1. F(x,y) قيمة البيكسل الواحد ....... توجد 3 مراحل لمعالجة الصورة

2. فى المرحلة الاولى بنعمل preprocessing وهنا بنشيل الضوضاء المحيطة بالصورة يعنى اللى مش عاوزينها تظهر مثلا انا عاوز اعمل تحديد ل عنصر معين فى الصورة اذا اى شئ فى الصورة عدا العنصر يعتبر ضوضاء وممكن نعمل تحسين للصورة فى هذه المرحلة ونخلصها قبل المرحلة التانية ولما ندخل على الثانية بنعمل تقطيع للصورة فيها والتعرف على العناصر وهكذا ثم الثالثة وهذه المرحلة خاصة بالرؤية بالحاسب مهم جدا

3. FUNDAMENTAL STEPS IN DIGITAL IMAGE PROCESSING
Representation
and description
Segmentation
Preprocessing
Recognation
and
interpretation
Result
knowledge base
اولا استخلاص الصورة ثانيا مرحلة قبل المعالجة ثالثا تقطيع الصورة رابعا تمثيل الصورة ووصفها خامسا تمييز الصورة بحيث كل حالة من الخمسة هنا ممكن اشتغل عليها منفصله لوحدها وبيكون عندى داتا بيز بقارن بيها الناتج عشان اتعرف على الصورة او اخزن الصورة فيها وهكذا
Problem
domain
Image
acquisition

4. Image Acquisition
Imaging sensor & capability to digitize the signal collected by the sensor:
Video camera
Digital camera
Conventional camera & analog-to-digital converter

5. Preprocessing
To improve the image to ensure the success of further processes:
Enhancing contrast
Removing noise

6. Segmentation To partition the image into its constituent parts
(objects)
Autonomous مستقل segmentation (very difficult)
– can facilitate or disturb subsequent processes
Output (representation):
– raw pixel data, depicting either boundaries or
whole regions (corners vs. texture for example)
– need conversion to a form suitable for
computer processing
(Description)
هنا بقطع الصورة لاجزاء مثلا لو عندى تقنية اخذ رقم سيارة مسرعه على الطريق باخد صورة وبحيث بشوف فين المستطيل بتاع رقم العربية وبقطعه من الصورة وابدا العمليات بتاعتى عليه

7. Representation & Description
Feature selection (description) deals with extracting:
Features that result in quantitative information of interest or
Features that are important for differentiating one class of objects from another
بحاول اوصف الصورة وافرق بين كل عنصر والتانى فيها وبستخدم طريقة مثل chain code زى الشكل البيانى من 0 ل 3 او من 0 ل 7

8. Recognition & Interpretation
To assign a label to an object based on information provided by the descriptors
To assign meaning to a group of recognized objects

9. Knowledge Base Knowledge database:
Guides the operation of each processing module and controls the interaction between modules.

10. Key Stages in Digital Image Processing
Image Restoration
Morphological Processing
Image Enhancement
Segmentation
Image Acquisition
Object Recognition
Representation & Description
Problem Domain
Colour Image Processing
Image Compression

11. Key Stages in Digital Image Processing: Image Aquisition
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
Image Restoration
Morphological Processing
Image Enhancement
Segmentation
Image Acquisition
Object Recognition
Representation & Description
Problem Domain
Colour Image Processing
Image Compression

12. Key Stages in Digital Image Processing: Image Enhancement
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
Image Restoration
Morphological Processing
Image Enhancement
Segmentation
Image Acquisition
Object Recognition
Representation & Description
Problem Domain
Colour Image Processing
Image Compression

13. Key Stages in Digital Image Processing: Image Restoration
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
Image Restoration
Morphological Processing
Image Enhancement
Segmentation
Image Acquisition
Object Recognition
Representation & Description
Problem Domain
Colour Image Processing
Image Compression

14. Key Stages in Digital Image Processing: Morphological Processing
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
Image Restoration
Morphological Processing
Image Enhancement
Segmentation
Image Acquisition
Object Recognition
Representation & Description
Problem Domain
Colour Image Processing
Image Compression

15. Key Stages in Digital Image Processing: Segmentation
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
Image Restoration
Morphological Processing
Image Enhancement
Segmentation
Image Acquisition
Object Recognition
Representation & Description
Problem Domain
Colour Image Processing
Image Compression

16. Key Stages in Digital Image Processing: Object Recognition
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
Image Restoration
Morphological Processing
Image Enhancement
Segmentation
Image Acquisition
Object Recognition
Representation & Description
Problem Domain
Colour Image Processing
Image Compression

17. Key Stages in Digital Image Processing: Representation & Description
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
Image Restoration
Morphological Processing
Image Enhancement
Segmentation
Image Acquisition
Object Recognition
Representation & Description
Problem Domain
Colour Image Processing
Image Compression

18. Key Stages in Digital Image Processing: Image Compression
Image Restoration
Morphological Processing
Image Enhancement
Segmentation
Image Acquisition
Object Recognition
Representation & Description
Problem Domain
Colour Image Processing
Image Compression

19. Key Stages in Digital Image Processing: Colour Image Processing
Image Restoration
Morphological Processing
Image Enhancement
Segmentation
Image Acquisition
Object Recognition
Representation & Description
Problem Domain
Colour Image Processing
Image Compression

20. Digital Image Definitions
A digital image a[m,n] described in a 2D discrete space is derived from an analog image a(x,y) in a 2D continuous space through a sampling process that is frequently referred to as digitization. التحويل لارقام
The 2D continuous image a(x,y) is divided into N rows and M columns.
Sampling التحويل من تناظرى لرقمى

21. The intersection of a row and a column is termed a pixel.
The value assigned to the integer coordinates [m,n] with {m = 0,1,2,...,M-1} and {n = 0,1,2,...,N-1} is a[m,n] .

22. The image has been divided into N = 16 rows and. M = 16 columns
The image has been divided into N = 16 rows and M = 16 columns. The value assigned to every pixel is the average brightness in the pixel rounded to the nearest integer value.
The process of representing the amplitude نطاق ومدى of the 2D signal at a given coordinate as an integer value with L different gray levels is usually referred to as amplitude quantization or simply quantization.حساب الكم
مهم جدا

23. Why Digital? “Exactness” الدقة
Perfect reproduction without degradation عدم التقليل من الدقة فى حالة نسخها اكتر من مرة
Perfect duplication of processing result
Convenient & powerful computer-aided processing
Can perform rather sophisticated معقد ومتطور processing through hardware or software
Even kindergartners رياض اطفال can do it!
Easy storage and transmission
1 CD can store hundreds of family photos!
Paperless transmission of high quality photos through network within seconds

24. Human Vision System Image is to be seen.
Perceptual Based Image Processing
Focus on perceptually significant information
Discard perceptually insignificant information
Issues:
Biological
Psychophysical

25. 2.5 Basic Relations between Pixels
Neighbors of a pixel
Horizontal and vertical neighbors.
(x+1, y), (x-1, y), (x, y+1), (x, y-1)
Four diagonal neighbors: ND(p)
(x+1, y+1), (x+1, y-1), (x-1, y+1), (x-1, y-1)
4-neighbors of p: N4(p).
8-neighbors of p: N8(p).
8-neighbors = 4-neighbors +Four diagonal neighbors N8(p) = N4(p) +ND(p)

26. كل ما بنزل لتحت بيزداد الموجب بالنسبة للاكس او اروح يمين بالنسبة للواى

27. Relations between Pixels
Adjacency p
4-adjacency: N4(p) p
8-adjacency: N4(p)+ND(p)
نستخدم المتجاورات فى حالة عندى خط تخين برفعه او رفيع وتخنه وهكذا

28. A mixed adjacency combines 4- and 8-adjacency to avoid the ambigities.
m-Adjacency
A mixed adjacency combines 4- and 8-adjacency to avoid the ambigities.
Multiple 8-adjacency
m-adjacency
Two pixels p and q are m-adjacent if
q is in N4(p) or,
q is in ND(p) and N4(p)∩ N4(q) has no pixel.

29. Connectivity Path: Connectivity:
(x0, y0), (x1, y1), …, (xn, yn) where (xi, yi) and (xi+1, yi+1) are adjacent.
Closed path: (xn, yn) = (x0, y0) انتهت بنفس البداية
Connectivity:
Two pixels are said connected if they have the same value and there is a path between them.
If a S is a set of pixels,
For any pixel p in S, the set of pixels that are connected to it is called a connected component of S.
If S has only one connected component, S is called a connected set.

30. Regions R is a region if R is a connected set.
The pixel in the boundary (contour) محيط has at least one 4-adjacent neighbor whose value is 0.

31. Distance measures Euclidean distance
City-block distance or D4 distance.
D4(p, q)= |x - s | + |y - t |
D8 distance or chessboard distance.
D8(p, q)= max (|x - s |, | y - t |)
P=x,y ; q=s,t;
الصورة والمصفوفة مشتركين فى كل حاجة الا الضرب والمعكوس بحيث معكوس الصورة هو السالب بتاع الصورة اما الضرب فبضرب العناصر المتناظرة ببعضها البعض ولازم شروط الضرب ان الصورتين يكونوا نفس الحجم

32. Matrices and Vectors Review
To provide background material in support of topics in Digital Image Processing that are based on matrices and/or vectors.

33. Review: Matrices and Vectors
Some Definitions
An m×n (read "m by n") matrix, denoted by A, is a rectangular array of entries or elements (numbers, or symbols representing numbers) enclosed typically by square brackets, where m is the number of rows and n the number of columns.

34. Definitions (Con’t)
The transpose AT of an m×n matrix A is an n×m matrix obtained by interchanging the rows and columns of A.
A square matrix for which AT=A is said to be symmetric.
Any matrix X for which XA=I and AX=I is called the inverse of A.
Let c be a real or complex number (called a scalar). The scalar multiple of c and matrix A, denoted cA, is obtained by multiplying every elements of A by c. If c = 1, the scalar multiple is called the negative of A.

35. Definitions (Con’t)
A column vector is an m × 1 matrix:
A row vector is a 1 × n matrix:
A column vector can be expressed as a row vector by using
the transpose:

36. Some Basic Matrix Operations
The sum of two matrices A and B (of equal dimension), denoted A + B, is the matrix with elements aij + bij.
The difference of two matrices, A B, has elements aij  bij.
The product, AB, of m×n matrix A and p×q matrix B, is an m×q matrix C whose (i,j)-th element is formed by multiplying the entries across the ith row of A times the entries down the jth column of B; that is,

37. Some Basic Matrix Operations (Con’t)
The inner product (also called dot product) of two vectors
is defined as
Note that the inner product is a scalar.

38. Vectors and Vector Spaces
A vector space is defined as a nonempty set V of entities called vectors and associated scalars that satisfy the conditions outlined in A through C below. A vector space is real if the scalars are real numbers; it is complex if the scalars are complex numbers.
Condition A: There is in V an operation called vector addition, denoted x + y, that satisfies:
1. x + y = y + x for all vectors x and y in the space.
2. x + (y + z) = (x + y) + z for all x, y, and z.
3. There exists in V a unique vector, called the zero vector, and denoted 0, such that x + 0 = x and 0 + x = x for all vectors x.
4. For each vector x in V, there is a unique vector in V, called the negation of x, and denoted x, such that x + ( x) = 0 and ( x) + x = 0.

39. Vectors and Vector Spaces (Con’t)
Condition B: There is in V an operation called multiplication by a scalar that associates with each scalar c and each vector x in V a unique vector called the product of c and x, denoted by cx and xc, and which satisfies:
1. c(dx) = (cd)x for all scalars c and d, and all vectors x.
2. (c + d)x = cx + dx for all scalars c and d, and all vectors x.
3. c(x + y) = cx + cy for all scalars c and all vectors x and y.
Condition C: 1x = x for all vectors x.

40. Vectors and Vector Spaces (Con’t)
We are interested particularly in real vector spaces of real m×1 column matrices. We denote such spaces by m , with vector addition and multiplication by scalars being as defined earlier for matrices. Vectors (column matrices) in m are written as

41. Vectors and Vector Spaces (Con’t)
Example
The vector space with which we are most familiar is the two-dimensional real vector space 2 , in which we make frequent use of graphical representations for operations such as vector addition, subtraction, and multiplication by a scalar. For instance, consider the two vectors
Using the rules of matrix addition and subtraction we have

42. Vectors and Vector Spaces (Con’t)
Consider two real vector spaces V0 and V such that:
Each element of V0 is also an element of V (i.e., V0 is a subset of V).
Operations on elements of V0 are the same as on elements of V. Under these conditions, V0 is said to be a subspace of V.
A linear combination of v1,v2,…,vn is an expression of the form
where the ’s are scalars.

43. Vectors and Vector Spaces (Con’t)
A vector v is said to be linearly dependent on a set, S, of vectors v1,v2,…,vn if and only if v can be written as a linear combination of these vectors. Otherwise, v is linearly independent of the set of vectors v1,v2,…,vn .

44. Vectors and Vector Spaces (Con’t)
A set S of vectors v1,v2,…,vn in V is said to span some subspace V0 of V if and only if S is a subset of V0 and every vector v0 in V0 is linearly dependent on the vectors in S. The set S is said to be a spanning set for V0. A basis for a vector space V is a linearly independent spanning set for V. The number of vectors in the basis for a vector space is called the dimension of the vector space. If, for example, the number of vectors in the basis is n, we say that the vector space is n-dimensional.

45. Vectors and Vector Spaces (Con’t)
An important aspect of the concepts just discussed lies in the representation of any vector in m as a linear combination of the basis vectors. For example, any vector
in 3 can be represented as a linear combination of the basis
vectors

46. Definition of Elements
Let A be a set in Z2. If a = (a1,a2) is an element of A, then we write
Similarly, if a isn’t an element of A we write
An arbitrary set in Zn has elements n-tuples as (z1,z2,. . .,zn)
The set with no elements is called the null or empty set

47. What subset is
If every element of a set A is also an element of another set B then A is said to be a subset of B, denoted as
Example:
X={(1,1),(1,2),(1,3),(2,1),(2,2),
(2,3),(3,1),(3,2),(3,3)}
and
Y={(1,2),(2,1),(2,2),(2,3),(3,2)}
So,

48. Union Operation The union of two sets A and B denoted by
Set C is the set of all elements belonging to either A, B, or both

49. Intersection Operation
The intersection of two sets A and B denoted by
Set D is the set of all elements belonging to both A and B

50. Mutually Exclusive Property
Two sets A and B is disjoint or mutually exclusive if they have no common elements A B

51. Complement & Difference
The complement of a set A is the set of elements not contained in A:
Difference of two sets A and B, denoted A-B, is defined as
This is the set of elements that belong to A, but not to B.

52. Summary

53. Addition definition
Two additional definition that are used extensively in morphology
The reflection of set B is defined as
The translation of set A by point z=(z1,z2) is defined as

54. Logic Operations & Binary Images
The principal logic operations used in image processing are AND, OR, and NOT (Complement)
Logic operations are preformed on a pixel by pixel basis between corresponding pixels of two or more images (except NOT)

55. Logic Operations & Binary Images
AND OR

56. Logic Operations & Binary Images
NAND
XOR

57. Spatial resolution is the smallest discernible detail in an image.
line pair width = 2W (line width + space)
No. of line pairs per unit distance = 1 / 2W
Resolution is the smallest number of discernible line pairs per unit distance.

59. Gray-level resolution refers to the smallest discernible change in gray level (subjective).

60. Arithmetic Operation
The arithmetic operations between two pixels p and q are denoted as followed:
Subtraction : p – q
Addition : p + q
Multiplication : p * q
Division : p / q

61. Arithmetic Operation
Operation on entire images are carried out pixel by pixel.
If the result is real, truncate its value
If the result is over range, pick the maximum value
If the result if under range, pick the minimum value

62. Addition Operation IMAGE 2 IMAGE 1 + IMAGE 2 IMAGE 1 100 100 100 200
100
100
100
200
100
100
200
100

63. Subtraction Operation
IMAGE 2
IMAGE 1 - IMAGE 2
IMAGE 1 30
100
100 20
-100 10
100
Image subtraction is a basic tool in medical imaging, where it is used to remove static background information

64. Multiplication Operation
IMAGE 2
IMAGE 1 * IMAGE 2
IMAGE 1 10
100
100 10
-100
100
10000
10000
-100

65. Division Operation IMAGE 2 IMAGE 1 / IMAGE 2 IMAGE 1 100 100 -100 1 1
100
100
-100 1 1
-100

66. Arithmetic Operation Let there is 1 input images
p is denoted of a pixel in digital image and
c is a constrain.
Addition : p + c
Subtraction : p – c
Multiplication : p * c
Division : p / c

67. Logic Operation
Principal logic operations used in image processing are AND, OR, and COMPLEMENT, denoted as follows:
AND : p AND q
OR : p OR q
NOT : NOT q

68. OR Operation IMAGE 2 1 OR 2 IMAGE 1 255 255 255 255 255 255 255 255
255
255
255
255
255
255
255
255
255
255
255
255
255
255

69. AND Operation
IMAGE 2
1 AND 2
IMAGE 1
255
255
255
255

70. Not Operation
NOT IMAGE 1
IMAGE 1
255
255

71. 4-adjacency: if q is in the set N4(p).
m-adjacency: if
if q is in the set N4(p), or
if q is in the set ND(p) and the set N4(p)∩N4(q) has no pixels whose values are from V.

72. Example let v = {0,1} compute 4,8 and m-path between p and q p
Fig 2 8 path
Fig 1 4 path

73. From fig.3 there is one m- path the length of this path is 5
From fig 1 the 4- path doesn't exist there are more than one 8- path the shortest 8- path is 4 as shown in fig 2
From fig.3 there is one m- path the length of this path is 5 q p
Fig 3 m- path

74. Summary We have looked at: What is a digital image?
What is digital image processing?
History of digital image processing
State of the art examples of digital image processing
Key stages in digital image processing