03 digital image fundamentals DIP

Digital Image Fundamentals: 1
Digital Image FundamentalsDigital Image Fundamentals

Electromagnetic SpectrumElectromagnetic Spectrum

Attributes of Light SourceAttributes of Light Source
Achromatic or monochromatic light
Intensity: grey level
Chromatic light
Radiance
 measured in watts (W)
 total amount of energy that flows from the light source
Luminance
 measured in lumens (lm)
 gives a measure of the amount of energy an observer perceives
from a light source
Brightness
 a subjective descriptor of light perception that is practically
impossible to measure
 one of the key factors in describing color sensation

Image SensingImage Sensing

Digital Image AcquisitionDigital Image Acquisition
ExampleExample

Simple Image Formation ModelSimple Image Formation Model
( , ) ( , ) ( , )f x y i x y r x y=
0 ( , )f x y< < ∞
0 ( , )i x y< < ∞
0 ( , ) 1r x y< <

Image Sampling and QuantizationImage Sampling and Quantization

ExampleExample

Digital Image RepresentationDigital Image Representation

(0,0) (0,1) (0, 1)
(1,0) (1,1) (1, 1)
( , )
( 1,0) ( 1,1) ( 1, 1)
f f f N
f f f N
f x y
f M f M f M N
− 
 − =
 
 
− − − − 
K
L
M M O M
L
0,0 0,1 0, 1
1,0 1,1 1, 1
1,0 1,1 1, 1
N
N
M M M N
a a a
a a a
A
a a a
−
−
− − − −
 
 
 =
 
 
 
K
L
M M O M
L

M – number of rows
N – number of columns
L – number of gray levels (dynamic range)
b – number of bits required to store a digital image
when M=N
2k
L = [0, 1]L −
b M N k= × ×
2
b N k= ×

Gray-Level ResolutionGray-Level Resolution

Digital ZoomingDigital Zooming
Zooming requires two steps
Creation of new pixel locations
Assignment of grey levels to those new locations

Nearest neighbor interpolation
Look for closest pixel in original image
Pixel replication
Fast but causes undesirable checkerboard effect

Bilinear interpolation
Determines pixel value based on four nearest neighbors
Do linear interpolation in x direction
Do linear interpolation in y direction based on results of
interpolation from x direction
Does not suffer from checkerboard effect but can result in a blurred
appearance

Bicubic Interpolation
Determines pixel value based on sixteen nearest neighbors
Do cubic spline interpolation in x direction
Do cubic spline interpolation in y direction based on results of
interpolation from x direction
Does not suffer from checkerboard effect like nearest neighbor
interpolation and preserves fine details better than bilinear
interpolation

Neighbors of a PixelNeighbors of a Pixel
A pixel p at coordinates (x,y) has four horizontal and vertical
neighbors called 4-neighbors
The four diagonal neighbors of a pixcel are
N4(p) and ND(p) are combined to make 8-neighbors ( N8(p) )
4 ( ) ( 1, ),( 1, ),( , 1),( , 1)N p x y x y x y x y→ + − + −
( ) ( 1, 1),( 1, 1),( 1, 1),( 1, 1)DN p x y x y x y x y→ + + + − − + − −

AdjacencyAdjacency
Let V be the set of gray-level values used to define adjacency
4-adjacency. Two pixels p and q with values from V are
4-adjacent if q is in the set N4(p)
8-adjacency. Two pixels p and q with values from V are
8-adjacent if q is in the set N8(p).
m-adjacency (mixed adjacency). Two pixels p and q with
values from V are m-adjacent if:
 q is in N4(p), or
 q is in ND(p) and the set has no pixels whose
values are from V.
Two image subsets S1 and S2 are adjacent if some pixel in S1 is
adjacent to some pixel in S2.
4 4( ) ( )N p N q∩

ConnectivityConnectivity
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:
where
and pixels (xi,yi) and (xi-1,yi-1) are adjacent for
if
the path is a closed path
Let S represent a subset of pixels in an image.
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.
For any pixel p in S, the set of pixels that are connected to it in S is
called a connected component of S
0 0 1 1( , ),( , ), ,( , )n nx y x y x yL
0 0( , ) ( , ),( , ) ( , )n nx y x y x y s t= =
1 i n≤ ≤
0 0( , ) ( , )n nx y x y=

Regions and BoundariesRegions and Boundaries
Let R be a subset of pixels in an image
R is a region of the image if R is a connected set.
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.
If R happens to be an entire image, then its boundary is defined
as the set of pixels in the first and last rows and columns of the
image.

Distance MeasuresDistance Measures
For pixels p, q, and z, with coordinates (x, y), (s, t), and (v, w),
respectively, D is a distance function if
The Euclidean distance between p and q is defined as:
( ) ( , ) 0 ( ( , ) 0 iff )
( ) ( , ) ( , ), and
( ) ( , ) ( , ) ( , )
a D p q D p q p q
b D p q D q p
c D p z D p q D q z
≥ = =
=
≤ +
2 2
( , ) ( ) ( )eD p q x s y t= − + −

Distance MeasuresDistance Measures
The D4 distance (city-block distance) between p and q is defined as:
The D8 distance (chessboard distance) between p and q is defined as:
4 ( , )D p q x s y t= = − + −
2
2 1 2
2 1 0 1 2
2 1 2
2
( )8 ( , ) max ,D p q x s y t= = − −
2 2 2 2 2
2 1 1 1 2
2 1 0 1 2
2 1 1 1 2
2 2 2 2 2

03 digital image fundamentals DIP

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03 digital image fundamentals DIP