CE-201CE-201_Week3_2010

INDIAN INSTITUTE OF TECHNOLOGY ROORKEEDEPARTMENT OF CIVIL ENGINEERING

CE‐201: Computer Aided GraphicsWeek 3

Rajat Rastogi

[email protected]@iitr.ernet.in

Last weekLast week

• Graphic pipelineGraphic pipeline

• CG Processes

i l S d h l i• Display Systems and technologies

• Display Devices

• Input‐Output Devices

August 19, 2010 2Rajat Rastogi

OutlineOutline

• Random / Raster scanRandom / Raster scan

• Pixels

C l d l• Colour Models

• Colour Model Conversions

• Image representation

August 19, 2010 Rajat Rastogi 3

SCAN DISPLAY SYSTEMSComputer Aided Graphics

SCAN DISPLAY SYSTEMS

August 19, 2010 4Rajat Rastogi

Scan Display SystemsScan Display Systems

• Random‐scan displayRandom scan display

• Raster‐scan display


Random‐Scan DisplayRandom Scan Display

• Also called vector or stroke‐writing or calligraphic displays• Early computer displays: basically an oscilloscope• Refresh display file or buffer or list or programme, a

memory area, stores a set of line drawing commands.memory area, stores a set of line drawing commands. • These have higher resolution than raster‐scan systems.• Lines drawn are smoother in contrast to raster system,

which produces jagged lines plotted as discrete point setswhich produces jagged lines, plotted as discrete point sets.• Pen‐plotter is a example of random‐scan, hard copy device.• Disadvantages:

– Just does wireframe, like line drawing applications– Complex scenes cause visible flicker


Random‐Scan Display…1Random Scan Display…1

• Electron beam is directed only to the parts of theElectron beam is directed only to the parts of the screen where a picture is to be drawn

• Draw picture one line at a timeDraw picture one line at a time.


Raster‐Scan DisplayRaster Scan Display

• Raster: A rectangular array of points or dotsRaster: A rectangular array of points or dots

• Pixel: One dot or picture element (pel) of the rasterraster

• Scan line: A row of pixels


Raster‐Scan Display…1Raster Scan Display…1

• The electron beam is swept across the screenThe electron beam is swept across the screen, one row at a time from top to bottom. As the electron beam moves across each row theelectron beam moves across each row, the beam intensity is turned on and off to create a pattern of illuminated spotspattern of illuminated spots.

• Picture definition is stored in a memory area called the refresh buffer or frame buffercalled the refresh buffer or frame buffer.



• The intensity range of pixel positions define e te s ty a ge o p e pos t o s de ecapability of raster system. The frame buffer may be called:– Bitmap: with one bit per pixel, ex. Black and white systemPixmap: with multiple bits per pixel 24 in high– Pixmap: with multiple bits per pixel, 24 in high definition systems

• Refreshing on raster‐scan display is carried out at g p ya rate of 60 to 80 frames per second (Hz). This creates new image.



• Scanning (left to right, top to bottom)Scanning (left to right, top to bottom)– Vertical Sync Pulse: Signals the start of the next field

– Vertical Retrace: Time needed to get from the bottom Vertical Retrace: Time needed to get from the bottomof the current field to the top of the next field

– Horizontal Sync Pulse: Signals the start of the new scan line

– Horizontal Retrace: The time needed to get from the d f th t li t th t t f th tend of the current scan line to the start of the next

scan line


Raster‐Scan DisplayRaster Scan Display

• Interlaced Refresh Procedure:Interlaced Refresh Procedure:– Assume we can only scan all pixels of entire screen at30 frames / second. Some flicker will be noticed here.

– To reduce flicker, divide each frame into two “fields” of odd and even lines. This reduces the scan time of screen from top to bottom to half as the beam will sweep every alternate scan line in one pass in 1/60s.

1/30 Sec 1/30 Sec

1/60 Sec 1/60 Sec 1/60 Sec 1/60 Sec

Field 1 Field 1Field 2 Field 2


Field 1Field 2 Field 2

Frame Frame

PixelsPixels

• An image is composed of discrete pixels or picture age s co posed o d sc e e p e s o p c u eelements.

• These are arranged in a row‐column fashion to form a rectangular area (raster).

• The total number of pixels in a image is a function of the i f th i d b f i l it l th isize of the image and number of pixels per unit length in the horizontal as well as vertical direction (Resolution).

• Image size is defined as total number of pixels in theImage size is defined as total number of pixels in the horizontal direction times the total number of pixels in the vertical direction (512 x 512, 640 x 480, 1024 x 768).


Pixels…1Pixels…1

• Size of image, at 400 pixels per inch for 640 x 480 imageS e o age, a 00 p e s pe c o 6 0 80 age– 640/400 x 480/400 = 1.6 x 1.2 inch

• Aspect ratio, for 640 x 480 image = 640/480 = 4/3

• Pixel at lower left corner of an image is considered to be at the origin (0,0) of a pixel coordinate system.

(639,479)(0,479)

(0,0) (639,0)


COLOURMODELSComputer Aided Graphics

COLOUR MODELS


Colour ModelsColour Models

• The purpose of a colour model (also called colour space orp p ( pcolour system) is to facilitate the specification of colours insome standard, generally accepted way.

I l d l i ifi ti f di t• In essence, a colour model is a specification of a coordinatesystem and a subspace within that system where each colouris represented by a single point.

• Most colour models in use today are oriented either toward hardware (such as for colour monitors and printers) or toward application where colour manipulation is a goal (such as in theapplication where colour manipulation is a goal (such as in the creation of colour graphics for animation).


Colour Models…1Colour Models…1

• Hardware‐oriented models most commonly used in practicey pare the RGB (red, green, blue) model for colour monitors anda broad class of colour video cameras;

CMY ( t ll ) d CMYK ( t• CMY (cyan, magenta, yellow) and CMYK (cyan, magenta,yellow, black,) models for colour printing; and

• HSI/HSL/HSB (hue, saturation, intensity/lightness/brightness)/ / ( , , y/ g / g )model, which corresponds closely within the way humansdescribe and interpret colour.


The RGB Colour ModelThe RGB Colour Model

• Spectral ColourSpectral Colour


The RGB Colour Model…1The RGB Colour Model…1

• Trichromatic TheoryTrichromatic Theory



• Trichromatic Theory • There are three types of Trichromatic Theory ypcones, referred to either as S, M, and L, which are roughly (very roughly)roughly (very roughly) equivalent to blue, green, and red sensors, respectively. Their peak sensitivities are located at approximately 430nm, pp y ,560nm, and 610nm for the "average" observer



• RGB ModelRGB Model



• Colour Coordinate systemColour Coordinate system– Colour specification using RBG model is an additive process. It starts with Gpblack and necessary primary components

dd d t i ld

GreenYellow

(0,1,0)

(1 1 0)are added to yielddesired colour.

– This is a working

CyanWhite

(1,1,0)

(1,1,1)(0,1,1)

Grey axisThis is a workingprincipal of displaymonitor. R

Black

BlueRed(0,0,0)

(0,0,1)(1,0,0)


B Magenta

( , , )(1,0,1)


• CRT arrangementCRT arrangement

Delta electron gun In-line electron gun arrangement arrangement



• Converting 3‐D colour space to 2‐D colour space on aConverting 3 D colour space to 2 D colour space on a plane X+Y+Z=1

CIE Chromaticity Diagram



• CIE XYZ colour space and RGB cubeCIE XYZ colour space and RGB cube

Conversion from RGB to CIE XYZRGB to CIE XYZ


The CMY Colour ModelThe CMY Colour Model

• Complementary Colour ModelComplementary Colour Model– This defines colours using a subtractive processes. It starts with white and appropriate primary colour is pp p p ysubtracted to get desired colour.

– It is working principal of printers.

11

and11

⎟⎟⎞

⎜⎜⎛

−⎟⎟⎞

⎜⎜⎛

=⎟⎟⎞

⎜⎜⎛

⎟⎟⎞

⎜⎜⎛

−⎟⎟⎞

⎜⎜⎛

=⎟⎟⎞

⎜⎜⎛

GR

MC

MC

GR

11and

11

⎟⎟

⎠⎜⎜

⎝⎟⎟

⎠⎜⎜

⎝⎟⎟

⎠⎜⎜

⎝⎟⎟

⎠⎜⎜

⎝⎟⎟

⎠⎜⎜

⎝⎟⎟

⎠⎜⎜

⎝ BG

YM

YM

BG

Subtractive colour mixing


colour mixing

Comparing RGB and CMY ModelComparing RGB and CMY ModelRGB Color Model CMYK Color Model

Additive color modelFor computer displays

U li ht t di l l

Subtractive color modelFor printed material

U i k t di l lUses light to display colorColors result from transmitted

light

Uses ink to display colorColors result from reflected

lightRed+Green+Blue=White Cyan+Magenta+Yellow=Black


Comparing RGB and CMY Model


Colour PrintingColour Printing

Dye color Absorbs Reflects y f

cyan red blue and green

magenta green blue and red

yellow blue red and green

Black all none

• Image printed with CMYK model cannot be converted to RGB model, as the information gets lost.

• To produce blue one has to mix cyan and magentaTo produce blue one has to mix cyan and magenta

• Black is used to ensure high quality printing. This is represented by ‘K’ and hence CMYK model.


Hue‐based Color ModelsHue based Color Models

• HSL ‐ Hue, Saturation, Lightness, , g

• HSI and HSB, where ‘I’ stands for intensity and ‘B’ stands for brightness

• HSV ‐ Hue, Saturation, Value

• Both HSL and HSV describe colors as points in a cylinder whose central axis ranges from black at the bottom to whitewhose central axis ranges from black at the bottom to white at the top with neutral colours between them, where angle around the axis corresponds to “hue”, distance from the axis

d “ i ” d di l h icorresponds to “saturation”, and distance along the axis corresponds to “lightness”, “value”, or “brightness”.

• The HSV model is commonly used in computer graphicsThe HSV model is commonly used in computer graphics applications.


Hue‐based Color Models…1Hue based Color Models…1

• HSV Color Model:– HSV Color Wheel

– HSV Color Cone

HSV Color Cylinder– HSV Color Cylinder

• HSV Colour Wheel– The hue is represented by a circular region

– A separate triangular region may be used to represent saturation and value.

– Typically, the vertical axis of the triangle indicates saturation, while the yp y, g ,horizontal axis corresponds to value. In this way, a color can be chosen by first picking the hue from the circular region, then selecting the desired saturation and value from the triangular region.



• HSV Colour Cone– 3‐D in nature

– The saturation is represented by the distance from the center of a circular cross‐section of the cone and the value is the distance fromcircular cross section of the cone, and the value is the distance from the pointed end of the cone.

– Some representations use a hexagonal cone, or hexcone, instead of a circular conecircular cone



• HSV Colour Cylindery– Most appropriate for mathematical modelling

– The number of visually distinct saturation levels and hues decreases as the value approaches blackthe value approaches black

– The constraints of precision, coupled with the limitations of human color perception, make the cone visualization more practical.



• HSL– HSL conceptually represents a double‐cone or sphere (with white at

the top, black at the bottom, and the fully‐saturated colors around the edge of a horizontal cross‐section with middle gray at its center)g g y )

Color sphere of

Runge, 1810



• HSI– HSI model is more suitable than the RGB model for many image

processing tasks.

– The three components are hue (H) saturation (S) and intensity (I)The three components are hue (H), saturation (S) and intensity (I).

– H and S specify colour where H specifies the dominant pure colour asperceived by an observer, S measures the degree to which that purecolour has been diluted by white lightcolour has been diluted by white light.

– Since colour and intensity are independent, it is possible tomanipulate one without affecting the other.

HSI colour space is described by a cylindrical coordinate system and is– HSI colour space is described by a cylindrical coordinate system and iscommonly represented as a 'double cone'.



• HSI White

– A colour is a single pointinside or on the surface of thedouble cone, while the height

H, g

of the point corresponds tointensity.

– If a point lies in a horizontalGreen

SH

Cyan

Yellow

Redpplane, a vector can defined inthis plane from the axis of thecones to that point, the

Cyan

Blue Magenta

Red

saturation is the length of thisvector and hue is itsorientation, expressed as an

l i d

I

angle in degrees.


Black


HSL / HSI / HSB HSVHSL / HSI / HSB

• Double cone system

• In HSL, the Saturation

HSV

• Inverted cone system

• In HSV, with V at maximum,In HSL, the Saturation component always goes from fully saturated color to the equivalent gray

In HSV, with V at maximum, saturation component goes from saturated color to white which may bethe equivalent gray.

• The Lightness in HSL always spans the entire range from

white, which may be considered counterintuitive

• In HSV, the V component p gblack through the chosen hue to white

ponly goes half that way, from black to the chosen huehue



HSL HSVHSL

• Applications– The CSS3 specification

HSV

• Applications– Apple Mac OS X system color

– Inkscape (starting from version 0.42)

– Macromedia Studio

picker (has a color disk for H/S and a slider for V)

– Xara XtremeMacromedia Studio

– Microsoft Windows system color picker (including Microsoft Paint)

– Paint.NET (has a color disk for H/S and a slider for V)

– Adobe graphic applicationsMicrosoft Paint)

– Paint Shop Pro

– ImageMagick

Adobe graphic applications (Illustrator, Photoshop, and others)

– PB MapInfo Pro p



HSL HSVHSL HSV



RGB to HSL RGB to HSVRGB to HSL RGB to HSV


Courtesy: John Moulton Barn


• Common Applications:pp– Pixel image editor (starting from Beta5)

– Pixia

Bryce– Bryce

– The GIMP (HSV for color selection, HSL for image color adjustment)

– Paint.NET (HSV for color selection, HSL for image color adjustment)

– Photoshop (HSV for color selection, HSL for image color adjustment)


COLOR MODEL CONVERSIONSComputer Aided Graphics

COLOR MODEL CONVERSIONS


RGB to HSLRGB to HSL

• Let r, g, b [0,1], g, [ , ]• Let max = Max (r, g, b) and min = Min (r, g, b)he least.

• Hue angle h [0, 360]

• s, l [0,1]


RGB to HSVRGB to HSV

• Let r, g, b [0,1], g, [ , ]• Let max = Max (r, g, b) and min = Min (r, g, b)he least.


• s, v [0,1]


RGB to HSIRGB to HSI

• Let r, g, b [0,1], g, [ , ]


⎨⎧ ≤

=gbif

hθ

• Normalize ‘h’ to [0,1], where⎩⎨ >−

=gbif

hθ360

1 ⎫⎧

• s v [0 1]

( ) ( )[ ]

( ) ( )( )[ ] .21

cos 2/121

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

−−+−

−+−= −

bgbrgr

brgrθ

• s, v [0,1] ⎭⎩

( ) ( )[ ]bgrbgr

s ,,min31++

−=

1


( )bgri ++=31

HSL to RGBHSL to RGB

• Let h [0, 360] and s, l [0,1][ , ] , [ , ]• If s = 0 then the colour is achromatic or grey and r, g, b = l

• Computing parameters:


HSL to RGB…1HSL to RGB…1

• Computing parameters:p g p

• color component ColorC i.e. (ColorR, ColorG, ColorB) = (r, g, b),


HSV to RGBHSV to RGB

• Let h [0, 360] and s, l [0,1][ , ] , [ , ]• If s = 0 then the colour is achromatic or grey and r, g, b = l

• Computing parameters:


HSV to RGB…1HSV to RGB…1

• Computing color vectors:p g


ExampleExample

RGB HSL HSV Result

(1, 0, 0) (0°, 1, 0.5) (0°, 1, 1)

(0.5, 1, 0.5) (120°, 1, 0.75) (120°, 0.5, 1)

(0, 0, 0.5) (240°, 1, 0.25) (240°, 1, 0.5)


HSI to RGBHSI to RGB

• Let h [0, 360]⎤⎡

[ , ]• If 00 < h < 120o :

)1( sib −=( )⎥⎥⎦

⎤

⎢⎢⎣

⎡

−+=

hsir 060cos

cosh1

0

)1( sib =)(1 brg +−=

0'• If 1200 < h < 240o : 0120−= hh

( )⎥⎥⎦⎤

⎢⎢⎣

⎡+= '060cos

cosh1h

sig

)1( sir −=( )⎥⎦⎢⎣ −60cos h

)(1 grb +−=


)( g

HSI to RGB…1HSI to RGB…1

• If 2400 < h < 360o :0' 240−= hh

( )⎥⎥⎤

⎢⎢⎡+= '0

cosh1 sib

)1( sig −=( )⎥⎥⎦⎢

⎢⎣ −060cos h

)(1 gbr +−= )(1 gbr +=


Image RepresentationImage Representation

• Direct CodingDirect Coding– Certain space is allotted to a pixel to code its colour Ex 3 bit per pixel 24 bit (3 bytes) per pixelcolour. Ex. 3 bit per pixel, 24 bit (3 bytes) per pixel

Bit1:r Bit 2:g Bit 3: b Colour name

0 0 0 Black

0 0 1 Blue

0 1 0 Green

0 1 1 Cyan

1 0 0 Red

1 0 1 Magenta

1 1 0 Yellow


1 1 1 white

Image Representation…1Image Representation…1

• Direct CodingDirect Coding– Each primary colour can have 256 different intensities and a pixel can have 256 x 256 x 256 possible choices.

– This 24‐bit format is called true colour representation.

– In case of black‐and‐white and grey scale images, the three primaries have the same value Black and white imageprimaries have the same value. Black‐and‐white image requires only one bit per pixel, 0 representing black and 1 representing white. Grey scale is coded with 8 bits per pixel to allow a total of 256 intensity of grey levels.

– High storage space is required for this format.



• Colour DepthColour Depth– The number of possible colors would be 2 to the power of the number of bits per pixel i.e. 2b

– A color depth of 4 bits would be 2 times itself 4 times:• 2 x 2 x 2 x 2 = 16 colors

– A color depth of of 8 bits would be 2 times itself 8 times:– A color depth of of 8 bits would be 2 times itself 8 times:• 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 colors.

– A color depth of of 24 bits would be 2 times itself 24 times:• 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x

• 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 16,777,216 colors



• Colour DepthColour Depth– In case of black‐and‐white and grey scale images, the three primaries have the same value. Black‐and‐white image requires only one bit per pixel, 0 representing black and 1 representing white. Grey scale is coded with 8 bits per pixel to allow a total of 256 intensity of grey levels.p y g y

– In R‐G‐B colour model, the colour is represented by colour intensity or its mix, whereas, in C‐M‐Y‐K colour model, the l i i d i ti E d l bcolour is mixed in proportions. E.g. red color may be

composed of 14% cyan, 100% magenta, 99% yellow and 3% black.



• True ColourTrue Colour– RGB true color would have a 24‐bit color depth and CMYK true color would have a 32‐bit color depth (8 bits per colour)

– CMYK true colour would have 256x256x256 possible colours x 256 variations of black It still takes smaller colourcolours x 256 variations of black. It still takes smaller colour space or gamut than RGB.

www.sketchpad.net/basics4.htm#gamut



• Lookup tableLookup table– Low storage space is required for this format. Pixels do not code colours directly. They refer to a table where colour value related to that pixel is stored.

– These colour values form a colour map for the image.

This 24 bit 256 entry lookup table representation is often– This 24‐bit 256 entry lookup table representation is often referred to as the 8‐bit format.



• 24‐bit 256‐entry Lookup table24 bit 256 entry Lookup table0

1

2

.

.

.

2

r g b

.

.8 bit pixel value

.

.

25524 bits


(8 bits per primary)


• Indexed ColourIndexed Colour– Colours derived from a palette. These are restricted in numbers and hence do not produce images as realistic as it can be on using RGB or CMYK model.

– This type of color is known as "Indexed Color" because colors in the palette are referenced by index numberscolors in the palette are referenced by index numbers which are used by the computer to identify each color

– Some file formats restrict the number of colors to fewer than 256. The GIF format has a color depth of 8 bits per pixel or less. GIF files use indexed color and allow a maximum of 256 colors. TIFF files can be stored as indexed color or true color.



• Grey Scale ImagesGrey Scale Images– Grayscale images have a maximum color depth of 8 bits.

– When defining shades of gray in terms of RGB, each of the 3 red, green and blue components must be equal to each other. Examples of grays are R=192 G=192 B=192, and R=128 G=128 B=128R=128 G=128 B=128.

– Since all three components must be equal for any shade of gray there are only 256 possible combinations.






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CE-201CE-201_Week3_2010