Image Processing and Sampling

Aaron Bloomfield

CS 445: Introduction to Graphics

Fall 2006

Overview

Image representation What is an image?

Halftoning and dithering Trade spatial resolution for intensity resolution Reduce visual artifacts due to quantization

What is an Image?

An image is a 2D rectilinear array of pixels

Continuous image Digital image

What is an Image?

An image is a 2D rectilinear array of pixels

Continuous image Digital image

A pixel is a sample, not a little square!A pixel is a sample, not a little square!

What is an Image?

An image is a 2D rectilinear array of pixels

A pixel is a sample, not a little square!A pixel is a sample, not a little square!

Continuous image Digital image

Image Acquisition

Pixels are samples from continuous function Photoreceptors in eye CCD cells in digital camera Rays in virtual camera

Image Display

Re-create continuous function from samples Example: cathode ray tube

Image is reconstructedby displaying pixels

with finite area(Gaussian)

Image Resolution

Intensity resolution Each pixel has only “Depth” bits for colors/intensities

Spatial resolution Image has only “Width” x “Height” pixels

Temporal resolution Monitor refreshes images at only “Rate” Hz

Width x Height Depth Rate NTSC 640 x 480 8 30Workstation 1280 x 1024 24 75Film 3000 x 2000 12 24Laser Printer 6600 x 5100 1 -

Typ

ica

lR

eso

lutio

ns

Sources of Error

Intensity quantization Not enough intensity resolution

Spatial aliasing Not enough spatial resolution

Temporal aliasing Not enough temporal resolution

),(

22 ),(),(yx

yxPyxIE

Overview

Image representation What is an image?

Halftoning and dithering Reduce visual artifacts due to quantization

Quantization

Artifacts due to limited intensity resolution Frame buffers have limited number of bits per pixel Physical devices have limited dynamic range

P(x, y) = trunc(I(x, y) + 0.5)

I(x,y)

P(x

,y)

P(x,y)(2 bits per pixel)

I(x,y)

Uniform Quantization

Uniform Quantization

8 bits 4 bits 2 bits 1 bit

Images with decreasing bits per pixel:

256 bpp 32 bpp 8 bpp 2 bpp

Reducing Effects of Quantization

Halftoning Classical halftoning

Dithering Error diffusion dither Random dither Ordered dither

Classical Halftoning

Use dots of varying size to represent intensities Area of dots proportional to intensity in image

P(x,y)I(x,y)

Classical Halftoning

Newspaper image from North American Bridge Championships Bulletin, Summer 2003

Halftone patterns

Use cluster of pixels to represent intensity Trade spatial resolution for intensity resolution

Figure 14.37 from H&B

Dithering

Distribute errors among pixels Exploit spatial integration in

our eye Display greater range of

perceptible intensities Uniform quantization

discards all errors i.e. all “rounding” errors

Dithering is also used in audio, by the way

Floyd-Steinberg dithering

Any “rounding” errors are distributed to other pixels Specifically to the pixels below and to the right

7/16 of the error to the pixel to the right 3/16 of the error to the pixel to the lower left 5/16 of the error to the pixel below 1/16 of the error to the pixel to the lower right

Assume the 1 in the middle gets “rounded” to 0

00.000.000.0

00.000.100.0

00.000.000.0 0.00 0.00 0.00

0.00 0.00 0.44

0.19 0.31 0.06

Error Diffusion Dither

Spread quantization error over neighbor pixels Error dispersed to pixels right and below

Figure 14.42 from H&B

Floyd-Steinberg dithering

Floyd-Steinberg dithering is a specific error dithering algorithm

UniformQuantization

(1 bit)

Floyd-SteinbergDither (1 bit)

Original(8 bits)

Floyd-Steinberg

Dither (1 bit)(pure B&W)

Random Dither

Randomize quantization errors Errors appear as noise

P(x, y) = trunc(I(x, y) + noise(x,y) + 0.5)

I(x,y)P

(x,y

)I(x,y)

P(x

,y)

Random Dither

UniformQuantization

(1 bit)

RandomDither(1 bit)

Original(8 bits)

Ordered Dither

Pseudo-random quantization errors Matrix stores pattern of thresholds

i = x mod nj = y mod ne = I(x,y) - trunc(I(x,y))if (e > D(i,j))

P(x,y) = ceil(I(x, y))else

P(x,y) = floor(I(x,y))

20

132D

Ordered Dither

Bayer’s ordered dither matrices Reflections and rotations of these are used as well

20

132D

10280

614412

91113

513715

4D

22

222

2

22

222

2

)2,2(4)1,2(4

)2,1(4)1,1(4

nnnn

nnnn

n UDDUDD

UDDUDDD

Ordered Dither

UniformQuantization

(1 bit)

4x4 OrderedDither(1 bit)

Original(8 bits)

Dither Comparison

RandomDither(1 bit)

Original(8 bits)

OrderedDither (1 bit)

Floyd-SteinbergDither (1 bit)

Color dithering comparison

Original image Web-safe palette, no dithering Web-safe palette, FS dithering

Optimized 256 color palette Optimized 16 color palette Optimized 16 color palette

FS dithering No dithering FS dithering

Summary

Image representation A pixel is a sample, not a little square Images have limited resolution

Halftoning and dithering Reduce visual artifacts due to quantization Distribute errors among pixels

Exploit spatial integration in our eye

Sampling and reconstruction Reduce visual artifacts due to aliasing Filter to avoid undersampling

Blurring is better than aliasing