Image coding/compressionImage coding/compression

EE5364 DSP Project

Pradeep Suthram, David Hemmert, Tammo Heeren

All Mathcad files [MCD/PDF] can be found on:http://webpages.acs.ttu.edu/theeren

OverviewOverview

Quantization– Linear quantization– Adaptive quantization

Compression– DCT– JPEG– Wavelet

Linear QuantizationLinear Quantization

Image intensities are quantized into equidistant quantization steps [Mathcad 2001 File]

0 17 34 51 68 85 102 119 136 153 170 187 204 221 238 2550

17

34

51

68

85

102

119

136

153

170

187

204

221

238

255Quantization steps

Grayscale levels

quan

tized

gra

ysca

le le

vels

Linear Quantization resultsLinear Quantization results

1 Bit

8 Bit

Linear Quantization errorLinear Quantization error

Linear Quantization SNRLinear Quantization SNR

1 2 3 4 5 6 7 80

10

20

30

40

50

60SNR vs. grayscale resolution

Grayscale resolution [Bits]

SN

R [

dB]

6.2dB per grayscale bit

Adaptive QuantizationAdaptive Quantization

Quantization steps are scaled by the characteristic image probability density function [Mathcad 2001 File]

0 17 34 51 68 85 102 119 136 153 170 187 204 221 238 2550

17

34

51

68

85

102

119

136

153

170

187

204

221

238

255Quantization steps

Grayscale levels

quan

tized

gra

ysca

le le

vels

0 17 34 51 68 85 102 119 136 153 170 187 204 221 238 2550

17

34

51

68

85

102

119

136

153

170

187

204

221

238

255Quantization steps

Grayscale levels

quan

tized

gra

ysca

le le

vels

Adaptive Quantization resultsAdaptive Quantization results

Adaptive quantization Linear quantization

Adaptive Quantization errorAdaptive Quantization error(adaptive vs. linear)(adaptive vs. linear)

Adaptive Quantization SNRAdaptive Quantization SNR

1 2 3 4 5 6 7 80

10

20

30

40

50

60SNR vs. grayscale resolution

Grayscale resolution [Bits]

SN

R(d

B]

5.6dB per grayscale bit for adaptive quantization [red]6.2dB per grayscale bit for linear quantization [blue]

8x8 pixel block

DCT QuantizerLevel-shift Encoder Data

• Lenna BMP file used

• Gray scale image level-shifted by –128

• for n = 8, 2^(n-1) = 128

JPEG AlgorithmJPEG Algorithm

Quantization

using a typical normalization matrix

[ 16 11 10 16 24 40 51 61

12 12 14 19 26 58 60 55

14 13 16 24 40 57 69 56

14 17 22 29 51 87 80 62

18 22 37 56 68 109 103 77

24 35 55 64 81 104 113 92

49 64 78 87 103 121 120 101

72 92 95 98 112 100 103 99 ]

Encoding

• Zig-Zag Pattern

• Huffman Coding

• Run-length Coding

• Tables

DC

Size | Amplitude

AC

Run/Size | Amplitude

JPEG AlgorithmJPEG Algorithm

To come:To come:

Compression– DCT– JPEG decompression– Wavelet

References:References:

1. Rafael C. Gonzalez, Richard E. Wood, “Digital Image Processing”, Addison Wesley, 1993

2. Geoffrey M. Davis, Aria Nosratinia, “Wavelet-based Image Coding: An Overview”, http://www.geoffdavis.net/

3. Subhasis, Saha, “Image Compression - from DCT to Wavelets : A Review”, http://www.acm.org/crossroads/xrds6-3/sahaimgcoding.html

4. Weidong Kou, “Digital Image Compression Algorithms and Standards,” Kluwer Academic Publishers, 1995.

5. “Selected Papers on Image Coding and Compression,” Majid Rabbani, Ed., Brian J. Thompson, Gen. Ed., SPIE Milestone Series, Vol MS-48, SPIE Optical Engineering Press, 1992.

6. “Fractal Image Compression Theory and Application,” Yuval Fisher, Ed., Springer-Verlag New York, 1995.

7. Bernd Jaehne, “Digital Image Processing”, Third Edition, Springer-Verlag, New York 1995