Contemporary issues in IT

1. Contemporary issues in IT Lecture 2 Tuesday Lecture 10:00 – 12:00, Room 3.27 Lab 13:00 – 15:00, Lab 6.12 Lecturer: Dr Abir Hussain Room 633, a.hussain@ljmu.ac.uk Lecture 2

2. Lecture contents • Introduction to lossy image compression methods • Differential pulse code modulation. • Vector quantisation. • Transform coding.

3. Previous lecture • Introduction to the concept of image compression • Various image lossless compression methods were studied.

4. Introduction • In contrast to error free coding, lossy image compression reduces the accuracy of the coded image in exchange for higher compression ratio. • At the encoder, there exists a quantiser which limits the number of bits required to represent the image • The purpose of the quantiser is to remove psychovisual redundancy.

5. Introduction • There are different approaches to lossy image compression such as • vector quantisation • predictive coding also known as differential pulse code modelation • transform coding

6. Introduction • Predictive coding image compression uses previous values obtained during the scanning of the image to predict the next value along the line.

7. Introduction • Transform coding differs from predictive coding by dividing the image into a number of blocks.

8. Introduction • Vector quantisation has wide areas of application, such as speech coding, speech recognition and image coding.

9. Predictive coding • Pixels in images show a high degree of correlation among their neighbouring samples. • A high degree of correlation means a high degree of redundancy in the raw data. • If the redundancy is removed by decorrelating the data, much more efficient and better compressed coding of the signal is obtained

10. Predictive coding (DPCM) • Predictive coding uses values of the previous samples to estimate the value of the next sample in the raw data. • The difference between the actual value of the signal and the estimate value is quantised and transmitted through the digital channel or stored. • the better the prediction, the smaller the transmitted error, hence the better the coding process.

11. Predictive coding (DPCM) • The predictors are classified into linear and nonlinear types. • For linear predictors, the previous samples are linearly coded to predict the current value • Nonlinear predictors use nonlinear functions for coding the previous samples

12. Predictive coding • There are two types of quantiser structures, uniform and non-uniform quantisers. • The uniform quantiser uses the same value of separation between its levels. • Non-uniform quantisers use different separations between their levels. • Since the probability of the errors has a non-uniform distribution, then the design of non-uniform quantisers is more appropriate to predictive coding systems than uniform quantisers.

13. Structure of the predictive coding system • The system is constructed from two parts, the transmitter and the receiver.

14. Quantisation • Quantisation is the process of reducing the representation of signals to a limited number of discrete values. • Each set of inputs is represented by an approximate output value. • The sets of inputs are called decision levels and the sets of representation outputs are called reconstruction levels.

15. Quantisation

16. Quantisation

17. Transform coding • Transform coding is one of the classical approaches to image compression. • It is a block coding technique, where the image is divided into nonoverlapping subimages. • A linear reversible transform operation is performed to each subimage and the pixel values are mapped to transform coefficients having small or zero values.

18. Transform coding • The transformed coefficients with high values are quantised and transferred to the decoder or stored for latter processing • The small transform coefficient values are deleted

19. Transform coding • Transform coding achieves high compression due to three mechanisms. • Transform coding is a block technique where a block of data is processed rather than a single element of the image. • The quantisation of the transformed coefficients results in removing the correlation defined among the pixels of each subimage. • Not all transformed coefficients are quantised and transmitted to the receiver

20. Transform coding

21. Processing of the transformed coefficients

22. Vector quantisation • Vector quantisation is a block technique used in various applications, such as speech coding, image coding and speech recognition. • It is superior to predictive and transform coding because it achieves optimal rate distortion performance subject to constraints on the memory or block length of the observable signal segment being encoded

23. Vector quantisation

24. Vector quantisation • In vector quantisation, the image is divided into nonoverlapped blocks and each block is transferred into one-dimensional vectors. • The element values of the transferred one-dimensional vector are compared to different vectors provided in a lookup table known as the codebook • The index of the location of the codebook vector (codeword) that gives the minimum distortion is transmitted to the receiver.

25. Vector quantisation • At the decoder, the same lookup table is used and the vector is reconstructed from the index provided from the encoder.

26. Vector quantiser design • classical approach in this case is the one reported by Linde and two more researchers. • known as the LBG algorithm • The algorithm assumes the presence of an initial codebook and a training set for implementing an optimal vector quantiser

27. Vector quantiser design (LBG algorithm) • Assume the presence of an initial N-level alphabet codebook • A = {yi, i =1,......,N} • training set TS = {xi, i = 1,......n} which contain n-vectors and n > N. • Suppose a distortion reduction threshold value  is defined with the iteration index m = 0 and the initial distortion Dm-1 = a very large number.

28. LBG algorithm • The LBG algorithm works using the following two steps: • Step one: Find the partition P(A) = { S1, S2,........SN} such that: • Then compute

29. LBG algorithm • if (Dm-1 –Dm)/Dm >  Go to step two Else • The fractional in distortion between successive iterations, m-1 and m, as D converges to its asymptotic value, i is acceptably low. Therefore, Am is the desired codebook

30. LBG algorithm • Step two: Determine the centroids of all Si in Am to give the optimal set of yi. Therefore Am is now Am+1, and the procedure returns to step one.

31. Today’s lab • In today’s lab, we will be given two images in which you have to decided which one is the original image and which one is the compressed. • You will learn how to be able to determine the non-compressed images.

32. Summary • There are various image compression techniques. • Three classical lossy image compression techniques include vector quantisation, predictive coding and transform coding