1. D10K-6C01 Pengolahan Citra PCD-05 Algoritma Pengolahan Citra 2 Area Process
Program Studi S-1 Teknik Informatika
FMIPA Universitas Padjadjaran
Semester Genap

2. Algoritma Pengolahan Citra 2
Operasi berbasis area (Area Process)
Deskripsi Area Process
A category of image-processing techniques that calculate the value of each output-image pixel from the corresponding input-image pixel and its neighbours.
Examples include halftoning, sharpening and median filtering.
Point Process vs Area Process
Point processes: operate on a pixel based solely on that pixel’s value.
Area processes: use the input pixel as well as the pixels around it to generate a new pixel.
Point processes are easily implemented as “look -up tables”.

3. Limitations of Point Operations
They don’t know where they are in an image
They don’t know anything about their neighbors
Most image features (edges, textures, etc) involve a spatial neighborhood of pixels
If we want to enhance or manipulate these features, we need to go beyond point operations

4. What Point Operations Can’t Do
Blurring/smoothing
Sharpening

5. Pixel Neigborhood
Any pixel p(x, y) has two vertical and two horizontal neighbors, given by
This set of pixels are called the 4-neighbors of P, and is denoted by N4(P).
Each of them are at a unit distance from P.

6. Pixel Neigborhood The four diagonal neighbors of p(x,y) are given by,
This set is denoted by ND(P).
Each of them are at Euclidean distance of from P.

7. Pixel Neigborhood
The points ND(P) and N4(P) are together known as 8-neighbors of the point P, denoted by N8 (P).
Some of the points in the N4, ND and N8 may fall outside image when P lies on the border of image.

8. Terminologi Lainnya Pixel Adjacency Pixel Connectivity Path
Connected Components
Regions
Boundaries
Distances (Jarak)

9. Konvolusi

10. Konvolusi Image 1 6 3 2 9 11 10 5 7 8 4 1/9 New value:5 7 8 4
1/9
Filter/mask/
operator
New value:
6/9 + 9/9 + 7/9 + 0/9 + 2/9 + 8/9 + 2/9 + 9/9 + 10/9 = 5.889
Image 03

11. Konvolusi 1 6 3 2 9 11 10 5 7 8 4 1/9 5 Filtered Image:
Original Image:
Filtered Image: 1 6 3 2 9 11 10 5 7 8 4
1/9 5
value = 1x1/9 + 6x1/9 + 3x1/9 + 2x1/9 + 11x1/9 + 3x1/ x1/9 + 10x1/9 + 6x1/9 = 47/9 = 5.222 03

12. Konvolusi 1 6 3 2 9 11 10 5 7 8 4 1/9 5 7 Filtered Image:
Original Image:
Filtered Image: 1 6 3 2 9 11 10 5 7 8 4
1/9 5 7
value = 6x1/9 + 3x1/9 + 2x1/9 + 11x1/9 + 3x1/9 + 10x1/ x1/ x1/ x1/9
= 60/9 = 6.667 03

13. Konvolusi 1 6 3 2 9 11 10 5 7 8 4 5 7 5 5 6 5 4 5 6 Filtered Image:
Original Image:
Filtered Image: 1 6 3 2 9 11 10 5 7 8 4 5 7 5 5 6 5 4 5 6 03

14. PROBLEM PADA KONVOLUSI (BOUNDARY PROBLEM)
Bagaimana untuk menentukan piksel-piksel yang berada pada batas citra
Solusi:
Zero padding
Treat the empty cells in the convolution window as zero
Fit-Position
Start convolving at the first position where the window doesn’t overlap the image
Enlarging
Enlarging the original image before convolving by duplicating the edges
Wrapping
Wrap the image.

15. Penanganan Boundary Pixels

16. Spatial Filtering
The word “filtering” has been borrowed from the frequency domain.
Filters are classified as:
Low-pass (i.e., preserve low frequencies)
High-pass (i.e., preserve high frequencies)
Band-pass (i.e., preserve frequencies within a band)
Band-reject (i.e., reject frequencies within a band)

17. Spatial Filtering Linier Spatial FIltering Teknik
Dengan mask (konvolusi)
Tanpa mask
Kombinasi: Filer morfologis
Mask/Operator/Subwindows
Matriks berukuran kecil, pada umumnya bujursangkar dan berordo ganjil
Digunakan dalam proses konvolusi

18. Ilustrasi
Output
Image
w(i,j)
f(i,j)

19. Efek-efek Spatial Filtering
Smoothing/Blurring
Low-pass (i.e., preserve low frequencies)
Sharpening
High-pass (i.e., preserve high frequencies)
Edge Detection
Emboss

20. Filter Low Pass

21. Smoothing
original
3x3
9x9
15x15

22. Smoothing dg Gaussian Mask
The weights are samples of the Gaussian function
σ = 1.4
mask size is
a function of σ :

24. CONVOLUTION MASKS LAIN
Embossing
Blurring
Sharpening
W=9a-1

25. HIGH PASS FILTERING Tujuan Lawan dari Low Pass Filtering
Mempertajam tepi citra
Lawan dari Low Pass Filtering
Nama lain : edge sharpening
Pengolahan Citra Dijital

26. HIGH PASS FILTERING Syarat Contoh
Elemen filter boleh positif, negatif atau nol
Jumlah semua elemen pada filter adalah 0 atau 1
Contoh
Pengolahan Citra Dijital

27. Sharpening Filters (High Pass filtering)
Useful for emphasizing transitions in image intensity (e.g., edges).

28. Sharpening Filters (cont’d)
Note that the response of high-pass filtering might be negative.
Values must be re-mapped to [0, 255]
sharpened images
original image

29. Sharpening Filters: Unsharp Masking
Obtain a sharp image by subtracting a lowpass filtered (i.e., smoothed) image from the original image: - =

30. Sharpening Filters: High Boost
Image sharpening emphasizes edges but details (i.e., low frequency components) might be lost.
High boost filter: amplify input image, then subtract a lowpass image.
(A-1) + =

31. Sharpening Filters: High Boost (cont’d)
If A=1, we get a high pass filter
If A>1, part of the original image is added back to the high pass filtered image.

32. Sharpening Filters: High Boost (cont’d)

33. Sharpening Filters: Derivatives
Taking the derivative of an image results in sharpening the image.
The derivative of an image can be computed using the gradient.

34. Sharpening Filters: Derivatives (cont’d)
The gradient is a vector which has magnitude and direction: or
(approximation)

35. Sharpening Filters: Derivatives (cont’d)
Magnitude: provides information about edge strength.
Direction: perpendicular to the direction of the edge.

36. Sharpening Filters: Gradient Computation
Approximate gradient using finite differences:
sensitive to vertical edges Δx
sensitive to horizontal edges

37. Sharpening Filters: Gradient Computation (cont’d)

38. Example

39. Sharpening Filters: Gradient Computation (cont’d)
We can implement and using masks:
(x+1/2,y)
good approximation
at (x+1/2,y)
(x,y+1/2) * *
good approximation
at (x,y+1/2)
Example: approximate gradient at z5

40. Sharpening Filters: Gradient Computation (cont’d)
A different approximation of the gradient:
good approximation
(x+1/2,y+1/2) *
We can implement and using the following masks:

41. Sharpening Filters: Gradient Computation (cont’d)
Example: approximate gradient at z5
Other approximations
Sobel

42. Example

43. Sharpening Filters: Laplacian
The Laplacian (2nd derivative) is defined as:
(dot product)
Approximate
derivatives:

44. Sharpening Filters: Laplacian (cont’d)
Laplacian Mask
detect zero-crossings

45. Sharpening Filters: Laplacian (cont’d)
Sobel
Laplacian

46. Filtering Median Filtering Averaging Filter Minimum/Maksimum Filter
Menghilangkan impulse noise (bedakan dengan Gaussian Noise yang dapat dihilangkan dengan Low-pass filter)
Impulse noise has a number of pixels that have conspicuosly wrong intensities like 0 or 255
Averaging Filter
Mengganti nilai piksel fokus dengan rata-rata jumlah piksel dalam window
Minimum/Maksimum Filter
Mengganti nilai piksel fokus dengan nilai piksel minimum/maksimum piksel sekitar

47. Median Filter

48. Ilustrasi Median Filer
3x3 median
7x7 median

49. Filter Morfologis Kasus Khusus Filtering Dua operasi dasar:
erosi : menipiskan
Dilasi : menebalkan
Operasi gabungan:
opening : an erosion followed by a dilation
closing: a dilation followed by an erosion
Menggunakan mask/operator yang disebut structuring element
Jenis Structuring element: Block, Plus, Cross, Ring, Square
Definisi:

50. Jenis-jenis Structuring Element
Box
Plus
Cross
Dot
Square
Custom

51. Erosi
Erosi

52. Dilasi
Dilasi

53. Ilustrasi Erosi Dilasi

54. Ilustrasi Erosi Dilasi

55. Skeletonization one-pixel thick,
through the "middle" of the object, and,
preserves the topology of the object.

56. Hole Filing

57. BLOB separation

58. Hole Removal

59. MATLAB

61. Examples: Deblurring

62. Examples: Image Enhancement

63. Examples: Image Registration

64. Examples: Image Segmentation

65. Examples: Spatial Transformation

66. Examples: Measuring Image Features