half toning. continuous half toning color half toning

Half Toning

Continuous Half Toning

Color Half Toning

Half toning and Colors

Digital 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

Original

Half Toning

Original

Dithering

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.

ThresholdingOriginal image. Simple threshold. n = 0.5

)),((),( 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

)),(),((),( yxnoiseyxvKtruncyxv

10 noise

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

Threshold

Threshold + Noise

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

Dithering

• It is possible to improve the quality of a quantized image by distributing the quantized error.

• Let’s have a closer look.

Dithering

Thresholding Dithering

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

Threshold + Noise

Dithering

Ordered 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 Xpixels For all Ypixels v = approximate(x,y) i = x mod 3 j = y mod 3 if 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

Original

Dithering

Error Diffusion

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

01

1D Error Diffusion

0

1

01 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

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

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

Space Filling Curves • order of scan

Space Filling Curves

Hilbert curve(1-4)

Space Filling Curves

Peano curve

Context Based SFC

Original Image

Threshholding

Bayer’s Ordered Dithering

Error Diffusion

Median Cut (4 levels)

Median Cut (8 levels)

half toning. continuous half toning color half toning

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