04 bitmapped images

8/6/2019 04 Bitmapped Images

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Bitmapped Images

Created : Rawesak Tanawongsuwan

[email protected]

Modified : Damras Wongsawang

[email protected]


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Bitmapped Images

Also known as raster graphics

Record a value for every pixelin the

image Often created from an external source

Scanner, digital camera,

Painting programs allow direct creationof images with analogues of naturalmedia, brushes,


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Resolution

A measure of how finely a device

approximates continuous images using

finite pixels (density ofdots or pixels)

755

299


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Device Resolution

Printers, scanners: specify as dots per unitlength, often dots per inch (dpi)

Desktop printer 600 dpi, typesetter 1270 dpi,

scanner 3003600 dpi, Video, monitors: specify aspixeldimensions

(pixel per inch - ppi)

PAL TV 768x576 px,

NTSC TV 640x480 px,

17" CRT monitor 1024x768 px,

dpidepends on physical size of screen


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55Image Resolution

Array of pixels haspixel

dimensions, but nophysicaldimensions

By default, displayed size depends onresolution (dpi) of output device

physicaldimension = pixeldimension

Can store image resolution (ppi) in image fileto maintain image's original size

Scale by displaying device resolution

originaldevice resolution

image resolution


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Resolution Calculation

128-pixel line displayed

at 72 dpi 45 mm

at 115 dpi

28 mm

at 600 dpi 5 mm

6 x 4 inches imagescanned at 600 dpi

3600 x 2400 pixels

Displayed at 72 dpi 50 x 33.3

To make it appear

at 6 x 4 inches must be scaled by72/600 = 0.12


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Changing Resolution

Changing Resolution can be done by

resampling

Reducing the pixel dimensions is calleddownsampling; increasing them is

called upsampling.

Both can lead to a loss of quality.


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Image Scaling

Scaling can be done either by applying a

transformation to each original pixel or

by applying the inverse transformationto each pixel in the scaled image.

Interpolation is needed because of the

finite size of pixels.


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1111

Trouble in scaling-up


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Forward mapping: x = s*x, y = s*y

Reverse mapping : x = x/s, y = y/s


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1313Interpolation

Nearest neighbour Use value of pixel whose centre is closest in the original

image to real coordinates of ideal interpolated pixel

Bilinear interpolation

Use value of all four adjacent pixels, weighted by

intersection with target pixel

Bicubic interpolation

Use values of all 16 adjacent pixels, weighted usingcubic splines

Nearest-neighbour interpolation is quickest but produces

poor-quality results; bicubic is slowest but produces very

good results; bilinear is in between.


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Nearest Neighbor

bilinear

bicubic


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Image files may be too big for networktransmission, even at low resolutions

Use more sophisticated data representation

or discard information to reduce data size Effectiveness of compression will depend on

actual image data

For any compression scheme, there willalways be some data for which'compressed' version is actually bigger thanthe original

Compression


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Always possible to decompress compresseddata and obtain an exact copyof theoriginal uncompressed data

Data is just more efficiently arranged, none isdiscarded

Run-length encoding (RLE)

Huffman coding Dictionary-basedschemes LZ77,LZ78,LZW

(LZW used in GIF, licence fee charged)

Lossless Compression


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2020

Run-length encoding (RLE)

RLE is an easy compression algorithm tounderstand

It replaces sequences of the same data values

within a file by a count number and a single value. Suppose the following string of data (17 bytes) has

to be compressed:

ABBBBBBBBBCDEEEEF

Using RLE compression, the compressed file takes

up 10 bytes and could look like this:

A*8BCD *4EF


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RLE


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Huffman code

Another use of binary trees

Binary trees are not only for searching alone

(binary search trees) Speedup the sending process over the Internet

or other communication medium

Efficient in compressing text or program files

Images are sometimes better handled by other

compression algorithms


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Character codes

ASCII code

Characters are represented by 8 bits (1 byte)

There are 256 possible valuesEvery character requires the same number of

bits (8 bits)

Example: A 65 01000000

B 66 01000001

C 67 01000010


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Compressing text

If using the same number of bitsfor each character, then thenumber of bits required torepresent N-character texts are

constant Goal: Try to reduce the number

of bits used to represent text toreduce the amount of data

A method: represent the mostused characters with the fewestbits as possible

SUSIE SAYS IT IS EASY

Character frequency

A 2

E 2

I 3

S 6

T 1

U 1

Y 2

Space 4

Linefeed 1


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Create the Huffman code

Make a Node object for each characterused in the message

Make a tree object for each of thesenodes

The node becomes the root of the tree

Insert these trees in a priority queue.

(order by frequency)

LF

1

U

1

T

1

Y

2

E

2

A

2

I

3

SP

4

S

6


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Remove two trees from the priorityqueue and make them into children of anew node

The new node has a frequency which is

the sum of the childrens frequencies


LF

1

U

1

T

1

Y

2

E

2

A

2

I

3

SP

4

S

6

LF

1

U

1

T

1

Y

2

E

2

A

2

I

3

SP

4

S

62


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Insert this new tree back into the priority queue Keep repeating the steps above until there is only

one tree left in the queue

LF

1

U

1

T

1

Y

2

E

2

A

2

I

3

SP4

S6

2

LF

1

U

1

T

1

Y

2

E

2

A

2

I

3

SP

4

S

6

2

3


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LF

1

U

1

T

1

Y

2

E

2

A

2

I

3

SP

4

S

6

2

3 4

5 7

9 13

22



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2929Character frequency Code

A 2 010

E 2 1111

I 3 110

S 6 10

T 1 0110

U 1 01111

Y 2 1110

Space 4 00

Linefeed 1 01110

S U S I E Sp S A Y S

10 01111 10 110 1111 00 10 010 1110 10


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Decoding the Huffman code

10 01111 10 110 1111 00 10 010 1110 10

S U S I E Sp S A Y S

LF U

T Y E

A I

SP S

0

1

0


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Dictionary-based Coding

LZW uses fixed-length codewords to represent

variable-length strings of symbols/characters thatcommonly occur together, e.g., words in English

text The LZW encoder and decoder build up the same

dictionary dynamically while receiving the data

LZW places longer and longer repeated entries intoa dictionary, and then emits the codefor anelement, rather than the string itself, if theelement has already been placed in the dictionary


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3232ALGORITHM LZW Compression


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3333LZW compression for string

ABABBABCABABBA Lets start with a very simple

dictionary (also referred toas a string table), initiallycontaining only 3 characters,with codes as follows:

Now if the input string isABABBABCABABBA, theLZW compression algorithmworks as follows:

The output codes are 1 2 4 52 3 4 6 1. Instead of sending14 characters, only 9 codesneed to be sent(compression ratio = 14/9 =1.56)


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3434LZW Decompression (simple version)

Input codes to the decoder are 1 2 4 52 3 4 6 1

LZW decompression output stringABABBABCABABBA

The initial string table is identical to what is

used by the encoder.


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3535LZW Decompression (simple version)

Apparently, the output

string isABABBABCABABBA, a

truly lossless result


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3636JPEG (Join Photographic Experts Group)

A photo of a flower compressed with successively higher

compression ratios from left to right.

http://en.wikipedia.org/wiki/Jpeg

Materials on the JPEG topic are obtainedfrom

fundamentals ofMultimedia byZe-Nian Li andMark

S. Drew

http://en.wikipedia.org/wiki/Jpeg

Digital multimedia text book


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Lossytechnique, well suited to photographs,images with fine detail and continuous tones

Consider image as a spatially varying signal

that can be analyzed in the frequency domain Experimental fact:people do not perceive the

effect ofhigh frequencies in images veryaccurately

Hence, high frequency information can bediscarded withoutperceptible loss of quality

JPEG Compression


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Overview ofJPEG

compression algorithm

http://

stargate.ecn

.purdue

.edu

/~ips

/tutorials

/jpeg

/jpegtut

1.html


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JPEG encoding process

Transform RGB to YIQ orYUV and subsample

color

DCT on image blocks

Quantization

Zig-zag ordering andrun-length encoding

Entropy coding


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Color Space Transformation

The image is converted from RGB into a

different color space called YUV

The Y component represents the brightnessof a pixel, and the Uand V components

together represent the hue and saturation

This part is useful because the human eyecan see more detail in the Y component

than in the others


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Similar to Fourier Transform, analyses a signalinto its frequency components

Takes array of pixel values, produces an arrayof coefficients of frequency components in

the image Computationally expensive process time

proportional to square of number of pixels

Apply to 8x8 blocks of pixels

Using blocks, however, has the effect of isolatingeach block from its neighboring context. This iswhy JPEG images look choppy blocky when ahigh compression ratio is specifiedby the user

Discrete Cosine Transform (DCT)


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Definition ofDCT

Given aninput functionf(i; j) overtwointegervariablesiandj(a pieceof animage), the2D DCT

transformsitinto a new functionF(u; v), withintegeru

andvrunningoverthesamerange asiandj. The

general definitionofthetransformis:

wherei;u = 0;1; : : : ; M 1; j;v = 0;1; : : : ; N 1; andtheconstantsC(u) andC(v) aredetermined by

!

!

!1

0

1

0

),(2

)12(cos

2

)12(cos

)()(2),(

M

i

N

j

jifN

vj

M

ui

MN

vCuCvuF

TT

!!

otherwise1

0if2

2)(

\\C


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2DDCT & IDCT

! !

!7

0

7

0

),(16

)12(cos

16

)12(cos

4

)()(),(

i j

jifvjuivCuC

vuFTT

! !

!7

0

7

0

),(16)12(cos

16)12(cos

4)()(),(~

u v

vuFvjuivCuCjif TT


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DCT (example)

If one such 8x8 8-bit subimage is:

and then taking the DCT results in


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Quantization

The human eye is fairly good at seeing small differencesin brightness over a relatively large area

but notso good at distinguishing the exact strength of a

high frequencybrightness variation

So we can get away with greatly reducing the amount of

information in the high frequency components.

Divide each component in the frequency domain by a

constantfor that component, and then round to thenearest integer

This is the main lossyoperation in the whole process.

!

),(

),(),(

vuQ

vuroundvu


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Applying DCT does not reduce data size

Array of coefficients is same size as array of pixels

Allows information about high frequency

components to be identified and discarded

Use fewer bits (distinguish fewer different values)

for higher frequency components

Number of levels for each frequency coefficient

may be specified separately in a quantization

matrix

JPEG Quantization


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4747Quantization

The entries of Q(u,v) tend to

have larger values towards

the lower right corner. This

aims to introduce more loss at

the higher spatial frequencies The tables below show the

default Q(u,v) values obtained

from psychophysical studies

with the goal of maximizing

the compression ratio while

minimizing perceptual losses

in JPEG images.

!

),(

),(),(

~

vu

vuFroundvuF

New result after quantization


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Example detail (1)

DCT Q


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Example detail (1)

DQ

IDCT

Q

Diff


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5050Example detail (2)


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Example detail (2)


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After quantization, there will be many zerocoefficients

Use RLEonzig-zag sequence (maximizes runs)

Use Huffman coding of other coefficients (bestuse of available bits)

JPEG Encoding


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Expand runs of zeros and decompressHuffman-encoded coefficients to reconstruct array offrequency coefficients

Use Inverse Discrete Cosine Transform (I

DCT) totake data back from frequency to spatial

domain

Data discarded in quantization step ofcompression procedure cannot be recovered

Reconstructed image is an approximation(usually very good) to the original image

JPEG Decompression


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5454Decoding process

Multiply by

quantization matrix

Apply IDCT


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If use low quality setting (i.e. coarserquantization), boundaries between 8x8blocks become visible

If image has sharp edges, these becomeblurred

Rarely a problem with photographic images,

but especially bad with text Better to use good lossless method with text

or computer-generated images

Compression Artifacts

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Example

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5757JPEG2000

JPEG2000 improves on JPEG in many areas,including image quality at highcompression ratios. It can be usedlosslesslyas well as lossily.

For JPEG2000 compression the image isdivided into tiles, but these can be anysize, up to the entire image.

Take advantage of a Discrete WaveletTransform (DWT)

Encode by using ArithmeticCoding

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File Formats

GIF(Graphics Interchange Format)

GIF files use LZW compression (lossless)

Restricted to 256 colours (indexed colour) One colour may be used to designate

transparency.

They are most suitable for simple imageswith areas of flat colour (cartoon-style

drawing, animation)

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PNG (Portable Network Graphics)

PNG was developed to supersede GIFbecause at that time LZW requiredlicence fee

It uses deflate compression (LZ77 +Hoffman Coding, lossless)

Not restricted to 256 colours

Supports alpha channels for partialtransparency and special effects

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JPEG Format

JPEG data can be stored in several differentformats.

JFIFand SPIFFare compatible formats for

JPEG images and are widely used on theWeb.

Exifcan hold either JPEG or TIFF data,

together with extensive metadata. JP2 andJPXformats are defined for storingJPEG2000 data.

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TIFF(Tag Image File Format)

TIFF is an extensible format

Store full-colour bitmaps

Uses several different compressions,LZW+JPEG, or may be no compression

Often used for storing uncompressed

digital photographs, and for interchangeof images.

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BMP (MS Windows Bitmap)

BMP is a simple bitmapped image

format that is native to Windows, but

widely supported. BMP files are often uncompressed

Platform-dependent

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PDF(Portable Document Format)

PDFdocuments can include bitmapped

image data, that may be compressed

usingJ

PEG,J

PEG2000, LZW, deflate, andothers.

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Raw Formats

Camera raw data is used when complete

control over image processing is required

There is no standardformat for camera raw

data.

Adobes DNG (Digital Negative) format is a

standard, based on the TIFF format,

intended for archiving camera raw images.

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A Raw File

A record of the data captured by the

camera sensor

Unprocessed sensor data

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Raw Image Files

File extension:.raf(Fuji)

.crw, .cr2 (Canon)

.kdc, .dcr(Kodak)

.mrw(Minolta)

.nef(Nikon)

.orf(Olympus)

.dng(Adobe)

.ptx, .pef(Pentax)

.arw, .srf(Sony)

.x3f(Sigma)

.erf(Epson)

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Digital Camera

Most digital cameras sample an imagewith red, green and blue sensors

arranged in a photoreceptor array

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Digital Camera

The purpose of the microlens arrayis to

focus the light onto each pixel

The color filter array changes the colorresponsivity of each pixel

Finally, the sensor array captures the

light and generates the electrical signal

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7171Mosaic Sensor / Color Filter Array (CFA) Camera

A 2D array to collect the photons that are recorded in

the image

Made up of rows and columns of photosensitive

detectors (CCD or CMOS) to form an image

Each element of the array contributes on pixel to thefinal image

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Color Filter Array (CFA)

The sensors count photons, produce acharge thats directly proportional to theamount of light that strikes them

The raw files from color filter array camerasare grayscale

Grayscale to Color

Each element in the array is covered by acolor filter, so that each element capturesonly red, green, or blue light

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A Bayer filter pattern

A mosaic of red, blue and green filters in alternatingrows ofRG and GB

Twice as many green filters are used as redor blue

because our eyes are most sensitive to green light

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Filter patterns

RGB or CMY or 4-color-mix are possible

Each element in the sensor capturesonly one color

The red-filtered elements produce agrayscale value proportional to theamount of red light reaching the sensor

Same as the green-filtered and bluefiltered elements

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Info. in the raw files

The image pixels themselves

The image metadata (data about data)

Records shooting data such as the cameramodel, serial number, shutter speed,

aperture, focal length, flash

Additional information that might beneeded to convert into an RGB image

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Raw Converter

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Demosaicing

To display the image, we must create an

image that has a red, green and blue

pixel at each location Interpolate the missing sensor values

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Demosaicing Illustration

This is the original image, made with AdobeIllustrator

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A simulated sampling taken by a Bayer filteredsensor array

Each pixel only has a value of either R or G or B

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A zoom-in version

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An example reconstruction

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A zoom-in version

original reconstruct

8383D i i Al ith


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Demosaicing Algorithms

Nearest Neighbor Replication

simply copies an adjacent pixel of the correct color component

Simple interpolation

Bilinear, Bicubic, Spline, Laplacian interpolation

Synthetic field based interpolation Compute an alternate representation

Hue interpolation, Log hue interpolation

Adaptive

Adapt their methods of estimation depending on features of the

area surrounding the pixel of interest

Proprietary

Commercial products

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Raw Conversion

In addition to demosaicingWhite balance

Colorimetric interpretation assigns the correct,

specific color meanings to the red, green, andblue pixels, usually in a colorimetrically definedcolor space such as CIE XYZ, which is baseddirectly on human color perception

Gamma correction is done to redistribute thetonal information so that it corresponds moreclosely to the way our eyes see light and shade

Noise reduction, anti-aliasing, and sharpening

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Benefits Finer control is easier for the settings

For example, the white point can be set to any value,not just discrete values like "daylight" or"incandescent"

The settings can be previewed and tweaked toobtain the best quality image or desired effect

Camera raw files have 12 or 14 bits of brightnessinformation

JPEG loses fine details and is ill-suited for majorcolor or brightness changes

The working color space can be set to whatever isdesired

Different demosaicing algorithms can be used, notjust the one coded into the camera

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Drawbacks Camera raw files are typically 2-6 times larger than

JPEG Fewer images can fit on a given memory card

It also takes longer for the camera to write rawimages to the card

fewer pictures can be taken in quick succession (a sportssequence)

No single widely-accepted standard raw format Adobe's DNG format has been put forward as a standard,

but is not adopted by major camera companies Specific software may be required to open raw files

on some systems, as opposed to JPEG or TIFF

Time taken in the image workflow

8787Software Supports


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Software Supports Dcraw

Adobe Photoshop / Adobe Photoshop Lightroom Microsoft's Digital Image

Mac OS X

added raw support directly to the system

which adds raw support automatically to the majority of MacOS X applications (such as Preview, Mac OS X's PDF and imageviewing application)

Helicon Filter

Bibble Pro

Picasa a free image editing and cataloging program from Google, but

only limited tools for RAW processing

UFRaw is free software based on dcraw

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References

Adobe.com

Wikipedia.org

http://www.imageval.com/public/Products/ISET/ISET_Manual/Demosaicing.htm

http://photo.net/learn/raw/

http://www.cambridgeincolour.com/tutorials/RAW-file-format.htm

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Image Manipulation

Image manipulation software provides highlevel operations for systematically alteringpixels

Most operations are described by analogy withtraditional photographic techniques, such asthe use ofmasks andfilters.

Bitmapped images are manipulated to correcttechnicaldeficiencies, alter the content(retouch) or create artificial compositions.

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Image Editing Software

Photoshop is the de facto industry

standard;

The Gimp is an Open Source alternative. Image Magickcan be used for

command-line processing.

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Compositing

The process ofassembling multipleimages to make a final image.

Images are often organized into layers,which are like overlaid sheets that mayhave transparent areas.

Layers are used for compositing or

experimenting with different versions ofan image.

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Selection

Areas may be selected by drawing with

marquee : geometrical shape

lasso tools or Bzier pen : free hand

magic wand: selected on the basis of colour

similarity

magnetic lasso : selected on the basis of edges

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(Selection based on color)

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(Selection based on edge detection)

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Mask & Alpha Channel

Any selection defines a mask the area that

is not selected. Masked areas of the image

are protected from changes (all or nothing).

A greyscale mask, which is partially

transparent, is an alpha channel.

An alpha channelcan be associated with a

layer as a layer mask, and used for effects

such as knock-outs and vignettes.

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(Knock-out)

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p = Ep1

+(1-E)p2

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Pixel Point Processing

In pixel point processing, each pixels

new value depends only on its oldvalue

Brightness, contrastand levels are

relatively crude pixel point adjustments.

p = f(p)

100100Brightness (increase B&W)


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(Original image)

(increase difference between B&W)

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Levels adjustment(Adjust B&W independently)

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dj


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Curve Adjustments

Curves adjustments provide full control

over the relationship between original

and new values.

A sigmoidcurve is often used to

enhance contrast.

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fixed

Increase white

Increase black

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Pi l G P i


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Pixel Group Processing

Pixel group processing uses the valuesof neighbouring pixels as well.

The convolution operation in the

frequency domain can be implementedas a weighted average in the spatialdomain: for each pixel in the filtered

image, the pixels of a convolution kernelare combined using a convolution mask.

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G i Filt


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Gaussian Filter

Simple blurring uses a 3 x 3 mask with

equal values but produces crude results.

Gaussian blur is preferred, as itproduces more natural results.

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Sh i


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Sharpening

Sharpening with a 3x3 mask is crude.

Unsharp masking combining an image

with a Gaussian blurred copy of itself produces better-looking results.

Over-sharpening should always be

avoided.

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I Editi d M i l ti


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Image Editing and Manipulation

Image Inpainting / Image Completion

Texture Synthesis

Shape manipulation .

.

.

04 bitmapped images

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