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Morfologi citra. Operasi Morfologi? Merubah bentuk. Morphing.

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Presentation on theme: "Morfologi citra. Operasi Morfologi? Merubah bentuk. Morphing."— Presentation transcript:

1 Morfologi citra

2 Operasi Morfologi? Merubah bentuk. Morphing

3 Dasar Operasi Himpunan Konsep himpunan dalam morfologi citra biner Setiap himpunan menyatakan satu objek. Setiap pixel (x,y) memiliki status : anggota himpunan atau bukan anggota himpuan.

4 Operasi Translasi dan Pencerminan ( Reflection) A (A) z z = (z 1,z 2 ) TranslasiPencerminan B

5 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Logical Operations* *For binary images only

6 Dilation Operations = Himpunan kosong A = Objek yang akan direntang B = Struktur element Dilatasi berarti “merentang”

7 Dilation Operations (cont.) Structuring Element (B) Original image (A) Reflection Intersect pixelCenter pixel

8 Dilation Operations (cont.) Result of Dilation Boundary of the “center pixels” where intersects A

9 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Example: Application of Dilation “Repair” broken characters

10 Operasi erosi A = Object untuk dirampingkan B = Struktur elemen Erosion berarti “ramping”

11 Operasi Erosi (cont.) Struktur elemen (B) Citra Asal (A) Intersect pixelCenter pixel

12 Erosion Operations (cont.) Result of Erosion Boundary of the “center pixels” where B is inside A

13 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Example: Application of Dilation and Erosion Menghilangkan objek kecil seperti noise

14 Keterkaitan Dilatasi dan Erosi Bukti: dimana c = komplemen

15 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Operasi Opening atau = Gabungan dari semua bagian dari A yang benar-benar berisi B Opening menghilangkan detail dan sudut

16 Contoh Opening

17 Operasi Closing Operasi Closing Closing mengisi celah sempit dan lekukan

18 Contoh Closing

19 Hubungan antara Opening dan Closing Sifat Opening Sifat Closing

20 Contoh: Aplikasi dari operasi morfologi (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Perbaikan Finger print

21 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Hit-or-Miss Transformation * dimana X = bentuk yang dideteksi W = window yang berisi X

22 Hit-or-Miss Transformation (cont.) * (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition.

23 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Boundary Extraction Original image Boundary

24 24 mask B 1 (MATLAB function: bwhitmiss) (X B 1 )  (X c B 2 ) __ X B= * HitMiss mask B 2 origin mask B x xx MATLAB 0 -1 -1 11 -1 0 1 0 Hit-or-Miss Operator Definition Structuring element example

25 25 X Example 1 mask B 1 mask B 2 origin XcXc X c B 2 X B 1 __ X B *

26 26 mask B 1 mask B 2 mask B MATLAB -1 -1 -1 11 -1 Contoh origin X XcXc X c B 2 X B 1 __ X B * Interseksi

27 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Region Filling Citra asal Hasil dari region filling dimana X 0 = p

28 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Extraction of Connected Components dimana X 0 = p

29 Example: Extraction of Connected Components X-ray image of bones Thresholded image Connected components (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition.

30 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Bentuk Struktur Elemen x = don’t care

31 SELESAI

32 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Gray-Scale Dilation 2-D Case 1-D Case

33 Subimage Original image Moving window Max Output image Gray-Scale Dilation (cont.) + Reflection of B Structuring element B Note: B can be any shape and subimage must have the same shape as reflection of B.

34 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Gray-Scale Erosion 2-D Case 1-D Case

35 Subimage Original image Moving window Min Output image Gray-Scale Erosion (cont.) - B Structuring element B Note: B can be any shape and subimage must have the same shape as B.

36 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Example: Gray-Scale Dilation and Erosion Original imageAfter dilation After erosion Darker Brighter

37 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Gray-Scale Opening Opening cuts peaks

38 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Gray-Scale Closing Closing fills valleys

39 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Example: Gray-Scale Opening and Closing Original imageAfter closingAfter opening Reduce white objects Reduce dark objects

40 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Gray-scale Morphological Smoothing Smoothing: Perform opening followed by closing Original imageAfter smoothing

41 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Morphological Gradient Original image Morphological Gradient

42 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Top-Hat Transformation Original image Results of top-hat transform

43 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd 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 together 3. Perform intensity thresholding Original imageSegmented result Small blob Large blob

44 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Example: Granulometry Objective: to count the number of particles of each size Method: 1. Perform opening using structuring elements of increasing size 2. Compute the difference between the original image and the result after each opening operation 3. The differenced image obtained in Step 2 are normalized and used to construct the size-distribution graph. Original image Size distribution graph

45 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Morphological Watershads

46 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Morphological Watershads

47 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Morphological Watershads

48 Surface of at edges look like mountain ridges. Original image Gradient Image

49 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Morphological Watershads

50 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Morphological Watershads

51 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Morphological Watershads

52 (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Convex Hull


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