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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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] .

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

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

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

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)

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

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

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.

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.

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.

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

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

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.

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.

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:

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,

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.

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.

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.

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

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

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.

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 .

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.

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

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

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,

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

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

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

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.

Summary

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

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)

Logic Operations & Binary Images AND OR

Logic Operations & Binary Images NAND XOR

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.

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

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

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

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

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

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

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

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

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

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

AND Operation IMAGE 2 1 AND 2 IMAGE 1 255 255 255 255

Not Operation NOT IMAGE 1 IMAGE 1 255 255

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.

Example let v = {0,1} compute 4,8 and m-path between p and q 3 1 2 1 2 2 0 2 1 2 1 1 1 0 1 2 3 1 2 1 2 2 0 2 1 2 1 1 1 0 1 2 p Fig 2 8 path Fig 1 4 path

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 3 1 2 1 2 2 0 2 1 2 1 1 1 0 1 2 p Fig 3 m- path

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