Digital Image Processing: Digital Image Fundamentals

CSC447: Digital Image
Processing
Chapter 2: Digital Image Fundamentals
Prof. Dr. Mostafa Gadal-Haqq M. Mostafa
Computer Science Department
Faculty of Computer & Information Sciences
AIN SHAMS UNIVERSITY

What is a Digital Image?
 Real Images
 A real image can be
represented as a two-
dimensional continuous
light intensity function
g(x,y); where x and y
denote the spatial
coordinates and the value
of g is proportional to the
brightness (or gray level)
of the image at that point.
g(x,y)
y
x
2CSC447: Digital Image Processing Prof. Dr. Mostafa GadalHaqq.

What is a Digital Image?
 Digital Images
 A digital image is the
sampling and quantization
of a two-dimensional real
image both in spatial
coordinates and brightness.
 A digital image I(m,n) =
samples of g(x,y); where m
and n are integers, and I is
the intensity at m and n .
n
m
I(m,n)

Digital Image Acquisition
 A digital imaging system (digital camera).

 Sampling & Quantization

 What is the best quantization level ?
 Digital images are typically quantized to 256
gray levels.

 Sampling & Quantization

 Effect of Quantization
256
64
128
32
16
4
8
2

Digital Image Representation
 A digital image can be
represented as a two-dimensional
matrix.
n
m
I(m,n)
i(1,1) i(1,2) ……. i(1, n-1)
i(2,1) i(2,2) ……. i(2, n-1)
. .
. . . . . . . . . . . .
. .
i(m-1,1) i(m-1,2) … i(m-1, n-1)
I(mn) =
• Each element is called a pixel (picture
element).
• A color (RGB) image is represented
by a 3-dimensional matrix I(mxnx3)

Digital Image Size
 The size of a digital image is determines by its
dimensions ( M x N ) multiplied by the number of
bits b required to store the intensity levels (L = 2b).
 image size = M x N x b (bits)
 Typical values of b are:
 b = 1 black and white (binary) images.
 b = 8 grayscale (256 gray levels), or
indexed color images
 b = 24 RGB color image.

Digital Image Resolution
 Digital image resolution is determined by the
number of pixels (samples) in the image.

Digital Image Resolution
 Digital image with low resolution has low
quality.
1024x1024x8 512x512x8 256x256x8
128x128x8 64x64x8 32x32x8

Digital image Types
 RGB (Color) Images
Each pixel is a mixture of
three values of Red, Geen,
and Blue.
R,G,B = {0-255, 0-255, 0-255}
0 = Black
255 = White
In normalized values:
R,G,B = {0-1, 0-1, 0-1}
0 = Black
1 = White

Color Map
Indices
R G BIndex
1
2
3
4
5
6
7
8
.
.
Digital image Types
 Indexed (Color) Images
In order to reduce the color image
size,each pixel is given the index
of a color In a color table (color
map).

Digital image Types
 Grayscale (Intensity) Images
Each pixel is given
a gray level value
between 0 – 255 or
between 0 – 1.
We need 8 bits to
store a grayscale
value.

Digital image Types
 Black and white (Binary) Images
• Each pixel has one of two gray levels either black (0) or white (1).
• We need 8 bits to store a grayscale value.

Types of Pixel Neighborhoods
•Image sampling:
•Rectangular sampling - In most cases, images are sampled by laying
a rectangular grid over an image.
•Hexagonal sampling - An alternative sampling scheme is shown.
•Pixel Neighborhoods:
•4-connected and 8-connected neighborhood (Rectangular sampling)
•6-connected neighborhood (Hexagonal sampling)

Types of Pixel Neighborhoods
4-connected 8-connected 6-connected
 Basic Relationships Between Pixels

Distance Measures
 If pixels p and q have coordinates (x, y) and (s, t),
respectively.
 The Euclidean distance between p and q
 De(p, q) = [(x – s)2 + (y – t) 2] ½
 The D4 (City-block ) distance between p and q
 D4(p, q) = |x – s| + |y – t|
 The D8 (Chessboard ) distance between p and q
 D8(p, q) = max( |x – s| , |y – t| )

Distance Measures
 Results of D4 and D8 distances
 The pixels with D4=1 are the 4-neighbors
 The pixels with D8=1 are the 8-neighbors

Adjacency, Connectivity, Regions, and Boundaries
 Adjacency:
 4-adjacency : Two pixels p and q are 4-adjacent if
q is in the set N4(p).
 8-adjacency. Two pixels p and q are 8-adjacent if
q is in the set N8(p).
 Connectivity: Let S represent a subset of pixels:
 Two pixels p and q are said to be connected in S
if there exists a path between them consisting
entirely of pixels in S.
 the set of pixels that are connected to each other
in S is called a connected component of S.

 Path:
 A (digital) path (or curve) from pixel p with coordinates (x, y)
to pixel q with coordinates (s, t) is a sequence of distinct
pixels with coordinates
(x0 , y0), (x1 , y1), …, (xn , yn)
where (x0 , y0)= (x, y); (xn , yn)= (s, t); and
pixels (xi , yi) and (xi-1 , yi-1) are adjacent for 1<= i <= n.
 In this case, n is the length of the path. If (x0 , y0)= (s, t) the
path is a closed path.
 We can define 4- or 8-paths depending on the type of
adjacency specified.

 Region:
 If R be a subset of pixels in an image, we call R a
region of the image if R is a connected set.
 Boundary:
 The boundary (also called border or contour) of a
region R is the set of pixels in the region that have
one or more neighbors that are not in R.

Types of image Operations
Operation Characterization Complexity/Pixel
Point
the output value at a specific coordinate is
dependent only on the input value at
that same coordinate.
constant
Local
dependent on the input values in the
neighborhood of that same coordinate.
P2
Global
dependent on all the values in the input
image.
N2
 Operation Domain

 Pixel Operations

 Local Operations

 Arithmetic Operations

 Logical Operations

 Sets Operations

 Geometric Operation
(Transformation)

 Space Transformations

 Space Transformation

Categories of Image Operations
 Linear and Nonlinear Operations
 H is said to be a linear operator if, for any two
images f and g and any two scalars a and b,
H( a f + b g ) = a H( f ) + b H( g )
 Operations that do not satisfy this condition is
called nonlinear operations

Homework 1
 Problems:
 Page 72: 2.9, 2.10, 2.11
 Page 73: 2.12, 2.14, 2.15, 2.20

Next time
Image Enhancement
In
The Spatial Domain

Digital Image Processing: Digital Image Fundamentals

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Digital Image Processing: Digital Image Fundamentals