Image Compression 3112021 Image Compression 1 Reference 1

Image Compression 3/11/2021 Image Compression 1

Reference [1] Gonzalez and Woods, Digital Image Processing. 3/11/2021 Image Compression 2

Objective • Reduce the number of bytes required to represent a digital image – Redundant data reduction – Remove patterns – Uncorrelated data confirms redundant data elimination • Auto correlation? 3/11/2021 Image Compression 3

Enabling Technology • Compressions is used in – FAX – RPV – Teleconference – REMOTE DEMO – etc 3/11/2021 Image Compression 4

Review • • What and how to exploit data redundancy Model based approach to compression Information theory principles Types of compression – Lossless, lossy 3/11/2021 Image Compression 5

Information recovery Data Processing Information • We want to recover the information, with reduced data volumes. • Reduce data redundancy. • How to measure the data redundancy. 3/11/2021 Image Compression 6

Relative Data Redundancy • Assume that we have two data sets D 1 and D 2. – Both on processing yield the same information. – Let n 1 and n 2 be the info – carrying units of the respective data sets. – Relative data redundancy is defined on comparing the relative dataset sizes RD = 1 – 1/CR where CR is the compression ratio CR = n 1 / n 2 3/11/2021 Image Compression 7

Examples • • RD = 1 – 1/CR CR = n 1 / n 2 D 1 is the original and D 2 is compressed. When CR = 1, i. e. n 1 = n 2 then RD=0; no data redundancy relative to D 1. When CR = 10, i. e. n 1 = 10 n 2 then RD=0. 9; implies that 90% of the data in D 1 is redundant. What does it mean if n 1 << n 2 ? 3/11/2021 Image Compression 8

Types of data redundancy • Coding • Interpixel • Psychovisual 3/11/2021 Image Compression 9

Coding Redundancy • How to assign codes to alphabet • In digital image processing – Code = gray level value or color value – Alphabet is used conceptually • General approach – Find the more frequently used alphabet – Use fewer bits to represent the more frequently used alphabet, and use more bits for the less frequently used alphabet 3/11/2021 Image Compression 10

Coding Redundancy 2 • Focus on gray value images • Histogram shows the frequency of occurrence of a particular gray level • Normalize the histogram and convert to a pdf representation – let rk be the random variable pr(rk) = nk/n ; k = 0, 1, 2 …. , L-1, where L is the number of gray level values l(rk) = number of bits to represent rk Lavg = k=0 to L-1 l(rk) pr(rk) = average number of bits to encode one pixel. For M x N image, bits required is MN Lavg For an image using an 8 bit code, l(rk) = 8, Lavg = 8. Fixed length codes. 3/11/2021 Image Compression 11

Fixed vs Variable Length Codes From [1] Lavg = 2. 7 CR= 3/2. 7 = 1. 11 RD = 1 – 1/1. 11 = 0. 099 3/11/2021 Image Compression 12

Code assignment view From [1] 3/11/2021 Image Compression 13

Interpixel Redundancy From [1] 3/11/2021 Image Compression 14

Run Length Coding From [1] CR=1024*343/12166*11 = 2. 63 RD = 1 -1/2. 63 = 0. 62 3/11/2021 Image Compression 15

Psychovisual Redundancy • Some visual characteristics are less important than others. • In general observers seeks out certain characteristics – edges, textures, etc – and the mentally combine them to recognize the scene. 3/11/2021 Image Compression 16

From [1] 3/11/2021 Image Compression 17

From [1] 3/11/2021 Image Compression 18

Fidelity Criteria • Subjective • Objective – Sum of the absolute error – RMS value of the error – Signal to Noise Ratio 3/11/2021 Image Compression 19

Subjective scale From [1] 3/11/2021 Image Compression 20

Image Compression Model Run length 3/11/2021 JPEG Image Compression Huffman From [1] 21