28378019 Digital Image Processing 2

8/8/2019 28378019 Digital Image Processing 2

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Chapter Two

Digital Image Fundamentals


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Agenda:

Light and Electromagnetic SpectrumImage Sensing & Acquisition

Image Sampling & quantization

Relationship Between Pixels


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Electromagnetic Spectrum

Wavelength = c/ (frequency )

Energy = h* frequency


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Definitions

Monochromatic (achromatic) light: Light that isvoid of color- Attribute: Intensity (amount) .

- Gray level is used to describe monochromatic intensity.

Chromatic light: To describe it, three quantitiesare used:- Radiance: The total amount of energy that flows from the light

source (measured in Watts).

- Luminance: The amount of energy an observer perceives from

a light source (measured in lumens).

- Brightness: A subjective descriptor of light perception that is

impossible to measure (key factor in describing color sensation)


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Image Sensing & Acquisition

How to transform

illumination energy

into digital images

using sensing

devices


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Image Sensing & Acquisition

Image Acquisition using single sensor


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Image Sampling

Continues image

f(x,y) needs to be

in digital form.

Digitizing the

coordinate values

called sampling.

Sampling shouldbe in both

coordinates and

in amplitude.


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Digitizing the Amplitude

values called image

quantization.

Sampling limits

established by no. of

sensors, but quantizationlimits by color levels.

Image Quantization


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Digital Image Representation

Each element called image element, picture

element, or pixel


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Consider an image which has :

M * N : size of the image

L : Number of discrete gray levels in this image

L= 2k Where k is any positive integer

The total number of bits needed to store this image b :

b = M * N * K,

If M = N, then b= N2 * K


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The dynamic range of an image can be described as:

High dynamic range:

Gray levels span a significant portion of the grayscale.

Low dynamic range:

Dull, washed out gray look.


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Spatial resolution:

- # of samples per unit length or area.

- Lines and distance: Line pairs per unit distance.

Gray level resolution:

- Number of bits per pixel.

- Usually 8 bits.

- Color image has 3 image planes to yield 8 x 3 = 24bits/pixel.

- Too few levels may cause false contour.


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Spatial Image Resolutions

No. of gray levels (K) is constant(8-bits images).

No. of samples (N) is reduced (No. of sensors)


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Comparison between all image sizes


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Gray Level Image Resolutions

No. of samples (N) is constant, but gray levels (K) decreases.

(false contouring)


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Little, Intermediate, and Large amount of details

What is the effect of changing N and K..?


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Isopreference Curve


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Zooming (digital image) can be viewed by

oversampling (continuous image).

1- Creation of new pixel locations

2- Assign a gray level value to this new location

using :

Nearest neighbor interpolation (Pixel replication )

Bilinear interpolation


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Shrinking (digital image) can be viewed by

undersampling (continuous image).

1- Deletion of row column pixels.

2- Assign a gray level value using :

Nearest neighbor interpolation

Bilinear interpolation



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Image Zoomed by 8, 16, 32 usingnearest neighbor interpolation


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Image Zoomed by 8, 16, 32 usingbilinear interpolation


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1- Neighbors of a Pixel:

The 4- neighbors of pixel p are:

N4(p)

The 4- diagonal neighbors are:

ND(p)

The 8-neighbors are :

N8(p)

P

P

P


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2- Adjacency of Pixel: Two pixels are adjacent if

their values are in the same (binary image).

4-Adjacency:Two pixels p and q with values from V

are 4-adjacent if q is in the setN4(p).

8- Adjacency:Two pixels p and q with values from V

are 8-adjacent if q is in the set N8(p).



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m- Adjacency:Two pixels p and q with values from V arem-adjacent if

- q is in the set N4(p) or

- q is in ND(p) and the set N4(p) N4(q) has no pixels

whose values are from V.


8-adjacent, m-adjacent


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Two image area subsets S1 and S2 are

adjacent if some pixel in S1 is adjacent

to some pixel in S2.


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Digitalpath (orcurve):a path 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

(xi,yi) is adjacent to (xi-1,yi-1)

n is the length of the path


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we can define 4-,8-, or m-paths depending

on type of adjacency specified.

8-adjacent, m-adjacent


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Distance Measures

for pixel p, q and z with coordinates

(x,y), (s,t) and (u,v) respectively, D is a distance function or metric if

(a) D(p,q) 0 ; D(p,q) = 0 iff D=q

(b) D(p,q) = D(q,p)

(c) D(p,z) D(p,q) + D(q,z)



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Distance Measures:

1- The Euclidean distance between p and q is

defined as:



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Distance Measures:

2- TheD4distance (city-block distance) between p

and q is defined as:



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Distance Measures:

3- TheD8distance (chessboard distance) between p

and q is defined as



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Distance Measures:

4- TheDmdistance: the shortest m-path between the

points.



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Image Operations on a Pixel Basis

used extensively in most branches of image processing.

Addition : p+q used in image average to reduce noise.

Subtraction : p-q basic tool in medical imaging. Multiplication : pxq

Division : pq

Arithmetic Operation entire images are carried out pixel by pixel.

AND : p AND q (pq)

OR : p OR q (p+q)

COMPLEMENT : NOT q ( ) logic operations apply only to binary images.

arithmetic operations apply to multivalued pixels. logic operations used for tasks such as masking, feature detection, and shape

analysis. logic operations perform pixel by pixel.


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Linear and Nonlinear Operations

H is a Linear operator if:

H(af + bg) = aH(f) + bH(g)

where a and b are two scalars

f and g are two images

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28378019 Digital Image Processing 2