This document discusses lossy compression techniques for multimedia elements. It covers lossy compression algorithms, distortion measures like MSE and PSNR, rate-distortion theory, quantization methods including scalar, non-uniform scalar and vector quantization, and transform coding techniques like DCT and DWT. It also discusses embedded zerotree wavelet coding and its use of the zerotree data structure and successive approximation quantization.

1. Course : COMP7094 – Multimedia
Programming Foundation
Effective Period: February 2018
Multimedia Data
Compression II
Session 10
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2. Learning Outcomes
• LO 2: Select multimedia elements builder
• LO 3: Compare formats in multimedia elements
Introduction to Multimedia
Introduction to Multimedia

3. COURSE OUTLINE
• Lossy Compression Algorithm
• Kind of Coding
Introduction to Multimedia
Introduction to Multimedia

4. LOSSY COMPRESSION
• The Compression ratio for image data using lossless
compression techniques ( Huffman Coding, Arithmetic
Coding, LZW) is low when the image histogram is
relatively flat.
• Lossy methods are usually adopted for image
compression in multimedia application where a higher
compression ratios is required.
• In Lossy compression , the compressed image is
usually not the same as the original image, but it is
approximation to the original image perceptually.
• So, the distortion measure is required to describe
quantitatively how close the approximation to the
original data.
Introduction

5. LOSSY COMPRESSION
• A distortion Measure is a mathematical quantity that
specifies how close an approximation is to its original.
• There are three distortion measure most commonly
used in image compression :
– The mean square error (MSE)
• If interested in the average pixel difference
• Where xn, yn, N are the input data sequence ,
reconstructed data sequence, and length of the
data sequence.
Distortion Measure

6. LOSSY COMPRESSION
• There are three distortion measure most commonly
used in image compression (Con’t) :
– Measure the Signal-to-Noise ratio (SNR)
• If interested in the size of the error relative to the
signal
• Where is the average square value of the
original data and is the MSE
Distortion Measure

7. LOSSY COMPRESSION
• There are three distortion measure most commonly
used in image compression (Con’t) :
• The peak-signal-to-noise ratio (PSNR)
– Which measures the size of the error relative
to the peak value of the signal xpeak
Distortion Measure

8. LOSSY COMPRESSION
• Lossy compression always involves a tradeoff between
rate and distortion .
• Rate is the average number of bits required to represent
each source symbol.
• The tradeoff between rate and distortion is represented
in the form of a rate-distortion function R(D).
• The rate-distortion function is meant to describe a
fundamental limit for the performance of a coding
algorithm and can be used to evaluate the performance
of different algorithms.
The Rate-Distortion Theory

9. LOSSY COMPRESSION
• Figure 1 show a typical rate-distortion function. The
minimum possible rate at D = 0 , no loss, is the entropy
of the source data.
• The distortion corresponding to a rate R (D) ≡ 0 is the
maximum amount of distortion incurred when “nothing”
is coded.
The Rate-Distortion Theory
Figure 1 Typical rate-
distortion function

10. LOSSY COMPRESSION
• Without quantization , it would losing little information.
• The input and output of each quantizer can be scalar
values or vector values.
• There are three quantizers :
– Uniform Scalar Quantization
• The goal is to minimize the distortion for a given
source input with a desired number of output
values.
– Non Uniform Scalar Quantization
• There are two common approaches :
– Llyod-Max Quantizer and Companed
Quantizer.
Quantization

11. LOSSY COMPRESSION
• There are three quantizers (continue):
– Vector Quantization (VQ)
• In VQ an n-component code vector represents
vectors that lie within a region in n-dimensional space.
• A collection of these code vectors forms the codebook
for the vector quantizer.
• In Fig. 2 the encoder find the closet code vector to the
input vector and outputs the associated index.
• On the decoder side , exactly the same codebook is
used. When the coded index of the input vector is
received , a simple table lookup is performed to
determine the reconstruction vector.
Quantization

12. LOSSY COMPRESSION
• The basic vector quantization procedure ( Fig.2)
Quantization
Figure 2 Basic Vector Quantization Procedure

13. KIND OF CODING
• There are three transform coding technique :
– Discrete Cosine Transform ( DCT)
• Able to perform decorrelation of the input signal in a
data-independent number manner
– Wavelet-based coding
• Represents a signal with good resolution in both time
and frequency , by using a set of basis functions
called wavelet.
• There are two types of wavelet transforms :
– The Continuous Wavelet Transform (CWT)
– The Discrete Wavelet Transform (DWT)
Transform Coding

14. KIND OF CODING
• The embedded Zerotree algorithm introduced by Shapiro is
an effective and computationally efficient technique in image
coding.
• This algorithm (EZW) addresses two problems :
– Obtaining the best image quality for a given bitrate
– Accomplishing this task in an embedded fashion
• An embedded code is one that contains all lower rate coded
“embedded’ at the beginning of the bit stream.
• An embedded allows the encoder to terminate the encoding
at any point and thus meet any target bitrate exactly.
• Similarly a decoder can cease to decode at any point and
produce reconstructions corresponding to all lower rate
encodings.
Embedded Zerotree of Wavelet Coefficients

15. KIND OF CODING
• Similarly a decoder can cease to decode at any point and
produce reconstructions corresponding to all lower rate
encodings.
• The EZW algorithms consists of two central components :
– the zerotree data structure
– The method of successive approximation quantization
Embedded Zerotree of Wavelet Coefficients

16. REFERENCES
• https://www.coleyconsulting.co.uk/lossy_compression_pt1
.htm
• https://www.sqa.org.uk/e-
learning/BitVect01CD/page_86.htm
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