Data compression

Data compression

• lossless – looking for unicolor areas or repeating patterns– Run length encoding– Dictionary compressions

• Lossy

– reduction of colors

- approximating methods (JPEG)

Grid graphics formats

• BMP – no compression• PCX – lossless compression RLE• PNG – lossless dictionary compression LZW • GIF – lossless dictionary compression LZW +

reduction to 256 color (adaptive palette)• JPG – approximating compression JPEG

JFIF format (JPEG File Interchange format)

sequential, common known

progressive, more effective, for computer net transmissions

lossless, not known and not widely supported

hierarchic, more resolutions in one file, quick preview

Sequential JFIF encoding

Color model transofmation

RGB → Y Cb CrY= 0,299*R + 0,587*G + 0,114*B (brightness)

Cb = - 0,1687*R - 0,3313*G + 0,5*B + 128

Cr = 0,5*R - 0,4187*G - 0,0813*B + 128

R = Y + 1.402*(Cr-128)

G = Y - 0.34414*(Cb-128) - 0.71414*(Cr-128)

B = Y + 1.772*(Cb-128)

Subsampling of Cb,Cr

Computing of average value for the block

• 2x1 pixels (6 bits sample), –6 bits -> 4 bits (compression 67%)

• or 2x2 pixels (12 bits sample), –12 bits -> 6 bits (compression 50%)

DCT transformation

Example

139 144 149 153 155 155 155 155144 151 153 156 159 156 156 156150 155 160 163 158 156 156 156159 161 162 160 160 159 159 159159 160 161 162 162 155 155 155161 161 161 161 160 157 157 157162 162 161 163 162 157 157 157162 162 161 161 163 158 158 158

DCT coefficientsAC coefficient (= 8 x average brightness

Quantization matrix – example for 90% “qality”

Quantization matrices• Defined by standardization committee JPEG. Separately for brightness and for color components.• Defined matrices for quality 10% and 90%.• For other values of quality between 10% and 90%obtained by linear interpolation.• For values under 10% or over 90% extrapolation can be used but it is not recommended.

Coefficients after quantisation

AC coefficients

• Stored separately• Not compressed• Possibility used for quick preview

•

Huffman encoding

Example

0, -2, -1, -1, -1, 0, 0, -1, -1, 0, 0, 0…..

Reconstruction of DCT coeffients

After inverse DCT transformation

Table of differences

Grid Pictures Modification

Geometrical Modifications

• Clip– Rectangular– Other shapes

• Rotate– Left, Right– 180 degrees– Flip

warping

warping

Morphing

Resolution modification

• Resolution / number of pixels /dimensions of picture

• Resolution Decreasing (average color of pixels)

• Resolution increasing

- copying of pixels

- dithering

Color depth decreasing

• Rounding of colors

• Establishing of color palette

• Half toning

• Dithering

Half Toning

• Half tone matrix– example

0 12 3 15

8 4 11 7

2 14 1 13

10 6 9 5

Floyd Steinberg dithering

7/16

3/165/16

1/16

Pixel color correction

• Color correction

• Saturation correction

• Brightness correction– Simple brightness correction– Contrast correction– Gamma correction

Saturation

S

Saturation correction

S

Brightness

Light

Brightness histogramm

K W

Color brightness

• Y = 0,299R + 0,587G + 0.114B

Simple brightness correction

Original br

New br

Simple brightness decreasing

Original br

New br

Contrast decreasing

Original br

New br

Contrast increasing

Original br

New br

Gamma correction of brightness

Original br

New br

Gamma function

Tedy

Y = 255 * (x/255)1/γ

Y = x1/γ

• Y = ymin + (ymax-ymin)*(x/xmax)1/γ

Gamma correction

Original brightness On <0,1> γ=0,5 γ=2,2

0 0 0 0 0 0

10 0,039216 0,001538 0,392157 0,229437 58,50645

20 0,078431 0,006151 1,568627 0,314409 80,17437

60 0,235294 0,055363 14,11765 0,518046 132,1018

128 0,501961 0,251965 64,25098 0,731039 186,4151

200 0,784314 0,615148 156,8627 0,895449 228,3395

255 1 1 255 1 255