BYST Seg-1 DIP - WS2002: Segmentation Digital Image Processing Image Segmentation Bundit Thipakorn,…

BYSTBYSTSeg-1DIP - WS2002: SegmentationDIP - WS2002: Segmentation

Digital Image ProcessingDigital Image Processing

Image SegmentationImage Segmentation

Bundit Thipakorn, Ph.D.Bundit Thipakorn, Ph.D.Computer Engineering DepartmentComputer Engineering Department


Image SegmentationImage SegmentationWhat picture are they?What picture are they?


Aim: Aim: partition an image into meaningful partition an image into meaningful regions (or categories) corresponding to part regions (or categories) corresponding to part of, or the whole of objects within the image.of, or the whole of objects within the image.

Complete Complete SegmentationSegmentation

A set of disjoint regions A set of disjoint regions corresponding uniquely with corresponding uniquely with objects in the original image.objects in the original image.

SegmentatiSegmentationon

Cont’d.Cont’d.


SegmentatiSegmentationonPartial Partial SegmentationSegmentation

A set of disjoint regions that are A set of disjoint regions that are homogeneous with respect to homogeneous with respect to selected property such as selected property such as brightness, colour, reflectivity, brightness, colour, reflectivity, texture, etc.texture, etc.

Every pixel in an image is assigned to oEvery pixel in an image is assigned to one of a number of the disjoint regions.ne of a number of the disjoint regions.

Cont’d.Cont’d.


A good segmentation is typically one in A good segmentation is typically one in which:which:


Cont’d.Cont’d.

pixels in the same categories have similar pixels in the same categories have similar selected property and form a connected region;selected property and form a connected region;

neighbouring pixels that are in different neighbouring pixels that are in different categories have dissimilar selected property.categories have dissimilar selected property.



Cont’d.Cont’d.

StartStart

Dividing Dividing the imagethe image

1. All regions of interes1. All regions of interest are identified.t are identified.oror2. Reach certain 2. Reach certain uniformity.uniformity.

StopStopNoNo

YesYes

Depends on the Depends on the problem being problem being

solved.solved. Easy : if outcome is known.Easy : if outcome is known. Otherwise, it is very difficult.Otherwise, it is very difficult.



Cont’d.Cont’d.

That is,That is,

Autonomous segmentation is one of the Autonomous segmentation is one of the most difficult tasks in image processing.most difficult tasks in image processing.

Two main approaches: Two main approaches: Boundary-Based (Edge) Methods: Boundary-Based (Edge) Methods: Object is Object is represented by its outlinerepresented by its outline..



Cont’d.Cont’d.

Region-Based (Area) Methods: Region-Based (Area) Methods: Object is represented Object is represented by its respective 2D regionby its respective 2D region..

Boundary-Based Object Boundary-Based Object RepresentationRepresentation

Region-Based Object Region-Based Object RepresentationRepresentation


SegmentationSegmentation

Input IInput Imagemage

1. Pixels along 1. Pixels along a boundary.a boundary.oror

2. Pixels contained 2. Pixels contained in a region.in a region.


Cont’d.Cont’d.


determine a closed boundary such that an determine a closed boundary such that an inside and an outside can be defined.inside and an outside can be defined.

Edge-Based Edge-Based SegmentationSegmentation


Edge-BasedEdge-BasedCont’d.Cont’d.

Detection of DiscontinuitiesDetection of Discontinuities Point Detection: Detect isolated points.Point Detection: Detect isolated points.



Line Detection: Detect Line Detection: Detect part of a image linepart of a image line..

= a dark narrow region = a dark narrow region bounded on both sides by bounded on both sides by lighter regions, or vice-versa.lighter regions, or vice-versa.





Edge Detection: Edge Detection: (See Image Filtering in Spatial Domain)(See Image Filtering in Spatial Domain)..

Edge is: Edge is:1. A boundary between two regions having the strong i1. A boundary between two regions having the strong intensity contrast.ntensity contrast.

2. A boundary having the maximum/minimum of inten2. A boundary having the maximum/minimum of intensity gradient (the 1sity gradient (the 1stst derivative of the gray-level profile derivative of the gray-level profile).).

3. A boundary where the zero-crossing of the 23. A boundary where the zero-crossing of the 2ndnd deriv derivative of the gray-level profile.ative of the gray-level profile.

oror

oror




Region =Region = group of pixels sharing comgroup of pixels sharing common featuresmon features

Region-Based SegmentationRegion-Based Segmentation


Formal Definition Formal Definition

Region-Region-BasedBased

Cont’d.Cont’d.

A segmentation of the array R for A segmentation of the array R for a uniformity predicate Pa uniformity predicate P is a partition of R into disjoint non-empty subsets Ris a partition of R into disjoint non-empty subsets R11, R, R22, , RR33, …, R, …, Rtt and can be defined mathematically as following: and can be defined mathematically as following:

RRii = R = R

RRii is a connected region; i = 1, 2, 3, …, n. is a connected region; i = 1, 2, 3, …, n.

RRii R Rjj = = for all i and j; i ≠ j. for all i and j; i ≠ j.

P(RP(Rii) = True for i = 1, 2, 3, …, n.) = True for i = 1, 2, 3, …, n.

n

i 1



Cont’d.Cont’d.

P(RP(Rii R Rjj ) = False for i ≠ j. ) = False for i ≠ j.

Where P(RWhere P(Rii) is the logical predicate over the points in set R ) is the logical predicate over the points in set R and and is the null set. is the null set.

00RR11 RR22

RR33RR44

RRii RRjj

RRnn



Cont’d.Cont’d.

- Region Based Method- Region Based Methodss Thresholding,Thresholding,

Region growing,Region growing, Region merging and splitting,Region merging and splitting, Clustering, etc.Clustering, etc.



Cont’d.Cont’d.

RegionRegionGrowingGrowing


RegionRegionMergingMerging



Cont’d.Cont’d.

Split-and MSplit-and Merge Algoriterge Algorithmhm

(d)(d)(c)(c)

(a)(a) (b)(b)



Cont’d.Cont’d.

Clustering =Clustering = partition a set of vectors (pixels) into partition a set of vectors (pixels) into groups having similar values.groups having similar values.

Classical Clustering AlgorithmsClassical Clustering Algorithms

Let consider a set of K clusters C1, C2, …, CK with means m1, m2, …, mK. We can use a lest squares error measurelest squares error measure to measure how close the data are to their assigned clusters. A least squares error measure can be defined as:

i k

K 2i k

k 1 x CD x m

Documents

BYST Seg-1 DIP - WS2002: Segmentation Digital Image Processing Image Segmentation Bundit Thipakorn,…