Segmentation - Computer Science & Eyiannisr/590/2018/Lectures/08-Segmentation.pdf · •...
Transcript of Segmentation - Computer Science & Eyiannisr/590/2018/Lectures/08-Segmentation.pdf · •...
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Ioannis Rekleitis
Segmentation
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MorphologicalSkeleton• Skeleton(De+inedbycentersofmaximaldisks):
• Applications:anabstractshaperepresentationforhighlevelimageunderstanding,e.g.OpticalCharacterRecognition(OCR)
If a point Z belongs to the skeleton of A, we can find a maximal disk that entirely lies in A and touches the boundary of A at no less than two positions.
CSCE 590: Introduction to Image Processing 2 Slides courtesy of Prof. Yan Tong
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MorphologicalSkeleton
𝑆↓𝑘 (𝐴)=(𝐴⊝𝑘𝐵)−(𝐴⊝𝑘𝐵)∘𝐵
𝐾=𝑚𝑎𝑥{𝑘|(𝐴⊝𝑘𝐵)≠∅}
𝐴=⋃𝑘=0↑𝐾▒(𝑆↓𝑘 (𝐴)⨁𝑘𝐵) Reconstruct A from its skeleton
The kth erosion
CSCE 590: Introduction to Image Processing 3 Slides courtesy of Prof. Yan Tong
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Examples
http://homepages.inf.ed.ac.uk/rbf/HIPR2/skeleton.htm
Potential issues with skeleton?
Maragos and Schafer, “Morphological Skeleton Representation and Coding of Binary Images”, IEEE Trans. on Acoustics, Speech, and Signal Processing, Vol. 34, No. 5, 1986.
Sensitive to noise
CSCE 590: Introduction to Image Processing 4 Slides courtesy of Prof. Yan Tong
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ImageSegmenta6on
Microsoft multiclass segmentation data set
nRRRR ,...,, subregions into partitions that processA 21
CSCE 590: Introduction to Image Processing 5 Slides courtesy of Prof. Yan Tong
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ImageSegmenta6on–Applica6ons
• Objectlocalization• Objectrecognition• Speciallyimportantformedicalimaging
CSCE 590: Introduction to Image Processing 6 Slides courtesy of Prof. Yan Tong
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BriefReviewofConnec6vity
• Path from p to q: a sequence of distinct pixels with coordinates
Starting point p ending point q
• p and q are connected: if there is a path from p to q in S • Connected component: all the pixels in S connected to p • Connected set: S has only one connected component • R is a region if R is a connected set • Ri and Rj are adjacent if is a connected set
adjacent
ji RR ∪
CSCE 590: Introduction to Image Processing 7 Slides courtesy of Prof. Yan Tong
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Image Segmentation
jiji
i
ji
i
n
ii
RRFALSERRQTRUERQ
jiRR,...,ni,R
RR
and regionsadjacent for )( (e))( (d)
, (c)1set connecteda is (b)
(a)1
=∪
=
≠∀=∩
=
==
φ
∪
Two categories based on intensity properties: • Discontinuity – edge-based algorithms • Similarity – region-based algorithms
⋃𝑖=1↑𝑛▒𝑅↓𝑖 =𝑅
CSCE 590: Introduction to Image Processing 8 Slides courtesy of Prof. Yan Tong
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Edge-based and Region-based Segmentation
CSCE 590: Introduction to Image Processing 9 Slides courtesy of Prof. Yan Tong
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Edge-basedSegmenta6on
• Thresholdingisrequiredtogetedgepixelsandrealizeedge-basedsegmentation
• Boundarydetection(edgelinking)isstillahotresearchtopicinimageprocessingandcomputervision
• Incorporatedomainknowledge:• Psychologyrulesontheboundary:smooth,convex,symmetry,closed,complete,etc
• Templateshapeinformation:hand,stomach,lip,etc• Appearanceinformation:region-basedtexture,intensity/color,etc.
CSCE 590: Introduction to Image Processing 10 Slides courtesy of Prof. Yan Tong
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Edge-based Segmentation -- Intensity Thresholding
⎩⎨⎧
≤
>=
TyxfTyxf
yxg),( if0),( if1
),(• AconstantT-globalthresholding• AvariableT-local/regionalthresholding;adaptivethresholding• MultipleT-multiplethresholding
Object/backgroundsegmentation:
CSCE 590: Introduction to Image Processing 11 Slides courtesy of Prof. Yan Tong
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Key Factors Affect Thresholding
• Separation between peaks • Noise level • Relative sizes of objects and background • Uniformity of the illumination source • Uniformity of the reflectance of the image
CSCE 590: Introduction to Image Processing 12 Slides courtesy of Prof. Yan Tong
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The Role of Noise in Image Thresholding
CSCE 590: Introduction to Image Processing 13 Slides courtesy of Prof. Yan Tong
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The Role of Illumination in Thresholding
CSCE 590: Introduction to Image Processing 14 Slides courtesy of Prof. Yan Tong
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HowtoPicktheThreshold
1. Selectaninitialestimatefortheglobalthreshold,T.
2. SegmenttheimageusingTbyproducingtwogroupsofpixels
3. Computethemeanofthesetwogroupsofpixels,saym1andm2.
4. UpdatethethresholdT=(m1+m2)/25. RepeatSteps2through4untilconvergence
T m1 m2 CSCE 590: Introduction to Image Processing 15 Slides courtesy of Prof. Yan Tong
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HowtoPicktheThreshold
1. Selectaninitialestimatefortheglobalthreshold,T.
2. SegmenttheimageusingTbyproducingtwogroupsofpixels
3. Computethemeanofthesetwogroupsofpixels,saym1andm2.
4. UpdatethethresholdT=(m1+m2)/25. RepeatSteps2through4untilconvergence
m1 m2 T CSCE 590: Introduction to Image Processing 16 Slides courtesy of Prof. Yan Tong
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An Example
CSCE 590: Introduction to Image Processing 17 Slides courtesy of Prof. Yan Tong
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Image Segmentation
jiji
i
ji
i
n
ii
RRFALSERRQTRUERQ
jiRR,...,ni,R
RR
and regionsadjacent for )( (e))( (d)
, (c)1set connecteda is (b)
(a)1
=∪
=
≠∀=∩
=
==
φ
∪
Two categories based on intensity properties: • Discontinuity – edge-based algorithms • Similarity – region-based algorithms
⋃𝑖=1↑𝑛▒𝑅↓𝑖 =𝑅
CSCE 590: Introduction to Image Processing 18 Slides courtesy of Prof. Yan Tong
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Region-BasedSegmenta6on
• Regiongrowing• Regionsplittingandmerging
CSCE 590: Introduction to Image Processing 19 Slides courtesy of Prof. Yan Tong
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RegionGrowingAlgorithm
- Aprocedurethatgroupspixelsorsubregionsintolargerregionsbasedonprede+inedcriteriaforgrowth
- Startwithasetof“seed”pointsandgrowregionsbyappendingneighboringpixelsthatsatisfythegivencriteria- Connectivity- Stoppingrules
- Localcriteria:intensityvalues,textures,color- Priorknowledge:sizeandshapeoftheobject
CSCE 590: Introduction to Image Processing 20 Slides courtesy of Prof. Yan Tong
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An Example
𝑄={█𝑇𝑟𝑢𝑒&𝑖𝑓 |𝐼↓𝑠𝑒𝑒𝑑 −𝐼(𝑥,𝑦)|≤𝑇@𝐹𝑎𝑙𝑠𝑒&𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
CSCE 590: Introduction to Image Processing 21 Slides courtesy of Prof. Yan Tong
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Region-Splitting and Merging Algorithm
Step1: Keep splitting the region while and Step 2: Merge the subregions while
FALSERQ i =)( SizeRi min>
TRUERRQ ji =∪ )(
CSCE 590: Introduction to Image Processing 22 Slides courtesy of Prof. Yan Tong
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An Example
⎩⎨⎧ <<>
=otherwiseFALSE
bmaifTRUEQ
0&σ
Extract the outer ring
CSCE 590: Introduction to Image Processing 23 Slides courtesy of Prof. Yan Tong
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AdvancedApproachesforImageSegmenta6on
• General-purposeimagesegmentationisfarfromwellsolved
• Itisstillaresearchproblemthatisbeinginvestigatedbymanyresearchers
• ImagesegmentationbyK-meansclustering• ImagesegmentationwithGraphicModels(MRF,CRF,etc)
• SemanticSegmentationwithDeepLearning• http://blog.qure.ai/notes/semantic-segmentation-deep-learning-review
CSCE 590: Introduction to Image Processing 24 Slides courtesy of Prof. Yan Tong
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MorphologicalImageProcessing–TechniquestoImproveImageSegmenta6on
• Objective:Extractimagecomponentsforrepresentationanddescriptionofregionshapeincluding• Boundaries• Skeletons• Convexhull
• Applications:• Edgedetection• Blob/connectedcomponentdetection
CSCE 590: Introduction to Image Processing 25 Slides courtesy of Prof. Yan Tong
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BasicConcepts• Union,intersection,complement,difference• Setre+lection• Settranslation--movethecenter/
originofBbyzpixels
• Structureelements(SEs):smallsets/subimagesusedinmorphology
{ }BB z ∈+== bzbcc ,|)(
{ }BbbwwB ∈−== ,|ˆ
reflection
translation 2D
SEs
SEs for images
Blackdotsarecenters/originsofSE
CSCE 590: Introduction to Image Processing 26 Slides courtesy of Prof. Yan Tong
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AnExampleofMorphology• CreateanewsetbyrunningBoverAsothattheoriginofBvisitseveryelementofA.
• Anexampleoferosion:IfBiscompletelycontainedinAforeachoperation,thenewelementisamemberofthenewset.
The shaded cell belongs to A/B
Erosion result CSCE 590: Introduction to Image Processing 27 Slides courtesy of Prof. Yan Tong
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CommonMorphologicalOpera6ons
• Twobasicoperations• Erosion• Dilation• Otheroperations• Opening/closing• Hit-or-Misstransform• Thinning/thickening• Hole+illing
CSCE 590: Introduction to Image Processing 28 Slides courtesy of Prof. Yan Tong
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Erosion
A { }ABzB z ⊆= )(| A { }0)(| =∩= cz ABzBor
Shrink or thin objects and remove the details smaller than the SE ∅
CSCE 590: Introduction to Image Processing 29 Slides courtesy of Prof. Yan Tong
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Dila6on
{ }0)ˆ(| ≠∩=⊕ ABzBA z
Grows or thickens objects and remove the gaps smaller than the SE CSCE 590: Introduction to Image Processing 30 Slides courtesy of Prof. Yan Tong
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Proper6esofErosionandDila6on• Dilationiscommutative
• Dilationisassociative
• Dilationisdistributiveovertheunionoperation
ABBA ⊕=⊕
( )CBACBA ⊕⊕=⊕⊕
𝐴⨁(𝐵∪𝐶)=(𝐴⊕𝐵)∪(𝐴⨁𝐶)
CSCE 590: Introduction to Image Processing 31 Slides courtesy of Prof. Yan Tong
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Proper6esofErosionandDila6on
• Erosion
• Erosionanddilationaredualsofeachother
• • ifandonlyif
• IfandBCBA ⊕⊆⊕,CA⊆ 𝐴⊝𝐵⊆𝐶⊝𝐵
𝐴⨁𝐵= (𝐴↑𝑐 ⊝ 𝐵 )↑𝑐
𝐴⊆(𝐶⊝𝐵) (𝐴⨁𝐵)⊆𝐶
CSCE 590: Introduction to Image Processing 32 Slides courtesy of Prof. Yan Tong
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Opening• Smooththecontourofanobject• Breaknarrowbridges• Eliminatethinprotrusions
ABA (=! BB ⊕)( ) BABBA !!! =( ) ABA ⊆! BCBACifA !! ⊆⊆ ,
The SE rolls within the boundary of A.
𝐴∘𝐵=∪{(𝐵)↓𝑧 | (𝐵)↓𝑧 ⊆𝐴}
CSCE 590: Introduction to Image Processing 33 Slides courtesy of Prof. Yan Tong
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Opening(Cont’d)Thin isthmus
Smoothed outer corners
Isthmus removed
CSCE 590: Introduction to Image Processing 34 Slides courtesy of Prof. Yan Tong
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Closing• Smooththecontourofanobject• Fillnarrowbreaksandgaps• Eliminatelongandthingulfs• Eliminatesmallholes
The SE rolls outside the boundary of A.
( ) BABBA •=••( )BAA •⊆ BCBACifA •⊆•⊆ ,
)( BABA ⊕=• B
cc BABA )ˆ( !=•Opening and closing are duals of each other
CSCE 590: Introduction to Image Processing 35 Slides courtesy of Prof. Yan Tong
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Closing(Cont’d)
Smoothed inner corners
Eliminated thin gulf CSCE 590: Introduction to Image Processing 36 Slides courtesy of Prof. Yan Tong
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Opening&Closing
𝐴⊝𝐵⊆𝐴∘𝐵⊆𝐴⊆ BABA ⊕⊆•
⊆ ⊆
⊆ ⊆
CSCE 590: Introduction to Image Processing 37 Slides courtesy of Prof. Yan Tong
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AnExampleofOpening&Closing
• Anopeningremovesallnoise• removingthewhite
noisebyerosion• removingtheblack
noisebydilation• Anadditionalclosing+ills
thegaps
CSCE 590: Introduction to Image Processing 38 Slides courtesy of Prof. Yan Tong
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Ques6ons?
CSCE 590: Introduction to Image Processing 39