecursive algorithm

Rarely used on generalRarely used on general--purpose computerspurpose computers Commonly used on parallel machinesCommonly used on parallel machines

22-- Sequential algorithmSequential algorithm

Usually require two passes over the imageUsually require two passes over the image

Works with only two rows of an image at a timeWorks with only two rows of an image at a time

so there is no need to bring the whole imageso there is no need to bring the whole imageinto memoryinto memory


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Recursive algorithmRecursive algorithm

1.1. Scan the image to find an unlabeled 1Scan the image to find an unlabeled 1

pixel and assign it a new label L.pixel and assign it a new label L.2.2. Recursively assign a label L to all itRecursively assign a label L to all its 1s 1

neighbors.neighbors.

3.3. Stop if there are no more unlabeled 1Stop if there are no more unlabeled 1

pixel.pixel.

4.4. Go to step 1.Go to step 1.


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Sequential algorithmSequential algorithm

11-- Scan the image left to right, top to bottomScan the image left to right, top to bottom

22-- If this pixel is oneIf this pixel is one(a) if only one of its upper and left neighbors has a label,

then copy the label

(b) If both have the same label, then copy the label.(c) If both have different labels, then copy the uppers

label and enter the labels in the equivalence table

as equivalent labels(d) Otherwise assign a new label to this pixel and enter

this label in the equivalence table.


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3- If there are more pixels to consider, then go tostep 2.

4- Find the lowest label for each equivalent set inthe equivalence table.

5- Scan the picture. Replace each label by thelowest label in its equivalent table.


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Example of Component LabelingExample of Component Labeling

S f


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Size filteringSize filtering

If we know that objects of interest are ofIf we know that objects of interest are of

size greater than Tsize greater than T0 ,0 , then we can use sizethen we can use sizefilter to remove noise after componentfilter to remove noise after component

labeling. In this case all components belowlabeling. In this case all components below

TT00 in size are removed by changing thein size are removed by changing thecorresponding pixels to 0.corresponding pixels to 0.

E l f i filt i


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Example of size filteringExample of size filtering

Original image ( noisy letter i ) size filtered image T=3

E l bE l b


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Euler numberEuler number

E (Euler No.) used as a feature of anE (Euler No.) used as a feature of an

object.object. E= CE= C HH

Where C = number of connectedWhere C = number of connectedcomponents (objects) and H = number ofcomponents (objects) and H = number of

Holes.Holes.

E is invariant to translation, rotation andE is invariant to translation, rotation and

scaling. (fixed feature of an object)scaling. (fixed feature of an object)

E l f E l bE l f E l b


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Example of Euler numberExample of Euler number

For this image:For this image:

C (number of objects)=?C (number of objects)=?H (number of holes) =?H (number of holes) =?

E=CE=C--H = ?H = ?

C=1 !!!C=1 !!!

H=3 !!!H=3 !!!

E=E= --22

Di tDi t


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Distance measureDistance measure

1.1. EuclideanEuclidean

2.2. CityCity--blockblock3.3. ChessboardChessboard

The cityThe city--block and chessboard measureblock and chessboard measureare preferred over Euclidean due to theirare preferred over Euclidean due to theirsimplicity of calculation.simplicity of calculation.

Euclidean distance is closest to theEuclidean distance is closest to thecontinue case, but it is computationallycontinue case, but it is computationallythe most expensive.the most expensive.

Di t t fDi t t f


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Distance transformDistance transform

Representing an image in terms ofRepresenting an image in terms of

distance.distance. It is useful in character recognition.It is useful in character recognition.

It can calculated by using a parallelIt can calculated by using a paralleliterative algorithmiterative algorithm

Distance MeasureDistance Measure


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s a ce easu e

--EuclideanEuclidean

The Euclidean distance is the straight lineThe Euclidean distance is the straight line

between two pixels.between two pixels.



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--CityblockCityblock

Measure the path between the pixels based on aMeasure the path between the pixels based on a

44--connected neighborhood.connected neighborhood.

Pixels whose edges touch are 1 unit apart.Pixels whose edges touch are 1 unit apart.

PixelsPixels diagnallydiagnally touching are 2 units apart.touching are 2 units apart.



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--ChessboardChessboard

Measure the path between the pixels based onMeasure the path between the pixels based on

an 8an 8--connected neighborhood.connected neighborhood.

Pixels whose edges or corners touch are 1 unitPixels whose edges or corners touch are 1 unit

apart.apart.

Medial Axis/Medial Axis/ SkeletonizationSkeletonization


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Medial Axis/Medial Axis/ SkeletonizationSkeletonization

Used to reduce foreground regions in a binary

image to a skeletal remnant that largely

preserves the extent and connectivity of the

original region while throwing away most of the

original foreground pixels. Methods of skeletonization:

Thinning

Calculate distance transformof the image -theskeleton then lies along the singularities(i.e. creasesor curvature discontinuities) in the distance transform.

ExampleExample


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ExampleExample

Skeletonization

ThinningThinning


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ThinningThinning

Thinning is an image processing operationThinning is an image processing operation

in which binaryin which binary--valued image regions arevalued image regions arereduced to lines that approximate theirreduced to lines that approximate their

center lines.center lines.

Also called asAlso called as skeletonskeleton ororcorecore

Reduce image components to theirReduce image components to their

essential informationessential information

Thinning requirementsThinning requirements


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Thinning requirementsThinning requirements

1.1. Connected image regions must thin toConnected image regions must thin toconnected line structures.connected line structures.

2.2. The thinned result should be minimally 8The thinned result should be minimally 8--connected.connected.

3.3. ApproximateApproximate endlineendline location should belocation should bemaintained.maintained.

4.4. The thinning results should approximate theThe thinning results should approximate the

medial lines.medial lines.5.5. Short branches caused by thinning should beShort branches caused by thinning should be

minimized.minimized.

Example of ThinningExample of Thinning


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Example of ThinningExample of Thinning

Threshold = 60

Expanding and shrinkingExpanding and shrinking


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Expanding and shrinkingExpanding and shrinking

Expanding : Change a pixel from 0 to 1 ifExpanding : Change a pixel from 0 to 1 if

any neighbors of the pixel are 1.any neighbors of the pixel are 1. Shrinking : Change a pixel from 1 to 0 ifShrinking : Change a pixel from 1 to 0 if

any neighbors of the pixel are 0.any neighbors of the pixel are 0.

According to the above definition,According to the above definition,

Shrinking may be consider as expandingShrinking may be consider as expanding

the background.the background.

Properties of Shrinking andProperties of Shrinking and


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ExpandingExpanding Expanding followed by Shrinking can beExpanding followed by Shrinking can be

used for filling undesirable holes.used for filling undesirable holes. Shrinking followed by Expanding can beShrinking followed by Expanding can be

used for removing isolated noise pixels.used for removing isolated noise pixels.

Expanding and Shrinking can be used toExpanding and Shrinking can be used to

determine isolated components anddetermine isolated components and

clusters.clusters.

Example of Shrinking andExample of Shrinking and


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ExpandingExpanding

An example of expanding and shrinking operations on the letter s

Left: the original image Middle: Expanded image Right: Shrunken


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References (books)References (books)


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Machine VisionMachine Vision ((RameshRamesh Jain,Jain, RangacharRangacharKasturiKasturi, Brian G., Brian G.SchunckSchunck))

Automated Visual InspectionAutomated Visual Inspection (B. G. Batchelor, D. A.(B. G. Batchelor, D. A.Hill, and D. C. Hodgson )Hill, and D. C. Hodgson )

Intelligent Image Processing in PrologIntelligent Image Processing in Prolog (B. G.(B. G.Batchelor )Batchelor )

References (Web)References (Web)


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http://bruce.cs.cf.ac.uk/bruce/Machine_vision_tutorial/Binhttp://bruce.cs.cf.ac.uk/bruce/Machine_vision_tutorial/Bin

ary_image_processing.htmlary_image_processing.html

University of North Dakota, Department of ComputerScience, computer vision website

http://www.machinevisiononline.org/public/articles/archiv

edetails.cfm?id=1396 Computer Engineering Department, Ko University

(course website)(course website)
http://bruce.cs.cf.ac.uk/bruce/Machine_vision_tutorial/Binary_image_processing.htmlhttp://bruce.cs.cf.ac.uk/bruce/Machine_vision_tutorial/Binary_image_processing.htmlhttp://bruce.cs.cf.ac.uk/bruce/Machine_vision_tutorial/Binary_image_processing.htmlhttp://bruce.cs.cf.ac.uk/bruce/Machine_vision_tutorial/Binary_image_processing.htmlhttp://www.machinevisiononline.org/public/articles/archivedetails.cfm?id=1396http://www.machinevisiononline.org/public/articles/archivedetails.cfm?id=1396http://eng.ku.edu.tr/academic/computer/computer.htmlhttp://www.ku.edu.tr/http://www.ku.edu.tr/http://eng.ku.edu.tr/academic/computer/computer.htmlhttp://www.machinevisiononline.org/public/articles/archivedetails.cfm?id=1396http://www.machinevisiononline.org/public/articles/archivedetails.cfm?id=1396http://bruce.cs.cf.ac.uk/bruce/Machine_vision_tutorial/Binary_image_processing.htmlhttp://bruce.cs.cf.ac.uk/bruce/Machine_vision_tutorial/Binary_image_processing.html

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