1

Half ToningColor Half Toning

Half toning and ColorsDigital Half Toning

(0) (1) (2) (3) (4)

(0) (1) (2) (3)

(0) (1) (2) (3) (4)

Emulating 5 different levels

Half Toning

(0) (1) (2) (3) (4)

(5) (6) (7) (8) (9)

Half Toning

10 levels

2

OriginalDithering

Dithering and HalftoningTrade spatial for intensity resolution(works well for printing where dot printing is very

high)• Thresholding. • Random dither; Robert’s algorithm• Ordered dither• Error diffusionYour eye will average over an area

- Spatial Integration

Thresholding

Assume we want to quantize a gray-level image to a binary colormap.

Map the upper half of the gray-level scale to white, and the lower half to black – a simple threshold operation, preformed independently at each pixel.

3

Thresholding

Original image. Simple threshold.n = 0.5 n= 0.7

)),((),( nyxvtruncyxv �� �Errors are low spatial frequencies.

Robert’s Algorithm

• First add noise

• Then quantize

x

i

0

1

r

r + 1Quantized to 1

Quantized to 0

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10 �� noise

Moves errors to higher spatial frequencies.-> eye averages over an area.

Robert’s Algorithm

Pink Blue

The trouble with noise

• Difficult to compute quickly.

• Not reproducible.

• Pre-compute pseudo-random function and store in table.

• Small tiled patterns sufficient

Each pixel produces a quatization error

The quality of the result may be improved by adjusting the threshold locally, so that adjacent pixels in small areas are quantized with different thresholds.

This reduces the average local quantization error. Matrices of these threshold are called dither matrices.

Dithering

4

ComparisonOrdered Dithering

• Trade off spatial resolution for intensity resolution.

• Use dither patterns.

• Can be represented as a matrix.

Other possibilities

9 4 8

6 1 2

573

For all XpixelsFor all Ypixels

v = approximate(x,y)i = x mod 3j = y mod 3if v >= M[i,j] then

Set_Pixel(x,y, BLACK)else

Set_Pixel(x,y, WHITE)

The dithering matrix (3x3)

Dithering

9 4 8

6 1 2

573

9 4 8

6 1 2

573

9 4 8

6

1

2

5

73

9 4 8

6 1 2

573

9 4 8

6

157

3

2 5

54

4

4

2

2

2

2 2

3

3

3

3

6

8 444

4

2

28 3

8

8

9

9

9

8 8

7

7

7

7

6

4

2

4

4

2

2

12

2 2

3

3

8 44

9 4 8

6 1 2

573

0 1 0

0 1 1

000

Dithering mask

Image

Binary image

Comparison.

5

Floyd-Steinberg Error Diffusion

With this method, the average quatization error is reduced by propagating the error from each pixel to some of its neighbors in the scan order.

1D Error Diffusion

0

1

1

1D Error Diffusion

0

1

1D Error Diffusion

0

1

1D Error Diffusion

0

1

1D Error Diffusion

0

1

01

6

1D Error Diffusion

0

1

01 1

1D Error Diffusion

0

1

1D Error Diffusion

0

1

1D Error Diffusion

0

1

Floyd-Steinberg Error DiffusionWith this method, the average quatization error is reduced by propagating the error from each pixel to some of its neighbors in the scan order.

Note that the error propagation weights must sum to one

e -3e/8

-3e/8 -e/4

e-3e/8

-3e/8-e/4

Dither vs. Floyd-Steinberg

7

Original Picture

Dithering resultError diffusion result

Examples – Continue

DitheringDithering:

Note that each square ring is of different brightness

Error Diffusion

Error Diffusion:

Note that the error is distributed across the layers

8

Examples – ContinueOriginal:

Dithering

Error Diffusion Set AccErr[] to zero;For each pixel in the image scanning from left to right:value= Pixel_value(x,y) + AccErr[x,y];if (value > WHITE/2) {

Set_pixel(x,y, WHITE);Error = value - WHITE;}

else {Set_pixel(x,y, BLACK);Error = value - BLACK;}

if scanning from left to right {AccErr[x+1, y] += 3/8 * Error;

AccErr[x, y+1] += 3/8 * Error;

AccErr[x+1,y+1] += 2/8 * Error;}

Error Diffusion

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10

ThreshholdingBayer’s Ordered Dithering

Error DiffusionMedian Cut (4 levels)

Median Cut (8 levels)