![ Let a discrete random variable r k in [0,1] represent the gray
levels of an image.
pr(rk ) denotes the probability of occurrence of r
Pr(rk) = nk / n , k=0,1,2,….L-1
If the number of pixels used to represent each value of rk is
l(rk ), then the average number of bits required to represent
each pixel is
L-1
Lavg = £ l(rk)pr(rk)
k=0
CODING REDUNDANCY](https://image.slidesharecdn.com/fundamentalsandimagecompressionmodels-180818131548/85/Fundamentals-and-image-compression-models-5-320.jpg)
Fundamentals and image compression models
- 1. Presented by M.Lavanya M.Sc (cs & it) Nadar Saraswathi College of arts & science Theni.
- 2. Need for Compression: Huge amount of digital data Difficult to store and transmit Solution: Reduce the amount of data required to represent a digital image Remove redundant data Transform the data prior to storage and transmission Categories: Information Preserving Lossy Compression
- 3. Data compression Difference between data and information Data Redundancy If n1 and n2 denote the number of information-carrying units in two datasets that represent the same information , the relative data redundancy RD of the first dataset is defined as RD = 1-1/CR , where CR = n1/n2 is called the compression ratio
- 4. In digital image compression, three basic data redundancies can be identified and exploited: Coding Redundancy Interpixel Redundancy Psychovisual Redundancy Fidelity Criteria
- 5. Let a discrete random variable r k in [0,1] represent the gray levels of an image. pr(rk ) denotes the probability of occurrence of r Pr(rk) = nk / n , k=0,1,2,….L-1 If the number of pixels used to represent each value of rk is l(rk ), then the average number of bits required to represent each pixel is L-1 Lavg = £ l(rk)pr(rk) k=0 CODING REDUNDANCY
- 6. Hence, the total number of bits required to code an MxN image is MNLavg For representing an image using an m-bit binary code , Lavg= m. Example of variable length coding
- 7. Related to interpixel correlation within an image. The value of a pixel in the image can be reasonably predicted from the values of its neighbors. Information carried by individual pixels is relatively small. These dependencies between values of pixels in the image are called interpixel redundancy
- 10. Based on human perception Associated with real or quantifiable visual information. Elimination of psychovisual redundancy results in loss of quantitative information. This is referred to as quantization. Quantization - mapping of a broad range of input values to a limited number of output values. Results in lossy data compression.
- 13. Criteria Subjective: based on human observers Objective : mathematically defined criteria
- 15. Encoder - Source encoder + Channel encoder Source encoder Removes coding, interpixel, and psychovisual redundancies in input image and outputs a set of symbols. Channel encoder To increase the noise immunity of the output of source encoder. Decoder - Channel decoder + Source decoder
- 16. Mapper • Transforms input data into a format designed to reduce interpixel redundancies in input image. • Reversible process generally • May or may not reduce directly the amount of data required to represent the image. Examples • Run-length coding(directly results in data compression) •Transform coding
- 18. Essential when the channel is noisy or error-prone. Source encoded data - highly sensitive to channel noise. Channel encoder reduces the impact of channel noise by inserting controlled form of redundancy into the source encoded data. Example: Hamming Code – appends enough bits to the data being encoded to ensure that two valid code words differ by a minimum number of bits.
- 19. 7-bit Hamming(7,4) Code 7-bit code words 4-bit word 3 bits of redundancy Distance between two valid code words (the minimum number of bit changes required to change from one code to another) is 3. All single-bit errors can be detected and corrected. Hamming distance between two code words is the number of places where the code words differ. Minimum Distance of a code is the minimum number of bit changes between any two code words. Hamming weight of a codeword is equal to the number of non- zero elements (1’s) in the codeword
- 20. The 7-bit Hamming (7,4) code word h1,h2,….h5,h6,h7 associated with a 4-bit binary number b3,b2,b1,b0 is
- 21. The principal objectives of digital image compression to describe the most commonly used compression methods that form core of technology as it exits currently. Gray – scale imagery , compression methods are playing an increasingly important role in document image storage and transmission.