Digital Images. Analogic Signal

Transcription

1 Digital Images Analogic Signal t 1

2 Sampling T a t Samples T a t 2

3 Quantifying N2 N1 N4 N3 t Quantifying Error N2 N1 N4 N3 t 3

4 Coding N4= N3= N2=01 01 t N1=00 00 Digital Sinal: D/A Conversion t 4

5 D/A Conversion t Digital Representation Advantages A single storing device can be used for several data type. Transmission of different data types can be achieved over a unified digital network. Digital signal is stronger than analogic signals: Less noise sensitivity. Reconstruction capability. Avoids losses in transmission or storing. Several methods to detect and correct errors are available. Easy to secure data using cipher codes. 5

6 Digital Representation Disadvantages Converting from Analog to Digital can add distortion: Signal bandwidth is limited the sampling rate. The quantifying error depends on number of quantification classes and the bits per sample. Reducing distortion requires an increase in the sampling rate and/or the number bits used to code each sample. Successive A/D and D/A conversions can produce a signal different from the original. Resolution: Nr of pixels 3x6 12x24 48x96 192x384 NL linhas NPix = NC * NL NC colunas 6

7 Spatial Resolution Pixels per linear lenght unit (density). Can take different values for x and y. Usual Units: DPI (dots per inch) PPI (point per inch) PPM (points per meter) Examples: 300 DPI = High Resolution, for printing jobs. 72 DPI = Low Resolution, for monitor presentations. Res x = NC / X Res y = NL / Y Spatial Resolution X Y NL linhas Medium Resolution: Res m = (Res x + Res y ) / 2 Diagonal Resolution NC colunas Area resolution: Res A = (NL*NC) / (X*Y) = Res x * Res y [P/mm 2 ] ou [DPI 2 ] 7

8 Resolution: Example Photograph 4 x 6 ( 10 cm x 15 cm) Sampled by 1200 x 1800 pixels The sampling resolution is: Res x = 300 DPI Res y = 300 DPI Res = 300 DPI! Res = 300 DPI x 300 DPI Res = 300 x 300 DPI Res = DPI Res = DPI 2 - Correct - Acceptable - Wrong! Ambiguity if Res x!=res y Pixel Pitch Distance between pixels Pixel Size Pitch = 1 / Res p w = 1 / Res w = W / NC p h = 1 / Res h = H / NL Units: W p w mm, m, in, mm / pix m / pix in / pix H p h NL linhas NC colunas 8

9 Color Depth Defines the number of colors a pixel can take. Units: colors bits Bits Colors n colors = 2 b bits b bits = log 2 (n colors) Pixel Size (PS) Usually: PS = b bits = log 2 (n colors) Color in Images and Video Visible light is an electromagnetic wave in the 400 nm nm range. Most light we see is not one wavelength, it's a combination of many wavelengths. 18 9

10 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. 19 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: where E is the light and S is the sensitivity function 20 10

11 RGB A color can be represented by a vector of 3 distinct light intensities (R,G,B). PS = b r + b g + b b G R B CMY Models 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) CMYK Model: K (black) is used as a primary color to save ink deposited on paper => dry quicker - popularly used by printing press (minus red) Cyan C 1 R M 1 G Y 1 B Green Black Yellow (minus blue) Red Blue Magenta (minus green) 11

12 YUV Y luma, brightness, luminancia U, V chrominance, crominância Idea: Y = R + G + B -> monochromatic image U = Y-B V = Y-R R = Y-V B = Y-U G = Y-R-B Advantages: A monochromatic receiver can use only the Y channel. Resolution for U and V channels can be reduced... Variations: Y UV, YCbCr, YPbPr Y UV Y gamma corrected Y 12

13 Information Quantity Image Memory Size Image Byte Size [Image File Size] Space required to store a complete image without compression M = NPix * PS = NC * NL * PS Image File header Pixel Array Header can include: File format Identifier. Number of rows and columns. Pixel format Resolution (pixel density) Aspect Ratio Compression Method Data Author File Size (FS): FS = Header + M = = Header + NPix * PS = = Header + NC * NL * PS 13

14 Multiples IEC prefixes for binary multiples: Name Symbol Value quilo k 10 3 = mega M 10 6 = giga G 10 9 = tera T = peta P = exa E = zetta Z = yotta Y = Name Symbol Value kibi Ki 2 10 = mebi Mi 2 20 = = gibi Gi 2 30 = = tebi Ti 2 40 = pebi Pi 2 50 = exbi Ei 2 60 = zebi Zi 2 70 = yobi Yi 2 80 = GIF(GIF87a,GIF89a): File Formats: GIF 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 28 14

15 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 29 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 30 15

16 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. 31 XBM: X-windows BitMap XBM 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

17 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 33 Aspect Ratio Display Aspect Ratio (DAR) Image Aspect Ratio (IAR) Relation between the horizontal and vertical dimesions of an image or a device. DAR = W:H Storage Aspect Ratio (SAR) SAR = NC:NL 17

18 Aspect Ratio Pixel Aspect Ratio (PAR) Pixel Aspect Ratio Relation between the horizontal and vertical dimansions of one pixel. W pw p w H Y p h Usually: PAR 1 NC colunas NL linhas PAR p H W H W H NC NL NL NC W H NC NL 18

19 PAR <-> DAR PAR W NC H NL DAR NC NL DAR NL NC PAR = DAR / SAR DAR PAR NC NL When PAR = 1:1 => DAR = SAR = NC:NL 4:3 -> 16:9 19

20 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, ) 20

21 ImageMagick Animate Compare Composite Conjure Convert Display Identify Import Mogrify Montage Stream animate an image sequence on any X server. mathematically and visually annotate the difference between an image and its reconstruction. overlap one image over another. interpret and execute scripts written in the Magick Scripting Language (MSL). convert between image formats as well as resize an image, blur, crop, despeckle, dither, draw on, flip, join, re-sample, and much more. display an image or image sequence on any X server. describe the format and characteristics of one or more image files. 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. 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. 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. 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 21

22 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 Chapter 12 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 A d, S A s ) 22

23 Blender Hardware Buff Source Color (S) A D ALU R B G A s A s :Source Blending Factor A D :Destination Blending Factor Blending Function Frame Buffer (D) 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 23

24 Example: Simple blending Draw a blue rectangle (no blending) Define: Source blend factor: Destination blend factor: Blending function: Add Draw a red rectangle: A s = (0.7, 0.7, 0.7) A d = (0.2, 0.2, 0.2) D D S 0.7 D r D r S r 0.7 D g D g S g 0.7 D b D b S b 0.7 Blending images P 1 P 2 D 70% + 30% = D P P D P 1 D D P

25 Blending and Alpha Channel Store blending factor as part of color Instead of Color = (r, g, b) Include a 4 th 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 (A s ) o A s = α RGB Blending colors using Alpha is called: Alpha Blending 32 bit pixel values alpha Compositing with Alpha blending X1 X2 X3 X4 pandn pandn pandn pandn 0000h FFFFh 0000h FFFFh + = X1!=green Y1 Y2 Y3 Y4 X + Y = S pand pand pand green pand green 0000h FFFFh 0000h FFFFh X2=green X3!=green X4=green =? =? =? =? green green X1 0000h X3 0000h α X α 0000h FFFFh 0000h FFFFh 0000h Y2 0000h Y4 (1-α) Y S=α X + (1-α) Y 25

26 Alpha as: Opacity When: o Source Blend Factor o Destination Blend Factor o Blend Function: Add Alpha is opacity Alpha = 1 o Destination is over-written Alpha = 0 o Source is completely invisible! Transparency Example Draw a normal blue rectangle Pixel color (Destination) o D r D g D b = (0.1, 0.1, 0.8) Blending setting: Source blend: A s = S α Destination blend: A d = (1 - S α ) Blending Function: Add Now, a red rectangle with Source Color: o S r S g S b S α = (0.9, 0.1, 0.1, 0.8) 26

27 Transparency with Alpha Blending Transparent front color with opacity Solid back color rgb rgb f ( 1 ) rgb b Multiple Transparency Transparent color (rgb 1 )with opacity 1 Transparent color (rgb 2 )with opacity Solid back color rgb rgb (1 ) rgb rgb rgb (1 ) [ rgb 1 rgb rgb (1 ) rgb rgb' (1 ) rgb ] 1 2 (1 ) (1 ) rgb

28 Blending Alphas Transparent front color with opacity f Transparent back color with opacity b rgb rgb f f (1 ) 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. f (1 ) rgb f b f b b Alpha Buffer R G B A ALU Blending Function Frame Buffer (D) 28

29 Premultiply alpha Transparent front color with opacity f Transparent back color with opacity b rgb rgb f f (1 ) f (1 ) rgb f b f b b 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); 29

30 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 30

31 Alpha mask prodution Problem Definition: The separation of an image C into o A foreground object image C o, o a background image C b, o and an alpha matte C o 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 31

32 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-p 1 (B-p 2 G) Hope that foreground object doesn t look like background o no blue ties! Why blue? Why uniform? 32

33 Chroma Key Equipment The Ultimatte p 1 and p 2 33

34 Semi-transparent mattes Requires true alpha matte, which involves semi-transparency Alpha between 0 and 1 3D compositing 34

35 Images with Alpha Channel Some image file formats can include Alpha information for each pixel: Alpha Channel Example: PNG 1 pixel: RGBA = 32 bits 16 millions colors * 256 opacity levels. The GIF format supports a transparent color identification: 256 colors = 255 opaque colors + 1 transparent color Additional Reading