數(shù)字圖像處理英文課件：lecture9 Morphological Image Processing

1、9 Morphological Image ProcessingContentsIn this lecture we will considerWhat is morphology?Basic Concepts of Set TheoryDilation and ErosionOpening and ClosingHit or Miss TransformWhat Is Morphology?Morphological image processing (or morphology) describes a range of image processing techniques that d

2、eal with the shape (or morphology) of features in an imageThe basic ideal of Morphology is to use a special structuring element to measure or extract the corresponding shape or characteristics in the input images for further image analysis and object recognition.The mathematical foundation of morpho

3、logy is the set theory.In this chapter, the input images are binary images.A is a set, if a=(a1,a2) is an element of A, then, aAIf not, then, aA: null (empty) setTypical set specification: C=w|w=-d, for d DBasic Concepts of Set TheoryA subset of B: ABUnion of A and B: C=ABIntersection of A and B: D=

4、ABDisjoint sets: AB= Complement of A: Ac=w|wADifference of A and B: A-B=w|wA, wB=A BcBasic Concepts of Set Theory91 Preliminaries Basic morphology operatorsDilation, Erosion, Opening, ClosingBasic morphology algorithmsBoundary extractionRegion fillingHit-or-Miss transformationThinningThickeningPruni

5、ng Extensions to Gray-Scale ImagesSome basic concepts from set theoryBasic Set TheoryThe reflection of set BThe translation of set A by point z=(z1,z2), denoted (A)zBinary Images, Sets, and Logical Operators The language and theory of mathematical morphology often present a dual view of binary image

6、s. Using the set view, on the other hand, C is given byThe principal logic operations AND OR and NOTPerform on a pixel by pixel basisStructuring Elements, Hits, Fits, & MissingBACStructuring ElementFit: All on pixels in the structuring element cover on pixels in the imageHit: Any pixel in the struct

7、uring element covers a pixel in the imageMiss: no pixel in the structuring element covers a pixel in the imageAll morphological processing operations are based on these simple ideasStructuring ElementsStructuring elements can be any size and make any shapeHowever, for simplicity we will use rectangu

8、lar structuring elements with their origin at the middle pixel111111111001000111011111011100010001011101092 Dilation and Erosion The operations of dilation and erosion are fundamental to morphological image processing.Many of the algorithms presented later in this chapter are based on these operatio

9、ns, which are defined and illustrated in the discussion that follows.Dilation 膨脹 Ex906.mIPT function imdilate performs dilation. It basic calling syntax is A2=imdilate(A, B)The strel functionIPT function strel constructs structuring elements with A variety of shapes and sizes. It basic calling synta

10、x is: se=strel(shape, parameters) se=strel(diamond,5)DilationDilation of image f by structuring element s is given by f sThe structuring element s is positioned with its origin at (x, y) and the new pixel value is determined using the rule:Dilation ExampleStructuring ElementOriginal ImageProcessed I

11、mageDilation ExampleStructuring ElementOriginal ImageProcessed Image With Dilated PixelsB is the structuring element in dilation.DilationDilation:B is often called the “structuring element”Process consists of obtaining the reflection of B, about its originThen shifting this reflection of B by xThe d

12、ilation of A by B is the set of all x, displacements such that B and A overlap by at least one elementDilation ExampleStructuring ElementOriginal ImageProcessed ImageDilation ExampleStructuring ElementOriginal ImageProcessed Image?Note: For each structuring element, we should given a origin point. T

13、he origin point can be inside or outside the structuring element. The result should be different for different origin point.Dilation Example Original imageDilation by 3*3 square structuring elementDilation by 5*5 square structuring elementWhat Is Dilation For?Dilation can repair breaksDilation can r

14、epair intrusionsWatch out: Dilation enlarges objectsErosion腐蝕 Ex908.mErosion: exampleUse of morphological erosion for removing image componentsErosion ExampleStructuring ElementOriginal ImageErosion ExampleStructuring ElementOriginal ImageProcessed ImageErosion Example Original imageErosion by 3*3 s

15、quare structuring elementErosion by 5*5 square structuring elementWhat Is Erosion For?Erosion can split apart joined objectsErosion can strip away extrusionsWatch out: Erosion shrinks objectsErosion can split apart i.e. the erosion of A by B is the set of all points xsuch that B, translated by x, is

16、 contained in A.ErosionErosion & Dilation ApplicationObject connection：Compound Operations More interesting morphological operations can be performed by performing combinations of erosions and dilationsThe most widely used of these compound operations are:OpeningClosingOpening 開(kāi)An alternative mathem

17、atical formulation of opening is93 Combining Dilation and Erosion Opening ExampleStructuring ElementOriginal ImageAfter erosionOpening ExampleStructuring ElementOriginal ImageProcessed ImageOriginal ImageOpeningClosing 閉Closing ExampleStructuring ElementAfter dilationClosing ExampleAfter erosionAfte

18、r dilationStructuring ElementClosing ExampleStructuring ElementOriginal ImageProcessed ImageclosingClosing幾何解釋(1)用b對(duì)f 進(jìn)行開(kāi)操作的原理可以解釋為，推動(dòng)球沿著曲面的下側(cè)面滾動(dòng)，以便球體能在曲面的整個(gè)下側(cè)面來(lái)回移動(dòng)。當(dāng)球體的任何部分接觸到曲面的最高點(diǎn)就構(gòu)成了開(kāi)操作的曲面(2)相對(duì)應(yīng)的，閉操作就是在曲面的上側(cè)面滾動(dòng)，同時(shí)構(gòu)成了閉操作的曲面(a)一條灰度掃描線，(b)開(kāi)操作時(shí)滾動(dòng)球的位置，(c)開(kāi)操作的結(jié)果，(d)閉操作時(shí)滾動(dòng)球的位置，(e)閉操作的結(jié)果返回In essence, di

19、lation expands an image and erosion shrinks it.Opening:generally smoothes the contour of an image, breaks isthmuses (峽部), eliminates protrusions.Closing:smoothes sections of contours, but it generally fuses （熔合） breaks, holes, gaps, etc.Opening & ClosingCharacteristics of Opening and ClosingOpeningS

20、moothes the contourBreaks narrow isthmuses(峽部)Eliminates thin protrusions(突出) is a subset of AClosingSmoothes the contourFuses（熔合） narrow breaksEliminates small hollFill gaps in the contourA is a subset of Morphological Processing ExampleEx910.mEx911.mThe Hit-or-Miss Transformation設(shè)有兩幅圖像A和B，如果AB，那么稱

21、B擊中A，其中是空集合的符號(hào)；否則，如果AB=，那么稱B擊不中A（a）B擊中A； （b）B擊不中AOften, it is usefull to be able to identify specified configurations of pixels, such as isolated foreground pixels, or pixels that are end points of line segments.一般來(lái)說(shuō)，一個(gè)物體的結(jié)構(gòu)可以由物體內(nèi)部各種成分之間的關(guān)系來(lái)確定。為了研究物體（在這里指圖像）的結(jié)構(gòu)，可以逐個(gè)地利用其各種成分 (例如各種結(jié)構(gòu)元素)對(duì)其進(jìn)行檢驗(yàn)，判定哪些成分包括

22、在圖像內(nèi)，哪些在圖像外，從而最終確定圖像的結(jié)構(gòu)。擊中/擊不中變換就是在這個(gè)意義上提出的。Hit-or-miss transformationThe hit-or-miss transformation is useful for applications such as these. The hit-or-miss transformation of A by B is denotedHere,B is a structuring element pair, B=(B1,B2) , rather than a single element, as before.p352The hit-or-m

23、iss transformation is implemented in IPT by function bwhitmiss, which has the syntax C=bwhitmiss(A,B1,B2)Ex913.mHit-or-Miss Transform Definitions: B (B1,B2)B1 is the set of elements of B associated with an objectB2 is the set of elements of B associated with the corresponding background.Hit-or-Miss

24、Transform AB Contains all the origin points at which, simultaneously:B1 found a match (“hit”) in A and B2 found a match in Ac.Hit-or-Miss TransformHit-or-Miss TransformB1B2Hit-or-Miss TransformB1B2Hit-or-Miss TransformHit-or-Miss TransformThe reason for using B1 associated with objects and B2 associ

25、ated with background is based on an assumed definition that two or more objects are distinct only if they form disjoint.In some applications, we may be interested in detecting certain patterns of 0 and 1 within a set. In which case a background is not required.In such an instance, the hit-or-miss tr

26、ansform reduces to simple erosion. As indicated previously, erosion is still a set of matches, but without the additional requirement of a background match for detecting individual objects.Hit-or-Miss TransformIPT function bwmorph implements a variety of operations, which has the syntax: g=bwmorph(f

27、,operation,n) where f is an input binary image, operation is a string specifying the desired operation, and n is a positive integer specifying the number of times the operation is to be repeated.Thinning means reducing binary objects or shapes in an image to strokes that are a single pixel wide.Ex91

28、5.mSkeletonization is another way to reduce binary image objects to a set of thin strokes that retain important information about the shapes of the original objects.Skeletonization and thinning often produce short extraneous spurs, sometimes called parasitic components. The process of cleaning up th

29、ese spurs is called pruning.Ex915.m94 Labeling Connected Components L, num=bwlabel(f, conn)Where f is an input binary image and conn specifies the desired connectivity. Output L is called a label matrix, and num gives the total number of connected components found.If parameter conn is omitted, its v

30、alue defaults to8.Ex920.mBoundary ExtractionRegion FillingA: 8-connected boundaryBeginning with a point p inside A and letDo Until 區(qū)域填充這里討論一種簡(jiǎn)單的基于膨脹、取補(bǔ)和交的區(qū)域填充算法。下圖所需填充的區(qū)域邊界點(diǎn)是8連接的，先從界內(nèi)一點(diǎn)P開(kāi)始，用1去填充整個(gè)區(qū)域（設(shè)非邊界元素為0），填充過(guò)程如下：其中，B為對(duì)稱結(jié)構(gòu)元素，當(dāng)k迭代到Xk=Xk-1時(shí)，算法終止，集合Xk和A的并集即為填充結(jié)果。上述過(guò)程每一步與Ac的交起把結(jié)果限制在我們感興趣區(qū)域內(nèi)的作用（要不膨脹會(huì)一直進(jìn)行，直至填滿整個(gè)區(qū)域），所