Image ProcessingJason LawrenceCS445: GraphicsAcknowledgement: slides by Misha Kazhdan, Allison Klein, Tom Funkhouser,Adam Finkelstein and David DobkinOutline• Human Vision• Image Representation• Reducing Color Quantization Artifacts• Basic Image ProcessingHuman VisionModel of Human Visual SystemHuman eyeObjects in worldSunHuman VisionModel of Human Visual SystemHuman eyeObjects in worldSunVision Components:• Incoming Light• The Human EyeElectromagnetic Spectrum• Visible light frequencies range between ...oRed = 4.3 x 1014 hertz (700nm)oViolet = 7.5 x 1014 hertz (400nm)Figures 15.1 from H&BVisible Light• The human eye can “see” light in the frequency range 400nm – 700nmWhite LightFigure 15.3 from H&BFrequencyEnergyRed(700 nm)Violet(400 nm)Visible Light• The human eye can “see” light in the frequency range 400nm – 700nmWhite LightFigure 15.3 from H&BFrequencyEnergyRed(700 nm)Violet(400 nm)This does not mean that we can see the difference between the different spectral distributions.Metamers = Two spectral distributions that look the sameThe human retina contains two types of photoreceptors, cones and rods.Rods:• 120 million rods in the retina• 1000x more light sensitive than cones• Responsible for scotopic vision• Short-wavelength sensitive• Responsible for peripheral visionCones:• 6-7 million cones in the retina• Responsible for high-res vision• Color sensitive:o64% red, 32% green, 2% blue• Distributed in the fovea centralisTristimulus Theory of ColorFigure 13.18 from FvDFH Spectral-response functions of each of the three types of cones on the human retina.This motivates encodingcolor as a combination ofred, green, and blue (RGB).Outline• Human Vision• Image Representation• Reducing Color Quantization Artifacts• Basic Image ProcessingImage RepresentationWhat is an image?Image RepresentationAn image is a 2D rectilinear array of pixels:A width x height array where each entry of the array stores a single pixel.Continuous image Digital imagewhImage RepresentationWhat is a pixel?Continuous image Digital imageImage RepresentationA pixel is something that captures the notion of color• Luminance pixelsoGrey-scale images (aka “Intensity images”)o0 – 1.0 or 0 – 255• Red, Green, Blue pixels (RGB)oColor imageso0 – 1.0 or 0 – 255Image Resolution• Spatial resolution: width x height pixels• Intensity/Color resolution: n bits per pixel• Temporal resolution: n Hz (fps)Width x HeightBit DepthHzNTSC640 x 480830Handheld640 x 4801645Monitor1920 x 12002475CCDs3000 x 200036-Laser Printer6600 x 51001 -Image Quantization Artifacts• With only a small number of bits associated to each color channel of a pixel there is a limit to intensity resolutions of an imageoA black and white image allocates a single bit to the luminance channel of a pixel. » The number of different colors that can be represented by a pixel is 2.oA 24 bit bitmap image allocates 8 bits to the red, green, and blue channels of a pixel.» The number of different colors that can be represented by a pixel is 16,000,000.Outline• Human Vision• Image Representation• Reducing Color Quantization ArtifactsoHalftoning and Dithering• Basic Image ProcessingSTOPPED HERE18QuantizationImage with decreasing bits per pixel oNote contouring!8 bits 4 bits 2 bits 1 bitQuantization• When you have a small number of bits per pixel, you can coarsely represent an image by quantizing the color values:I(x, y)Q(x, y)2 bits per pixelb is the number of bits per pixel0852551700 1 2 3Reducing Effects of QuantizationTrade spatial resolution for intensity resolution:• Halftoning• DitheringoRandom ditheroOrdered ditheroError diffusion ditherClassical Halftoning• Varying-size dots represent intensities• Area of dots inversely proportional to intensityI(x, y)P(x, y)Classical HalftoningNewspaper ImageFrom New York Times, 9/21/99Digital Halftoning• Use cluster of pixels to represent intensity• Trades spatial resolution for intensity resolution• Note that halftoning pattern mattersoWant to avoid vertical, horizontal lines0 ≤ I ≤ 0.2 0.2 < I ≤ 0.4 0.4 < I ≤ 0.6 0.6 < I ≤ 0.8 0.8 < I ≤ 1.0Digital Halftoning• Use cluster of pixels to represent intensity• Trades spatial resolution for intensity resolution• Note that halftoning pattern mattersHalftoned(1 bit)Original(8 bits)Quantized(1 bit)Dithering• Distribute errors among pixelsoExploit spatial integration in our eyeoDisplay greater range of perceptible intensitiesRandom Dither• Randomize quantization errors• Errors appear as noiseP(x,y)I(x,y)Random Dither• Randomize quantization errors• Errors appear as noiseP(x,y)I(x,y)If a pixel is black, then adding random noise to it, you are less likely to turn it into a white pixel then if the pixel were dark gray.Random Dither• Randomize quantization errors• Errors appear as noiseP(x,y)I(x,y)If a pixel is black, then adding random noise to it, you are less likely to turn it into a white pixel then if the pixel were dark gray.How much noise should we add?Random Dither• Randomize quantization errors• Errors appear as noiseP(x,y)I(x,y)If a pixel is black, then adding random noise to it, you are less likely to turn it into a white pixel then if the pixel were dark gray.How much noise should we add?Enough so that we can effect rounding,but not so much that we overshoot:[-0.5,0.5]Random DitherUniformQuantization(1 bit)Random Dither(1 bit)Original(8 bits)Ordered Dither• Pseudo-random quantization errors• Matrix stores pattern of thresholdsi = x mod nj = y mod nif (I(x,y)/255 > D(i,j) / (n^2+1)) P(x,y) = 1else P(x,y) = 0For Binary DisplaysOrdered Dither• Pseudo-random quantization errors• Matrix stores pattern of thresholdsFor b bit displaysi = x mod nj = y mod nc = (I(x,y)/255)*(2^b-1)e = c - floor(c)if (e > D(i,j) / (n^2+1) ) P(x,y) = ceil(c)else P(x,y) = floor(c)Ordered DitherRandomDither(1 bit)Original(8 bits)OrderedDither (1 bit)Error Diffusion Dither• Spread quantization error over neighbor pixelsoError dispersed to pixels right and below• Below we see Floyd-Steinberg MethodFigure 14.42 from H&Bαβγ δα + β + γ + δ = 1.0Error Diffusion Ditherfor (i = 0; i < height; i++) for (j = 0; j < width; j++) Desti,j = quantize(Sourcei,j) error = Sourcei,j − Desti,j Sourcei,j+1 = Sourcei,j+1 + α * error Sourcei+1,j-1 = Sourcei+1,j-1 + β * error Sourcei+1,j = Sourcei+1,j + γ * error Sourcei+1,j+1 =
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