1. Department of Physics and Astronomy DIGITAL IMAGE PROCESSING
Course 3624
Topic 3 - Digital Images
Professor Bob Warwick

2. 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”).

3. Analogue versus Digital Image Formats
Analogue Image Digital Image (M x N Pixels) x y
(0,Y)
(0,0)
(X,0)
(X,Y)
f00
f01
f10
f02
f20 x’ y’
fM-1,N-1
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

4. Sampling on a M x N spatial grid:
The two-step process
Sampling on a M x N spatial grid:
Cell size is:
Δx = X/M
Δy = Y/N
Sampling points in x & y are:
x= (x’ + 0.5) Δx
y= (y’ + 0.5) Δy x’ y’ 1 2 .
………

5. Rounded down to an integer
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

6. Quantization Step
2p – 1
2p - 2 2 1
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

7. Construction of a Digital Colour Image
A digital monochrome image consists of a 2-d array of numbers.
A digital colour image consists of three such 2-d arrays (one for each component colour.

8. 3.2 Information Loss in Digitization
Quantization Step
Noise is added equivalent to roughly 1/3 of an ADC step (ie 1 bit)

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

10. 3.3 Image Quality Considerations
Whether 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 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)*
Eg. A high resolution digital camera recording 12 megapixel images in colour will generate files of 36 Mbytes /image (assuming 3 bytes per pixel).
CPU Memory Gbytes (typically)
CD ROMs Gbytes
DVDs Gbytes
Hard Disks Terabyte
Human Brain Terabytes

11. Adjusting the Number of Pixels

12. Adjusting the number of gray levels

13. False contouring at low bit representations

14. Binary Image
Halftone Image

15. 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”.

16. 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.

17. Image Data Compression

18. Effects of JPEG Compression
Maximum quality
38384 bytes
High quality
11331 bytes
Medium quality
6968 bytes
Low quality
5141 bytes
Low quality
3687 bytes
Low quality
1554 bytes