Lecture 9: Digital ImagesAnnouncementsGoals for TodayReview: Images vs. Sounds in BitsExamples of Bit TradeoffsBit Allocation TradeoffsGrayscale vs. ColorColor Digital ImagesIntensity FormatResizing ImagesImage Quality Depends on…Color Display: Computer vs. PaperHalftoningComputer vs. Printed DisplayImages have Frequency Too!Simple Cosines in TimeSimple Cosines in SpaceCombining Spatial CosinesMore Illustrations of Spatial FrequencyFrequency Content of Natural Time SignalsFrequency Content of ImagesLecture 9: Digital ImagesThe Digital World of MultimediaProf. Mari OstendorfEE299 Lecture 928 Jan 2008Announcements Guest lecture Friday Feb 1 (EEB 403, tentatively) A cultural history of JPEG… Dr. Joan Mitchell Another lecture by Dr. Mitchell on Thurs Patenting a wet suit… Thurs 1/31 10:30 EEB 125 Lab3 Read the lab *before* lab Do you want to change lab partners once or twice? Send Prof. Ostendorf anonymous emailEE299 Lecture 928 Jan 2008Goals for Today More on digital images More pixels vs. more bits/sample Gray-scale vs. color Consider the display Image have frequencies too! Foundation for image processing (filtering) and compressionEE299 Lecture 928 Jan 2008Review: Images vs. Sounds in Bits Sounds: Bits = sec x samples/sec x bits/sample Samples/sec = sampling rate Bits/sample = quantizer resolution Gray-scale images: Bits = inches horizontal x pixels/in (H) x inches vertical x pixels/in (V)x bits/pixel Pixels/in = spatial resolution Bits/pixel = gray scale resolutionEE299 Lecture 928 Jan 2008Examples of Bit TradeoffsSee Orsak et al. pp. 146-1478 bpp, 225x300=540kbits=67.5 k Bytes1 bpp, 225x300=8.4KB8 bpp, 75x1007.5kBEE299 Lecture 928 Jan 2008Bit Allocation Tradeoffs Grayscale: space sampling (pixels/inch) vs. number of gray levels (bits/pixel) Color: same, except now bits/pixel has to be allocated among 3 colors, need not be uniform See book pp.152-153  Other strategies for efficient bit usage: Tricks with color: Orsak et al. pp. 164-168 Compression (more after we learn about frequency)EE299 Lecture 928 Jan 2008Grayscale vs. Color Gray: MxN matrix  Color: MxNx3B/W intensity:• 0 = black• 1 = whiteX(i,j)=0.4X(i,j,2)=0.6 X(i,j,3)=1.0R/G/B intensity:• [0,1]=[none, full]• (0,0,0)=black• (1,1,1)=whiteX(i,j,1)=0.758 bits/pixel Æ256 gray levels8 bits/color-pixel Æ 2563colors, 24 bits/pixelEE299 Lecture 928 Jan 2008Color Digital ImagesComponent colorsEE299 Lecture 928 Jan 2008Intensity Format Reminder: Intensity is represented in… [0,1] range with floating point number (lots of bits) in display BUT, quantized and stored with fewer bits for storage For examples, 8 bits/color usually maps to:0 Æ 0.0 … 127 Æ 0.5 … 255 Æ 1.0 Quiz: Given a color image, if I increase the level by 10 steps (e.g. 0Æ10, 27Æ37, etc.) for all colors…is the image brighter or darker? Given a grayscale image, if I change the level index using Y(i,j)=255-X(i,j) [or Y(i,j)=1.0-X(i,j)]what will the image look like compared to the original?EE299 Lecture 928 Jan 2008Resizing Images Shrinking: Grayscale: replace KxK block with single pixel with average gray level of the K2 pixels in the original Color: Repeat for each color plane Enlarging: Grayscale: insert interpolated pixel values Color: repeat for each color plane, as in shrinkingEE299 Lecture 928 Jan 2008Image Quality Depends on… Skill of photographer Quality of recording device: optics, red-eye preflash, etc. Size of digital image: number of pixels (PPI), bits/pixel (BPI) Digital format: jpg, gif, etc. (see upcoming lectures on compression) Display mechanism (computer screen, printer)in the digital worldin the analog worldEE299 Lecture 928 Jan 2008Color Display: Computer vs. Paper Computer display Sampling: pixels per inch Color: RGB = red, green, blue[true color = 8x3 bits/pixel, 2563 colors per pixel] Printer display Sampling: dots per inch Color: CMY = cyan, magenta, yellow (+ black) [8 colors per dot] Printer dots not equal to digital pixels So… Need higher number of pixels to get good quality prints than for good quality computer displayEE299 Lecture 928 Jan 2008HalftoningReplace gray-scale image blocks with block that have varying amounts of B/WFrom: http://fhctech.org/fhc/imaging/halftone.htmEE299 Lecture 928 Jan 2008Computer vs. Printed Display Example: I200x1600 pixel digital image On a computer screen with 90PPI: Picture display can be 13.3”x16.7” Allows big display of small part of the image On a reasonable printer with 300DPI: Picture display can be 4”x5.3”QUIZ:In which case(s) do you want to buy a digital camera with lots of megapixels?a) You are using it for building web pages.b) You are using it for taking pictures of people for the class yearbook.c) You are using it for wildlife photography.d) You are using it on a spy mission.EE299 Lecture 928 Jan 2008Images have Frequency Too! You can build images out of 2-D “cosines”just as we build sounds out of 1-D cosines Why is this important: Simplify signal modification Facilitate signal compression Start with just gray-scale to understand concepts to simplify (and since color is just the combination of 3 gray scale images)EE299 Lecture 928 Jan 2008Simple Cosines in TimeLower frequency, fewer changes in timeHigher frequency, more changes in timeEE299 Lecture 928 Jan 2008Simple Cosines in SpaceEE299 Lecture 928 Jan 2008Combining Spatial CosinesEE299 Lecture 928 Jan 2008More Illustrations of Spatial FrequencyEE299 Lecture 928 Jan 2008Frequency Content of Natural Time SignalsAE in ‘ballot’, periodicS in ‘first’, aperiodicEE299 Lecture 928 Jan 2008Frequency Content of