Part1 [Compatibility Mode]

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Unacional Bogota

Image and Video ProcessingFundamentals

Professor Ebroul Izquierdo

Multimedia and Vision Research Group

Queen Mary, University of London

Summer Course, Universidad Nacional de Colombia

Bogota, Marzo-June 2012

Electronic Engineering

Road Map

Digital image representation

Sampling

Quantization

Colour spaces

Colour images


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What is a Digital Image?

A discrete function from a 2D domain in a set of realpositive numbers

Digital image:

Having values at discrete samples usually in a regular

rectilinear gridThe function values represent gray levels, colorchannels, opacities, transparency or tissue density in anMR Images

DI:


Types of Signals: Dimensions

Temporal signal: function of time

f(t): voice, music, nerve impulses, radar

Spatial signal: function of two (or three) spatial dimensions

f(x,y): images (grayscale, color, multi-spectral)

f(x,y,z): medical scans (CT, MRI, PET)

Spatial-temporal signal: 2/3-D space, 1-D time

f(x,y, t): video/movies


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Using a Single Sensor


Using Sensor Strips


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Using Sensor Arrays


What does this mean?

2D

Domain

Sampling Positions


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What does this mean?

Function

Values at

discrete

grid

points

0 200

128 60

128 60

128 60


Pixels or Pels

2D

Domain

Sampling Positions

A Single

sampling

position

and its

function

value


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Digital Images (I)

A digital image is a nD array of pixel values.

For example, in the 2D case the image data contains information

of the graylevel at each position in the image.

Magnifyed pixels at few

sampling positions


Digital Images (II)

94 100 104 119 125 136 143 153 157 158

103 104 106 98 103 119 141 155 159 160

109 136 136 123 95 78 117 149 155 160

110 130 144 149 129 78 97 151 161 158

109 137 178 167 119 78 101 185 188 161

100 143 167 134 87 85 134 216 209 172

104 123 166 161 155 160 205 229 218 181

125 131 172 179 180 208 238 237 228 200

131 148 172 175 188 228 239 238 228 206

161 169 162 163 193 228 230 237 220 199

Corresponding arrayPixels


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Grey Level Images

Standard pixel values for rows, columns and gray levels

The number of gray levels is usually a power of 2:

whereB is the number of bits in the binary representation of the

image.

E.g.,B = 8 impliesL = 256 gray levels numbered from 0,,255.

Parameter Symbol Typical ValuesRows N 256, 512, 525, 625, 1024, 1035Colum ns M 256, 512, 768, 1024, 1320

No. Gray Levels L 2, 64, 256, 1024, 4096, 16384

L

B

2


Image Formats (I)

GIF(GIF87a,GIF89a):

Graphics Interchange Format (GIF) devised by the

UNISYS Corp. and Compuserve, initially for transmitting

graphical images over phone lines via modems.Uses the Lempel-Ziv Welch algorithm (compression).

Supports only 8-bit (256) color images.

Supports interlacing

GIF89a supports simple animation


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Image Formats (II)

JPEG:

A standard for photographic image compression created by

the Joint Photographics Experts Group

Takes advantage of limitations in the human vision system

to achieve high rates of compression

Lossy compression which allows user to set the desired

level of quality/compression

More on JPEG later


TIFF:

Tagged Image File Format (TIFF), stores many

different types of images (e.g., monochrome, grayscale,

8-bit & 24-bit RGB, etc.)

Developed by the Aldus Corp. in the 1980's and latersupported by the Microsoft

TIFF is a lossless format (when not utilizing the new

JPEG tag which allows for JPEG compression)

It does not provide any major advantages over JPEG

and is not as user-controllable it appears to be declining

in popularity

Image Formats (III)


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A PPM header consists of at least three parts normally separated

by carriage returns and/or linefeeds but the PPM specification

only requires white space

The first "line" is a magic PPM identifier, it can beP3 orP6

The next line consists of the width and height of the image as ascii

numbers

The last part of the header gives the maximum value of the colour

components for the pixels, this allows the format to describe morethan single byte (0..255) colour values

In addition to the above required lines, a comment can be placed

anywhere with a "#" character, the comment extends to the end of

the line.

PPM Header


The following are all valid PPM headers.

Example 1P6 1024 788 255

Example 2P6

1024 788# My own comment on this image

255

Example 3P3

1024 # the image width

788 # the image height

# Another comment

1023

PPM Header


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The format of the image data itself depends on the

magic PPM identifier. If it is "P3" then:

the image is given as ascii text

the numerical value of each pixel ranges from 0 to the

maximum value given in the header

the lines should not be longer than 70 characters.

PPM Header


P3

# example from the man page

4 4

15

0 0 0 0 0 0 0 0 0 15 0 15

6 0 0 0 15 7 0 7 0 0 0 0

0 0 0 0 0 0 0 15 7 3 0 0

15 0 15 0 0 0 0 0 0 0 6 0

P3 PPM Header Example


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If the PPM magic identifier is "P6" then the image

data is stored in byte format, one byte per colour

component (r,g,b)

Comments can only occur before the last field of the

header and only one byte may appear after the last

header field, normally a carriage return or line feed

"P6" image files are obviously smaller than "P3" andmuch faster to read

Note that "P6" PPM files can only be used for single

byte colours

PPM Header


While not required by the format specification it is a

standard convention to store the image in top to

bottom, left to right order

Each pixel is stored as a byte

The value 0 represents black,

The value 255 represents white

The components are stored in the "usual" order, R/G/B

(red - green blue)

PPM Format


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This format is identical to PPM but it stores greyscale

information

That is, one value per pixel instead of 3 (r,g,b)

The only difference in the header section is the magic

identifiers which areP2 andP5

P2 corresponds to the ascii form of the data

P5 corresponds to the binary form of the data

PGM Format


P2

24 7

9

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 3 3 3 3 0 0 7 7 7 7 0 0 1 1 1 1 0 0 5 1 5 5 0

0 3 0 0 0 0 0 7 0 0 0 0 0 1 0 0 0 0 0 5 0 0 1 0

0 3 3 3 0 0 0 7 7 7 0 0 0 1 1 1 0 0 0 1 1 1 1 0

0 3 0 0 0 0 0 7 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0

0 3 0 0 0 0 0 7 7 7 7 0 0 1 1 1 1 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

PGM Example


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P2 - PGM grey scale image, stored in ASCII, onevalue per pixelP3 - PPM color image, stored in ASCII, 3 valuesrgb per pixelP5 - PGM grey scal image stored in binary(compressed) formatP6 - PPM color image stored in binary(compressed) format

PPM and PGM Magic Numbers


Road Map


Sampling

Quantization

Colour spaces

Colour images


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How Digital Images Are Generated

Two basic step (Digitization):

Sampling

Quantization


Image Digitization

Digitizer(e.g.,scanner)

SceneI(i, j)


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Sampling

Sampler

Continuous Domain

(i, j) array of

sampling positions

The continuous image domain D is scanned the brightness values

I(i, j) are measured or sampled at discrete locations to form an

array of intensity values

Converting the continuous 2D signal in a digital image

by sampling per scanlines

Definition


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Example

Example


Image sampling


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Image sampling

5122561286432

Image Resolution

Full Resolution 1/4 Resolution


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Image Resolution

1/8 ResolutionFull Resolution

Low Resolution

64 X 641/8 Resolution

The Image at 1/8 resolution appears blocky

To accurately represent the original continuous scene, the

sampling rate must be sufficiently high


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Methods for Image Sampling

Uniform - same sampling frequency everywhere

Adaptive - higher sampling frequency in areas with

greater detail (Compression strategy)


Representing a line with discrete pixel values leads tosampling error and loss of information

Standard midpoint line on a binary representation

Sampling Effects


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Same line with twice the linear resolution

Sampling Effects


Doubling resolution does not solve the problem

It costs 4 times memory, bandwidth and scan

conversion time!

The problem can be alleviated using more

grey-levels

Sampling Effects


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Happen whenever we try to sample a signal at less thantwice the maximum frequency

Analog sine wave

The sine wave sampled at too low a rate

Aliasing


The sine wave sampled at too low a rate

Reconstructed wave based on these samples

Aliasing


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Sine wave sampled at the Nyquist limit. This time it

works fine

The sample points shifted. Now we get no signal!

Nyquist Limit


Road Map


Sampling

Quantization

Colour spaces

Colour images


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Quantization

Each element in the matrix is quantized, i.e, replaced by an

integer

Quantized values are called gray levels

I(i, j)

Quantizer

Digital Image Visualization

Usually each pixel in the image is shown by a singlepixel on the screen.

E.g., forL = 256 gray levels, 0 maps into black,

255 into white and values in between map

linearly into various levels of gray.

0

0

0

0

0

0

0

0

0

0 0 0

127

127255

255

Image Screen


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Intensity Resolution

Refers to how accurately a pixels gray level represents the

brightness of the corresponding point in the original scene

During quantization, the brightness sampled at each point in

the continuous-tone image is replaced by an integer value

Scene brightness

Graylevelofimage

0

7

Imax

B = 3 bits



Intensity resolution depends on the number of bits

available

This figure shows a digital image quantized with 8 bits (256

gray levels). The image appears continuous


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The same image quantized with only 4 bits (16 gray

levels). Now the image brightness appears

discontinuous



With fewer bits, we cannot accurately represent thegradual intensity variations in the original scenebecause a wider range of intensities in the original

scene is mapped into a single gray level.

Generally, the more bits we have, the better the

brightness resolution


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256

Grey-level quantization

3282


Quantization Methods

Uniform or linear - intensity of object is lineary mapped to gray-

levels of image

Logarithmic - higher intensity resolution in darker areas (the

human eye is logarithmic)

object intensity

imageintensity

object intensity

imageintensity


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Common Quantization Levels

I(i,j) is given by integer values [0-max], max=2n-1

n=1 [0 - 1] binary image

n=5 [0 - 31] maximum the human

eye can resolve (locally)

n=8 [0 - 255] 1 byte, very common

n=16 [0 - 65535] common in research

n=24 [0 - 16.2*106] common in color images

(i.e. 3*8 for RGB)


Choice of Sampling andQuantization

What will the image be used for?

What are the limitations in memory and speed?

Will the image only be used for visual

interpretation or for any imageanalysis/processing?

What information is relevant for the analysis (i.e.

color, spatial and/or graylevel resolution)?


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Road Map


Sampling

Quantization

Colour spaces

Colour images


Light as a Waveform

Light can be split into its component wavelengths andintensity

The wavelength of visible light lies roughly between 400nmand 700nm

these measurements can be combined into a spectral

power distribution (SPD) a description of how the intensity of light from some

particular source varies with wavelength

The SPD for some light source corresponds closely to itscolour components:

short wavelength (440nm) = blue

medium (550) = green

long (590) = red


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Tristimulus Theory of

Colour Vision

This theory states that human perception of colour derives

from the eyes responses to three different groups of

wavelengths

i.e. those corresponding to red, green and blue (RGB)


Tristimulus Theory of

Colour Vision

Therefore: any sensation of colour can be produced bymixing together suitable amounts of these colours

Red, Green & Blue are called theadditive primarycolours

Although this is broadly true, the operation of the receptorsin the eye is not quite that simple:

the receptors inter-operate in a more complex way for somevisible colours

therefore it is notpossible to represent any visible colour asa combination or R, G & B


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Color in Images and Video

Light and Spectrum: visible light is an electro-

magnetic wave in the 400 nm - 700 nm range.

Most light we see is not one wavelength, it's acombination of many wavelengths


The Human Retina Simple Model-

The eye functions on the same principle as a camera

Each neuron is either a rod or a cone.

The rods contain the elements that are sensitive to light intensities. Rods are

not sensitive to color.

Cones come in 3 types: red, green and blue. Each responds differently to

various frequencies of light.


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Properties of the Human Visual

System

The eye is more sensitive to changes in brightness thancolour

The eye is unable to perceive brightness levels above orbelow certain thresholds

The eye cant distinguish minor changes in brightness orcolour. Certain ranges of brightness or colour are more

important visually than others. E.g. eye is more sensitive to minor changes in shades of

green than other colours

Sensitivity of the eye is not linear.


Color Composition

A color can be specified as the sum of three colors. So colorsform a 3 dimensional vector space.

The following figure shows the amounts of three primaries

needed to match all the wavelengths of the visible spectrum.


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Hue distinguishes among colors such as red, green,

purple, and yellow

Saturation refers to how pure the color is, how much

white/gray is mixed with it

red is highly saturated; pink is relativelyunsaturated

royal blue is highly saturated;

sky blue is relatively unsaturated

pastels are less vivid, less intense

Chromatic Color

Lightness embodies the achromatic notion of perceived intensity

of a reflecting object

Brightness is used instead of lightness to refer to the perceived

intensity of a self-luminous (i.e., emitting rather than reflecting

light) object, such as a light bulb, the sun, or a CRT

Can distinguish ~7 million colors when samples placed side-by-side (JNDs)

about 128 fully saturated hues are distinct

eye less discriminating for less saturated light (from16 to 23 saturation steps for fixed hue and lightness),and less sensitive for less bright light

Chromatic Color


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Occurs with inks for print medium, paints that absorb light. In

subtractive mixture, the light passed by two filters (or reflected

by two mixed pigments)

Subtractive Mixture

blue green yellow red

green


Used to mix R, G, B guns of CRT. The figure shows two

projectors throwing pure blue and yellow filtered light upon the

same portion of the screen. In contrast to what happens in a

subtractive mixture, the result of adding these two colors is gray.

Additive Mixture


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These complementary unique hues play a role in

opponent color perception discussed later

Note that only for perfect red and green do you get gray

Complementary Hues


The gray patches on the blue and yellow backgrounds arephysically identical. But they do not look similar

Color Contrast


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Hardware-oriented models: not intuitive

RGB, used with color CRT monitors

YIQ, the broadcast TV color system

CMY (cyan, magenta, yellow) for color printing

CMYK (cyan, magenta, yellow, black) for colorprinting

User-oriented models

HSV (hue, saturation, value) also called HSB (hue,saturation, brightness)

HLS (hue, lightness, saturation)

The Munsell system

CIE Lab

Color Models


Color Models for Images (I)

RGB Additive Model: A color image is a 2-D

array of (R,G,B) integer triplets. These triplets

encode how much the corresponding phosphor

should be excited in devices such as a monitor.Blue Cyan

Red Yellow

Green

Magenta

Black(0,0,0)

White(1,1,1)


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Main diagonal => gray levels

black is (0, 0, 0)

white is (1, 1, 1)

RGB Color Model


Color Models for Images (II)

BlueCyan

RedYellow

Green

Magenta

Black(1,1,1)

White(0,0,0)

CMY Subtractive Model: Cyan, Magenta, and Yellow(CMY) are complementary colors of RGB.

CMY model is mostly used in printing devices where the colorpigments on the paper absorb certain colors (e.g., no red light

reflected from cyan ink)


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Used in electrostatic and in ink-jet plotters that deposit pigment onpaper

Cyan, magenta, and yellow are complements of red, green , andblue

Subtractive primaries: colors are specified by what is removed orsubtracted from white light, rather than by what is added toblackness

Cartesian coordinate system

Subset is unit cube

white is at origin, black at (1, 1, 1):

The CMY(K) Color Model

B

G

R

Y

M

C

1

1

1


In the CMY model colours are specified by what is removed(absorbed) from white light, rather than by what is added toblackness.

C + M + Y at full intensity = Black

Subtractive scheme: E.g.Cyan objects absorb red, so cyan is whiteminus red (or blue + green)

C = G + B = W - R

M = R + B = W - G

Y = R = G = W - B

To obtain a good black for printing, another primary isadded: K (CMYK)

The CMY(K) Color Model


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Color Models (IV)

YUV Model: Human perception is more sensitive to brightnessthan chrominance. Therefore, instead of separating colors, one canseparate the brightness info. from the color info.

Y is luminance

Y = 0.299R + 0.587G + 0.114B

Chrominance is defined as the difference between a color and areference white at the same luminance. It can be represented by Uand V -- the color differences.

U = B - Y

V = R - YEye is most sensitive to Y. Therefore, any error in the resolution of theluminance (Y) is more important than the chrominance (U,V) values.

In PAL, 5 (or 5.5) MHz is allocated to Y, 1.3 MHz to U and V.

HSV models colour in terms of:

HUE:

the dominant wavelength, i.e. where most of the energy of thelight is concentrated.

hues usually identified by names: mixtures of red, yellow,green and blue.

SATURATION

a measure of the colours purity or intensity:

the presence of other hues makes the colour paler

BRIGHTNESS

a measure of how light or dark the colour is.

HSV corresponds more closely to the way humans think about

colour than RGB.

Color Models (VI)


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Hue, saturation, value (brightness)

Hexcone subset of cylindrical (polar) coordinate system

The V = 1 plane contains the RGB models R = 1, G = 1, B = 1, inthe regions shown

The HSV Color Model


Hue, lightness, saturation. Double-hexcone subset

Maximally saturated hues are at S = 1, L = 0.5

The HLS color Model


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Munsell color-order system

set of samples in 3D space

hue, value/lightness, chroma (saturation)

equal perceived distances between neighbors

Defining Color


Munsell color definition

Black

Grays

White Tints Purecolor

Tones

Shades

Decrease saturation

Decrease

lightness


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Road Map


Sampling

Quantization

Colour spaces

Colour images


Channels in Colour Images

Blue Channel of Image

1 sample per pixel

Green Channel of Image

1 sample per pixel

Red Channel of Image

1 sample per pixel

3 samples per pixel


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Colour Vs. Grey


Colour Vs. B&W

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