Distance measures in Image in Digital Image Processing

MODERN INSTITUTE OF
ENGINEERING AND TECHNOLOGY
NAME- ARKA SAHOO
ROLL NO- 26900321025
DEPT- ECE
7TH
SEMESTER, 4TH
YEAR
SUBJECT- DIGITAL IMAGE PROCESSING
PAPER CODE- PE-EC702B

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
g(x,y)
y
of g is proportional to
the brightness (or gray
level)
of the image at that
point. x

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.
n
I(m,n)

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

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

 Sampling & Quantization

 Effect of Quantization
256 128 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(2,1) i(2,2)
.
. .
.
……. i(1, n-
1)
……. i(2, n-
1)
.
. . .
.
I(mn) =
i(m-1,1) i(m-1,2) … i(m-1, n-1)
•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
 b = 8
black and white (binary) images.
grayscale (256 gray levels), or
 b = 24
indexed color images
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
G B
Index R
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
 D (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

Distance measures in Image in Digital Image Processing

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