interpixel redundancy

SUBMITTED BY :NAVEEN KUMARM.E.(ECE), 2011(REGULAR)ROLL NO. : 112610

Data is not the same thing as information. Data is the means with which information is

expressed. The amount of data can be much larger than the amount of information.

Data that provide no relevant information = redundant data or redundancy. Image coding or compression has a goal to reduce the

amount of data by reducing the amount of redundancy

n1 = data. n2 = data − redundancy (i.e., data after

compression). Compression ratio = CR = n1/n2

Relative redundancy = RD = 1 − 1/CR

CR Coding Redundancy.IR Interpixel Redundancy.PVR Psycho-Visual Redundancy

Image compression can be: Reversible (loss less), with no loss of information.

A new image is identical to the original image (after decompression).

Reversibility is necessary in most image analysis applications. The compression ratio is typically 2 to 10 times. Examples are Huffman coding and run-length coding.

Non reversible (lossy), with loss of some information. Lossy compression is often used in image communication,

video,WWW, etc. It is usually important that the image visually is still nice. The compression ratio is typically 10 to 30 times.

There is often correlation between adjacent pixels, i.e., the value of the neighbors of an observed pixel can often be predicted from the value of the observed pixel.

Coding methods: Run-Length coding. Difference coding

Every code word is made up of a pair (g, l) where g is the gray level, and l is the number of pixels with that gray level (length, or “run”).

E.g.,56 56 56 82 82 82 83 8056 56 56 56 56 80 80 80

creates the run-length code (56, 3)(82, 3)(83, 1)(80, 4)(56, 5). The code is calculated row by row.

Very efficient coding for binary data. Important to know position, and the image dimensions must

be stored with the coded image. Used in most fax machines.la University) Image Coding an

Compression Achieved

Original image requires 3 bits per pixel (in total - 8x8x3=192 bits).

Compressed image has 29 runs and needs 3+3=6 bits per

run (in total - 174 bits or 2.72 bits per pixel).

f (xi ) =

E.g.,original 56 56 56 82 82 82 83 80 80 80 80

Code f(xi ) 56 0 0 26 0 0 1 −3 0 0 0

The code is calculated rob by row.

Both run-length coding, and difference coding are reversible, and can be combined with, e.g., Huffman coding

Xi if i = 0,xi − xi-1 if i > 0

Requires no priori knowledge of pixel probability distribution values.

Assigns fixed length code words to variable length sequences.

Patented Algorithm US 4,558,302

Included in GIF and TIFF and PDF file formats

39 39 126 126

39 39 126 126

39 39 126 12639 39 126 126

- Is 39 in the dictionary……..Yes - What about 39-39………….No - Then add 39-39 in entry 256

Dictionary Location Entry

0 01 1. .255 255256 -

511 -

39-39

As the encoder examines image pixels, gray level sequences (i.e., blocks) that are not in the dictionary are assigned to a new entry.

A predictive coding approach. Each pixel value (except at the boundaries) is

predicted based on its neighbors (e.g., linear combination) to get a predicted image.

The difference between the original and predicted images yields a differential or residual image. i.e., has much less dynamic range of pixel values.

The differential image is encoded using Huffman coding.

Digital Image Processing by Gonzalez & Woods

web.uettaxila.edu.pk/CMS/.../notes/Image%20Compression.ppt

hpourreza.profcms.um.ac.ir/imagesm/196/.../ch08-compression.ppt

discovery.bits-pilani.ac.in/discipline/physics/.../compression-II.ppt