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Imagens digitais

www.dee.isep.ipp.pt/~jml/intmu/slides/imagem.pdf

Sinal Analógico

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Amostragem

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Amostras

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Quantificação

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Erro de Quantificação

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Codificação

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Sinal Digital: 11111110000010101111100100

Conversão D/A

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Conversão D/A

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Vantagens da Digitalização

Um único tipo de dispositivo de armazenamento é suficiente para todos os tipos de dados.

A transmissão automática é simplificada porque apenas são necessárias redes capazes de transportar bits.

O sinal digital é mais robusto do que o analógico • é menos sensível ao ruído.

• pode sempre ser reconstituído.

• não há perda de qualidade na transmissão ou reprodução.

• são possíveis mecanismos de deteção e até correção de erros.

Facilidade de cifragem/decifragem para implementar segurança.

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Desvantagens da digitalização

O processo de digitalização introduz sempre distorções

• A largura de banda do sinal é limitada pelo número de amostras (NA)

• Erro de quantificação dependente do número de bits/amostra

Reduzir distorção implica aumentar NA*bits/amostra

A conversão sucessiva A/D e D/A não produz um sinal idêntico ao original.

Resolução: Nº de pixels

3x6 12x24 48x96 192x384

NPix = NC * NL NL linhas

NC colunas

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Resolução espacial

Píxeis por unidade de medida linear (densidade).

Pode ser diferente em x e em y.

Unidades habituais:

• DPI (dots per inch)

• PPP (pontos por polegada)

• PPM (pontos por metro)

Exemplos: • 300 DPI = Alta resolução, para impressão

• 72 DPI = Baixa resolução, para apresentação em monitores

Resolução espacial

Resx = NC / X

Resy = NL / Y

Resolução média:

Resm = (Resx + Resy ) / 2

Resolução diagonal

Pontos por unidade de área: ResA = (NL*NC) / (X*Y) = Resx * Resy [P/mm2] ou [DPI2]

NL linhas

X

Y

NC colunas

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Resolução: Exemplo

Fotografia de 4” x 6” ( 10 cm x 15 cm)

Digitalizada com 1200 x 1800 pixels

A resolução utilizada foi:

Resx = 300 DPI

Resy = 300 DPI

Res = 300 DPI !

Res = 300 DPI x 300 DPI

Res = 300 x 300 DPI

Res = 90 000 DPI

Res = 90 000 DPI2

- Correcto - Aceitável - Errado ! - Ambíguo se Resx!=Resy

Pixel Pitch

Distância entre pixels

Pitch = 1 / Res

pw = 1 / Resw = W / NC

ph = 1 / Resh = H / NL

Unidades:

• mm, mm / pix

• m, m / pix

• in, in / pix

NL linhas

W

pw

ph

H

NC colunas

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Profundidade de cor

Indica o nº de cores que um pixel pode ter.

Unidades

• cores

• bits

• n cores = 2b bits

• b bits = log2(n cores)

Pixel Size (PS)

• Normalmente: PS = b bits = log2(n cores)

Bits Cores

1 2

2 4

4 16

8 256

16 65 536

24 16 777 216

Color in Images and Video

Visible light is an electromagnetic wave in the 400 nm - 700 nm range.

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Most light we see is not one wavelength, it's a combination of many wavelengths.

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The Human Retina 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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Cones and Color

The cones provide humans with vision during the daylight and are believed to be separated into three types, where each type is more sensitive to a particular wavelength

The color signal to the brain comes from the response of the 3 cones to the spectra being observed. That is, the signal consists of 3 numbers:

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where E is the light and S is the sensitivity function

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RGB

B

R

G

Cor pode ser representada pelo conjunto de 3 intensidades distintas (R,G,B).

PS = br + bg + bb

• Used in electrostatic and ink-jet plotters that deposit pigment on paper

• Cyan, magenta, and yellow are complements of red, green, and blue, respectively

• White (0, 0, 0), black (1, 1, 1)

B

G

R

Y

M

C

1

1

1

Magenta

Red

Yellow Green

Cyan

Blue

Black

(minus green)

(minus blue)

(minus red)

CMYK Model: K (black) is used

as a primary color to save ink

deposited on paper => dry quicker

- popularly used by printing press

CMY Models

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YUV

Y – luma, brightness, luminancia U, V – chrominance , crominância

Variantes: Y’UV, YCbCr, YPbPr

Ideia: Y = R + G + B -> imagem monocromática

U = Y-B V = Y-R R = Y-V B = Y-U G = Y-R-B

Vantagens: • Recetor monocromático pode usar apenas canal Y • Resolução dos Canais U e V pode ser reduzida ….

Y’UV

Y’ – gamma corrected Y

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Quantidade de informação

• Image Memory Size

• Image Byte Size

• [Image File Size]

Quantidade de memória necessária para armazenar a imagem sem compressão:

M = NPix * PS = NC * NL * PS

Ficheiro de Imagem

Cabeçalho pode conter: • Identificador de formato. • Número de linhas e de colunas. • Formato de píxel • Resolução (densidade de píxels) • Relação de Aspeto • Tipo de compressão • Data • Autor • …

Dimensão do ficheiro (FS):

header Pixel Array

FS = Header + M =

= Header + NPix * PS =

= Header + NC * NL * PS

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Múltiplos

Nome Símbolo Valor

kibi Ki 210 = 10241

mebi Mi 220 = 10242 = 1 048 576

gibi Gi 230 = 10243 = 1 073 741 824

tebi Ti 240 = 10244 ≈ 1 099 109

pebi Pi 250 = 10245 ≈ 1 125 1012

exbi Ei 260 = 10246 ≈ 1 152 1015

zebi Zi 270 = 10247 ≈ 1 180 1018

yobi Yi 280 = 10248 ≈ 1 208 1021

Nome Símbolo Valor

quilo k 103 = 10001

mega M 106 = 10002

giga G 109 = 10003

tera T 1012 = 10004

peta P 1015 = 10005

exa E 1018 = 10006

zetta Z 1021 = 10007

yotta Y 1024 = 10008

File Formats: GIF

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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File Formats: JPEG

JPG or 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

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TIFF

TIFF: Tagged Image File Format

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 later supported by 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

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BMP

BMP: Windows BitMap Picture:

A system standard graphics file format for Microsoft Windows.

It is capable of storing 1, 4, 8, 16, 24 or 32 bit/pixel.

Used in PC Paintbrush and many other programs.

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XBM

XBM: X-windows BitMap

Primary graphics format for the X Window system

Supports 24-bit color bitmap

Many public domain graphic editors, e.g., xv

Used in X Windows for storing icons, pixmaps, backdrops, etc.

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PNG

PNG: Portable Network Graphics Designed to replace the older and simpler GIF format W3C recommendation and ISO standard Features:

• Main image types: o Truecolor: 24 or 48 bits/pixel (as TIFF). o Grayscale: 1, 2, 4, 8 or 16 bits/pixel. o Palette-based: 1, 2, 4, or 8 bits/pixel (similar to GIF).

• Alpha channels (variable transparency) • Gamma correction • Two-dimensional interlacing (for progressive display) • Lossless compression (5-25% better than GIF)

Shortcomings: • No Animation

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Relação de Aspecto

• Display Aspect Ratio (DAR)

• Image Aspect Ratio (IAR)

Relação entre a dimensão horizontal e vertical de uma imagem ou de um dispositivo.

DAR = W:H

• Storage Aspect Ratio (SAR)

SAR = NC:NL

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Relação de Aspecto

Relação de Aspecto de pixel

• Pixel Aspect Ratio (PAR)

• Relação entre a dimensão horizontal e vertical de um pixel.

Normalmente: PAR 1 NLNC

HW

NCH

NLW

NLH

NCW

NL linhas

W

pw

ph

Y

NC colunas

H

H

W

p

pPAR

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PAR <-> DAR

Quando PAR = 1:1 => DAR = SAR = NC:NL

NL

NCPARDAR

NC

NLDAR

NLNC

DAR

NLNC

HWPAR

PAR = DAR / SAR

4:3 -> 16:9

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Resolução

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

ImageMagick

Conjunto de ferramentas para edição não interactiva de imagens

• Código aberto

• Usável na maioria dos sistemas operativos

• API para maioria das linguagens de programação

• Suporta mais de 100 formatos (PPM, GIF, JPEG, PDF, PhotoCD, PNG, Postscript, SVG, TIFF, …)

www.imagemagick.org

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ImageMagick

Animate animate an image sequence on any X server.

Compare mathematically and visually annotate the difference between an image and its reconstruction.

Composite overlap one image over another.

Conjure interpret and execute scripts written in the Magick Scripting Language (MSL).

Convert convert between image formats as well as resize an image, blur, crop, despeckle, dither, draw on, flip, join,

re-sample, and much more.

Display display an image or image sequence on any X server.

Identify describe the format and characteristics of one or more image files.

Import save any visible window on an X server and outputs it as an image file. You can capture a single window,

the entire screen, or any rectangular portion of the screen.

Mogrify resize an image, blur, crop, despeckle, dither, draw on, flip, join, re-sample, and much more. Mogrify

overwrites the original image file, whereas, convert writes to a different image file.

Montage create a composite image by combining several separate images. The images are tiled on the composite

image optionally adorned with a border, frame, image name, and more.

Stream copies one or more pixel components of the image or portion of the image to your choice of storage

formats. It writes the pixel components as they are read from the input image a row at a time.

Transparency

- Blending colors

- Alpha Blending

- Transparency

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Chapter 12

Opaque drawing (overwriting)

Drawing a rectangle or image:

• Source: color of rectangle or image

• Destination: pixels in frame buffer

Source written into Destination

Source overwrites Destination

Blending vs. Over writing

Instead of over writing

• D S

Compute a new value for D

• based on current D and S

• D f (D Ad , S As)

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Blender Hardware

B

G

R

ALU

Buff

Frame Buffer (D) Blending Function

Source Color (S)

As :Source Blending Factor AD :Destination Blending Factor

AD

As

Blending Functions / Factors

Blending Functions

Add

Sub

-Sub

Copy Destination

Copy Source

Max

Min

Blending Factors

One

Zero

Constant

SrcAlpha

DestAlpha

1 - SrcAlpha

1 - DestAlpha

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Example: Simple blending

Draw a blue rectangle (no blending)

Define:

• Source blend factor:

• Destination blend factor:

• Blending function: Add

Draw a red rectangle:

As = (0.7, 0.7, 0.7)

Ad = (0.2, 0.2, 0.2)

D ← D 0.2 + S 0.7

Dr ← Dr 0.2 + Sr 0.7

Dg ← Dg 0.2 + Sg 0.7

Db ← Db 0.2 + Sb 0.7

Blending images

70% + 30% =

D ← P1 0.7 + P2 0.3

D ← P1

D ← D 0.7 + P2 0.3

P1 P2 D

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Blending and Alpha Channel

Store blending factor as part of color • Instead of Color = (r, g, b)

• Include a 4th channel: (r, g, b, α)

• Pixel called RGBA, RGBα or 32 bits RGB

α cannot affect pixel color directly • (r, g, b) changes pixel directly

• α used as o source blend factor (As)

o…

Blending colors using Alpha is called: • Alpha Blending

As = α RGB alpha

32 bit pixel values

Compositing with Alpha blending

+ =

X + Y = S

X1!=green X5

…

green

X2=green

green

X3!=green

green

X4=green

green

0000h FFFFh 0000h FFFFh

=? =? =? =?X1 X2 X3 X4

0000h FFFFh 0000h FFFFh

X1 0000h X3 0000h

pandn pandn pandn pandn

Y1 Y2 Y3 Y4

0000h FFFFh 0000h FFFFh

0000h Y2 0000h Y4

pand pand pand pand

α

α X (1-α) Y

S=α X + (1-α) Y

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Alpha as: Opacity

When: o Source Blend Factor oDestination Blend Factor

oBlend Function: Add

Alpha is opacity • Alpha = 1

oDestination is over-written

• Alpha = 0 o Source is completely invisible!

Transparency Example

Draw a normal blue rectangle • Pixel color (Destination)

o Dr Dg Db = (0.1, 0.1, 0.8)

Blending setting: • Source blend: As = Sα

• Destination blend: Ad = (1 - Sα)

• Blending Function: Add

Now, a red rectangle with • Source Color:

o Sr Sg Sb Sα = (0.9, 0.1, 0.1, 0.8)

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Transparency with Alpha Blending

bf rgbrgbrgb )1(

Solid back color

Transparent front color with opacity

Multiple Transparency

32122111

3222111

111

)1()1()1(

])1([)1(

)1(

rgbrgbrgbrgb

rgbrgbrgbrgb

brgrgbrgb

Solid back color

Transparent color (rgb1)with opacity 1

1

2

3

Transparent color (rgb2)with opacity 2

rgb'

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Blending Alphas

bff

bbfff rgbrgbrgb

)1(

)1(

Transparent back color with opacity b Transparent front color with opacity f

Process in either front to back or back to front order But can’t insert surface between them later. Requires alpha channel on the destination.

Alpha Buffer

A

B

G

R

ALU

Frame Buffer (D)

Blending Function

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Premultiply alpha

bff

bbfff rgbrgbrgb

)1(

)1(

Transparent back color with opacity b Transparent front color with opacity f

Notice - rgb always appears multiplied by it’s

Can store rgb’s as premultiplied by

Transparency in OpenGL

glEnable(GL_BLEND);

glBlendEquation(GL_FUNC_ADD);

glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA)

// Draw polygons with alpha values set

glDisable(GL_BLEND);

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alpha channel

Encodes transparency (or pixel coverage):

• Alpha = 1: opaque object (complete coverage)

• Alpha = 0: transparent object (no coverage)

• 0<Alpha<1: semi-transparent (partial coverage)

Example: alpha = 0.7

Partial coverage or semi-transparency

Compositing - example

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Alpha mask prodution

Problem Definition:

• The separation of an image C into

oA foreground object image Co,

o a background image Cb,

o and an alpha matte

• Co and can then be used to composite the foreground object into a different image

Hard problem

• Background subtraction unknown

• For movies/TV, manual segmentation of each frame is infeasible

Chroma Key

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Blue Screen

Blue Screen matting

Most common form of matting in TV studios & movies

Petros Vlahos invented blue screen matting in the 50s. His Ultimatte® is still the most popular equipment. He won an Oscar for lifetime achievement.

A form of background subtraction: • Need a known background • Compute alpha as SSD(C,Cb) > threshold

o Or use Vlahos’ formula: = 1-p1(B-p2G)

• Hope that foreground object doesn’t look like background o no blue ties!

• Why blue? • Why uniform?

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Chroma Key Equipment

The Ultimatte

p1 and p2

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Semi-transparent mattes

Requires true alpha matte, which involves semi-transparency • Alpha between 0 and 1

3D compositing

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Imagens com Alfa

Alguns formatos de armazenamento de imagens digitais podem incluir o Canal Alfa. Exemplo: PNG

1 píxel: RGBA 8 + 8 + 8 + 8 = 32 bits 16 milhões de cores * 256 níveis de transparência. O formato GIF suporta a identificação de uma cor transparente.

256 cores = 255 cores opacas + 1 transparente