Topic 3 - Digital Images

DIGITAL IMAGE PROCESSING

Course 3624

Department of Physics and Astronomy

Professor Bob Warwick

3.1 What is a Digital Image?

• An analogue image is a 2-dimensional (2-d) continuous light intensity distribution, , where x and y are spatial coordinates.

• A digital image is a representation of the continuous (analogue) image by a 2-d array of numbers.

• The digital image is obtained by sampling at points on a regular grid. The amplitude at each sampling point is quantized, and represented (initially) as a binary number.

Notes: • After processing the digital image may be stored as a 2-d

array of integers, real or complex numbers.• Each element of the 2-d array is a pixel (derived from

“picture element”).

Analogue versus Digital Image Formats

Analogue Image Digital Image (M x N Pixels)

x

y (0,Y)(0,0)

(X,0) (X,Y)

Continuous variables x,y

x = 0 X

y = 0 Y

Indices x’,y’

x' = 0,1,2 M-1

y' = 0,1,2 N-1

f00 f01

f10 f02

f20x’

y’

fM-1,N-1

The two-step process

Sampling on a M x N spatial grid:

Cell size is:Δx = X/MΔy = Y/N

Sampling points in x & y are:x= (x’ + 0.5) Δxy= (y’ + 0.5) Δy

x’

y’

0 1 2...

0 1 2 ………

Quantization Step

where p is an integer which defines the number of

quantization levels, eg p = 8 implies 256 levels.

Then assign:

Rounded down to

an integer

value

Quantization Step

The exponent p corresponds to the number of bits in the Analogue-to-Digital conversion employed in the digitization.

Notes: Hereafter = the "gray level"

Range 0 2P-1 is known as the grayscale of the image

2p – 1

2p - 2

2

1

0

A digital monochrome image consists of a 2-d array of numbers.

Construction of a Digital Colour Image Construction of a Digital Colour Image

A digital colour image consists of three such 2-d arrays (one for each component colour.

3.2 Information Loss in Digitization

Noise is added equivalent to roughly 1/3 of an ADC step (ie 1 bit)

Quantization Step

Information Loss in Spatial Sampling

The above depicts two sinusoidal signals in an input 1-d (analogue) image that fit the same set of sample values.

x

If the input contains signals varying such that:

signal rate > sampling rate/2

then information may be lost (as above).

This problem is known as ALIASING – see topic 7.

3.3 Image Quality ConsiderationsWhether an image is classed as of “good”, “moderate” or “poor” quality” is invariably a very subjective assessment, dependent to a large degree on the amount of detail in the scene.

As a “rule-of-thumb” a grayscale image with:

512 x 512 pixels with 32 gray levels

will be comparable to an old b/w TV picture.

Nb 8 binary bits = 1 byte = 256 levels

1024 x 1024 x 1 byte 1 Megabyte (eg CPU memory)

1000 x 1000 x 1 byte 1 Megabyte (eg computer storage)*

CPU Memory - 2-8 Gbytes (typically)

CD ROMs - 0.6-0.9 Gbytes

DVDs - 4.7 Gbytes

Hard Disks - 1 Terabyte

Human Brain - 125 Terabytes

Eg. A high resolution digital camera recording 12 megapixel images in colour will generate files of 36 Mbytes /image (assuming 3 bytes per pixel).

Adjusting the Number of Pixels

Adjusting the number of gray levels

False contouring at low bit representations

Halftone ImageBinary Image

3.4 Image File Formats and Image Compression

Image file formats are standardized means of organizing and storing digital images. They consist of "header information" followed by the "image data".

The different image file formats apply a variety of image file compression algorithms to reduce the image file size for storage:

Lossless compression algorithms reduce file size without losing information (ie are error-free) - used when image integrity is valued above file size (eg scientific data).

Lossy compression algorithms take advantage of the inherent limitations of the human eye and discard "redundant" information. Most lossy compression algorithms allow for a variable quality level and compression ratio. As the latter is increased, file size is reduced. At the highest compression levels, when the image is decompressed (ie reconstructed), image deterioration becomes noticeable as "compression artefacting”.

Some Popular Image File Formats

JPG/JPEG (Joint Photographic Experts Group) is a compression method which (in most cases) is lossy. Nearly every digital camera can save images in JPEG format. It supports 8-bits per colour. The compression ratio is selectable.

GIF (Graphics Interchange Format) is limited to an 8-bit palette, or 256 colors. This makes the GIF format suitable for storing graphics with relatively few colours such as simple diagrams, shapes, logos and cartoon style image. It also supports animation. It uses a lossless compression that is most effective when large areas have a single colour, and ineffective for detailed images.

FITS (Flexible Image Transport System) is often used for scientific applications. It stores the original (image) data in a structured way.

Image Data Compression

M

Effects of JPEG Compression

Maximum quality

38384 bytes

Low quality

3687 bytes

Low quality

5141 bytes

High quality

11331 bytes

Medium quality

6968 bytes

Low quality

1554 bytes