03 digital image fundamentals DIP

Digital Image Fundamentals: 1

Digital Image FundamentalsDigital Image Fundamentals


Electromagnetic SpectrumElectromagnetic Spectrum


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 AcquisitionExampleExample


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 Nf x y

f M f M f M N

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 aA

a a a





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

2kL [0, 1]L

b M N k

2b 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 Pixel Neighbors 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 y

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

Education

digital zoomingdigital

image sensingimage sensing

f f f n f f f n f x

f x y i x y r x y

x direction

y direction

results of interpolation

bilinear interpolation