# Digital Image Processing

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```					Digital Image Processing

Chapter 2: Digital Image
Fundamentals
Elements of Visual Perception

   Structure
of the
human
eye
   Rods and cones in the retina
   Image formation in the eye
discrimination
   Brightness discrimination
   Weber ratio
   Perceived
brightness
   Simultaneous contrast
   Optical
illusion
Light and the Electromagnetic
Spectrum
   Wavelength
c


E  h
Image Sensing and Acquisition
   Image acquisition using a single
sensor
   Using
sensor
strips
   A simple
image
formation
model
   Illumination and reflectance
   Illumination and transmissivity

f ( x, y)  i( x, y)r ( x, y)
Image Sampling and Quantization
   Sampling
and
quantization
   Representing digital images
   Saturation and noise
   Number of storage bits
   Spatial and gray-level resolution
   Subsampled
and
resampled
   Reducing
spatial
resolution
   Varying
the
number
of gray
levels
   Varying
the
number
of gray
levels
   N and k in different-details images
   Isopreference
   Interpolations
   Zooming
and
shrinking
Some Basic Relationships Between
Pixels

   Neighbors of a pixel
     N 4 ( p) : 4-neighbors of p
( x  1, y ), ( x  1, y ) , ( x, y  1) , ( x, y  1)

N D ( p ) : four diagonal neighbors of p
( x  1, y  1) , ( x  1, y  1) , ( x  1, y  1) ,
( x  1, y  1)
N 8 ( p) : 8-neighbors of p
N 4 ( p) and N D ( p )
   V : The set of gray-level values used
   4-adjacency: Two pixels p and   q with
values from V are 4-adjacency   if q is in
the set N 4 ( p)
   8-adjacency: Two pixels p and   q with
values from V are 8-adjacency   if q is in
the set N 8 ( p)
pixels p and q with values from V are
 q is in N 4 ( p) , or
 q is in N ( p )and the set N 4 ( p )  N 4 ( q )
D
has no pixels whose values are from V
   S1 and S2 are adjacent if some pixel in
S1 is adjacent to some pixel in S2
   Path
 A path from 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 , y n )
where ( x0 , y0 )= ( x, y ) , ( xn , yn ) = ( s, t ) ,
and pixels ( xi , yi ) and ( xi 1 , yi 1 ) are
   Region
   We call R a region of the image if R is a
connected set
   Boundary
   The boundary of a region R is the set of
pixels in the region that have one or
more neighbors that are not in R
   Edge
   Pixels with derivative values that
exceed a preset threshold
   Distance measures
   Euclidean distance
1
De ( p, q )  [( x  s ) 2  ( y  t ) ]
2 2

   City-block distance
D4 ( p, q) | ( x  s) |  | ( y  t ) |

   Chessboard distance
D8 ( p, q)  max(| ( x  s) |, | ( y  t ) |)
   Dm distance: The shortest m-path
between the points
An Introduction to the Mathematical
Tools Used in Digital Image Processing

   Linear operation
   H is said to be a linear operator if, for
any two images f and g and any two
scalars a and b,

H (af  bg )  aH ( f )  bH ( g )
   Arithmetic
operations
   Arithmetic
operations
   Subtraction
   Digital
subtraction
angiography
   Image multiplication
   Set operations
   Complements
   Logical
operations
   Single-
pixel
operations
   Neighborhood
operations
   Affine transformations
   Inverse mapping
   Registration
   Vector
operations
   Image transforms
   Fourier transform
   Probabilistic methods

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