Data Compression Lecture 1 Image Compression The problem
Data Compression Lecture 1
Image Compression? • The problem of reducing the amount of data required to represent a digital image. • From a mathematical viewpoint: transforming the data into a statistically uncorrelated data set. • It is carried out to spare storage space and transmission time.
Why do We Need Compression? • For data STORAGE and data TRANSMISSION • • • DVD Transmission of media content over the internet Remote Sensing Video conference FAX Control of remotely piloted vehicle • The bit rate of uncompressed digital cinema data exceeds 1 Gbps
Information vs Data REDUNDANT DATA INFORMATION DATA = INFORMATION + REDUNDANT DATA
Sources of Data Inflation • Basic data redundancies: 1. 2. 3. Coding redundancy Spatial and temporal redundancy (Inter-pixel redundancy) Irrelevant information (Psycho-visual redundancy)
Coding Redundancy • • • A code is a set of symbols used to represent a body of information or a set of events. Each piece of information is assigned a code word. The number of symbols in the code comprise its length. Length redundancy happens when the code has more bits than required to represent the information. It happens when the coding scheme does not make use of the non-uniformity of intensities probabilities.
Coding Redundancy Let us assume, that a discrete random variable rk in the interval [0, 1] represent the gray level of an image: If the number of bits used to represent each value of rk is l(rk), then the average number of bits required to represent each pixel: The total number bits required to code an Mx. N image: H. R. Pourreza
Coding Redundancy Compression ratio: Relative data redundancy:
Coding Redundancy
Spatial and Temporal redundancy • It happens when the fact that pixels in image neighborhoods (frames) are spatially (temporally) correlated, is not made use of.
Spatial and Temporal redundancy Run-length pairs Original Binary • Run-length pairs is a non visual transformation of the representation. • This kind of transformations is called mapping H. R. Pourreza
Irrelevant Information • It happens when there is information that is not used/ ignored by the related perceptual system or it is extraneous to the intended use. • The basic technique to remedy the problem is omission. • It is a subjective application dependent criterion. H. R. Pourreza
Irrelevant Information Elimination of psych-visual redundant data results in a loss quantitative information. Quantization is used to map a broad range of input values to a limited number of output values. Improved Gray. Scale H. R. Pourreza
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