1、Digital Image ProcessingChapter 9Morphological Image Processing2019.10What are Morphological Operations? Morphological operations come from the word “morphing”in Biology which means “changing a shape”.MorphingImage morphological operations are used to manipulateobject shapes such as thinning, thicke

2、ning, and filling.Binary morphological operations are derived fromset operations.(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Basic Set Operations Concept of a set in binary image morphology: Each set may represent one object. Each pixel (x,y) has its st

3、atus: belong to a set or not belong to a set. Translation and Reflection Operations A(A)zz = (z1,z2)TranslationReflectionB(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Logical Operations* *For binary images only(Images from Rafael C. Gonzalez and Richard

4、E. Wood, Digital Image Processing, 2nd Edition.Dilation Operations = Empty setA = Object to be dilatedB = Structuring elementDilate means “extend”Dilation Operations (cont.) StructuringElement (B)Original image (A)ReflectionIntersect pixelCenter pixelDilation Operations (cont.) Result of DilationBou

5、ndary of the “center pixels”where intersects A(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Example: Application of Dilation“Repair” broken characters(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Erosion Operat

6、ion A = Object to be erodedB = Structuring elementErosion means “trim”Erosion Operations (cont.) StructuringElement (B)Original image (A)Intersect pixelCenter pixelErosion Operations (cont.) Result of ErosionBoundary of the “center pixels”where B is inside A(Images from Rafael C. Gonzalez and Richar

7、d E. Wood, Digital Image Processing, 2nd Edition.Example: Application of Dilation and ErosionRemove small objects such as noiseDuality Between Dilation and ErosionProof:where c = complement(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Opening Operation or

8、= Combination of all parts of A that can completely contain B Opening eliminates narrow and small details and corners. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Example of Opening (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Proc

9、essing, 2nd Edition.Closing Operation Closing fills narrow gaps and notches(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Example of Closing Duality Between Opening and ClosingProperties OpeningProperties ClosingIdem potent property: cant change any moreEx

10、ample: Application of Morphological Operations(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Finger print enhancement(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Boundary Extraction Original imageBoundary(Image

11、s from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Region Filling Original imageResults of region fillingwhere X0 = seed pixel p(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Extraction of Connected Components where X0 = s

12、eed pixel pExample: Extraction of Connected Components X-ray imageof bonesThresholdedimageConnectedcomponents(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Hit-and-Miss TransformBrief DescriptionGeneral binary morphological operation that can be used to lo

13、ok for particular patterns in an image.A tool for shape detectionBasic operation for binary morphology Almost all the other binary morphological operators can be derived from Hit-and-Miss Transform.Common names: Hit-and-miss Transform, Hit-or-miss TransformHow It WorksThe structuring element used in

14、 the hit-and-miss can contain both foreground and background pixels.OperationsIf the foreground and background pixels in the structuring element exactly match foreground and background pixels in the image, then the pixel underneath the origin of the structuring element is set to the foreground color

15、.If it doesnt match, then that pixel is set to the background color.Hit-and-Miss TransformEffect of the hit-and-miss based right angle convex corner detectorAfter obtaining the locations of corners in each orientation, we can then simply OR all these images together to get the final result . Four st

16、ructuring elements used for corner finding in binary imagesHit-and-Miss TransformGuidelines for UseThe hit-and-miss transform is used to look for occurrences of particular binary patterns.It can be used to look for several patterns.Simply by running successive transforms using different structuring

17、elements, and then ORing the results together.The operations of erosion, dilation, opening, closing, thinning and thickening can all be derived from the hit-and-miss transform in conjunction with simple set operations.Hit-and-Miss TransformSome structuring elements that can be used for locating vari

18、ous binary features1) is used to locate isolated points in a binary image.2) is used to locate the end points on a binary skeleton.Note that this structuring element must be used in all its orientations, and thus the four hit-and-miss passes are required.3a) and 3b) are used to locate the triple poi

19、nts on a skeleton.Both structuring elements must be run in all orientations so eight hit-and-miss passes are required.Some applications of the hit-and-miss transformHit-and-Miss TransformThe triple points (points where three lines meet) of the skeletonThe hit-and-miss transform outputs single foregr

20、ound pixels at each triple point by structuring elements 3a) and 3b).This image was dilated once using a cross-shaped structuring element in order to mark these isolated points clearly, and this was then ORed with the original skeleton.Hit-and-Miss TransformThe end points of the skeletonThe hit-and-

21、miss transform outputs single foreground pixels at each end point by structuring element 2).This image was dilated once using a square-shaped structuring element, and this was then ORed with the original skeleton.Hit-and-Miss Transform(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Imag

22、e Processing, 2nd Edition.Hit-or-Miss Transformation *where X = shape to be detected W = window that can contain XHit-or-Miss Transformation (cont.) *(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.(Images from Rafael C. Gonzalez and Richard E. Wood, Digita

23、l Image Processing, 2nd Edition.Convex Hull *Convex hull has no concave part.Convex hullAlgorithm:whereExample: Convex Hull (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Ed

24、ition.Thinning *Example: Thinning (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Make an object thinner.(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Thickening *.Make an object thicker*(Images from Rafael C. Go

25、nzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Skeletons Dot lines are skeletons of thisstructureSkeletons (cont.) withwherek timesandSkeletons (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.(Images from Rafael C. Gonzalez and Richard E.

26、 Wood, Digital Image Processing, 2nd Edition.Pruning *= thinning= finding end points= dilation at end points= Pruned resultExample: Pruning Original imagePruned resultAfter Thinning3 timesEnd pointsDilationof end points(Tables from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2n

27、d Edition.Summary of Binary Morphological Operations Summary of Binary Morphological Operations (cont.) (Tables from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Summary of Binary Morphological Operations (cont.) (Tables from Rafael C. Gonzalez and Richard E. Wood, D

28、igital Image Processing, 2nd Edition.Summary of Binary Morphological Operations (cont.) (Tables from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Basic Types of Structuring Ele

29、mentsx = dont care(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Gray-Scale Dilation 2-D Case1-D CaseSubimageOriginal imageMoving windowMaxOutput imageGray-Scale Dilation (cont.) +Reflectionof BStructuring element BNote: B can be any shape and subimage mus

30、t have the same shape as reflection of B.(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Gray-Scale Erosion2-D Case1-D CaseSubimageOriginal imageMoving windowMinOutput imageGray-Scale Erosion (cont.) -BStructuring element BNote: B can be any shape and subim

31、age must have the same shape as B.(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Example: Gray-Scale Dilation and ErosionOriginal imageAfter dilationAfter erosionDarkerBrighter(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2

32、nd Edition.Gray-Scale OpeningOpening cuts peaks(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Gray-Scale ClosingClosing fills valleys(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Example: Gray-Scale Opening and

33、ClosingOriginal imageAfter closingAfter openingReduce whiteobjectsReduce darkobjects(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Gray-scale Morphological Smoothing Smoothing: Perform opening followed by closingOriginal imageAfter smoothing(Images from Ra

34、fael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Morphological Gradient Original imageMorphological Gradient(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Top-Hat Transformation Original imageResults of top-hat transform(Images f

35、rom Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.Example: Texture Segmentation Application Algorithm:1. Perform closing on the image by using successively larger structuring elements until small blobs are vanished.2. Perform opening to join large blobs together3. Perform intensity thresholdingOriginal imageSegmented resultSmall blobLarge blob(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Pr