IntroductionWhat are Image Features?More Color WoesTopicsImage EnhancementSpatial Domain MethodsPoint Transforms: General IdeaGrayscale TransformsPoint Transforms: BrightnessPoint Transforms:ThresholdingPoint Transforms: Linear StretchLinear ScalingSlide 13Scaling Discrete ImagesExamplesNon-Linear Scaling: Power LawSquare Root Transfer: g=.5g=3.0Slide 19Slide 20Threshold SelectionHistogramsImage HistogramProbability InterpretationCumulative Density FunctionSlide 26Color HistogramsHistogram EqualizationSlide 29Desired HistogramBrute ForceSlide 32ExampleSlide 34ComparisonWhy?Why? continuedSlide 38Histogram Equalization AlgorithmObservationsNoise ReductionNoiseSources of NoiseNoise ModelEffect of sTwo Dimensional GaussianSlide 47Noise Reduction - 1Slide 49Neighborhood Operations2D Analog of 1D Convolution2D Blurring KernelConvolutionSlide 54Border ProblemConvolution SizeSlide 57Properties of ConvolutionSlide 59Noise Reduction - 1Slide 61hmmmmm…..Noise Reduction - 2: Median FilterNoise Reduction - 2Edge Preserving SmoothingNagao-Matsuyama FilterKuwahara FilterKuwahara Filter ExampleAnisotropic Diffusion FilteringExample: Perona-MalikObservations on EnhancementSummaryIntroduction toComputer VisionIntroductionIntroductionTOPIC 4Feature ExtractionIntroduction toComputer VisionWhat are Image Features?What are Image Features?Local, meaningful, detectable parts of the image.Introduction toComputer VisionMore Color WoesMore Color WoesSquares with dots in them are the same colorIntroduction toComputer VisionTopicsTopicsImage EnhancementBrightness mappingContrast stretching/enhancementHistogram modificationNoise Reduction……...Mathematical TechniquesConvolutionGaussian FilteringEdge and Line Detection and ExtractionRegion SegmentationContour ExtractionCorner DetectionIntroduction toComputer VisionImage EnhancementImage EnhancementGoal: improve the ‘visual quality’ of the imagefor human viewingfor subsequent processingTwo typical methodsspatial domain techniques....operate directly on image pixelsfrequency domain techniques....operate on the Fourier transform of the imageNo general theory of ‘visual quality’General assumption: if it looks better, it is betterOften not a good assumptionIntroduction toComputer VisionSpatial Domain MethodsSpatial Domain MethodsTransformation Tpoint - pixel to pixelarea - local area to pixelglobal - entire image to pixelNeighborhoods typically rectangulartypically an odd size: 3x3, 5x5, etccentered on pixel I(x,y)Many IP algorithms rely on this basic notionT(I(x,y))I(x,y) I’(x,y)neighborhood NI’(x,y) = T(I(x,y))O=T(I)Introduction toComputer VisionPoint Transforms: General IdeaPoint Transforms: General IdeaO = T(I)0255255INPUTOUTPUTInput pixel value, I, mapped to output pixel value, O, via transfer function T.TransferFunction TIntroduction toComputer VisionGrayscale TransformsGrayscale TransformsPhotoshop ‘adjust curve’ commandInput gray value I(x,y)Output gray value I’(x,y)Introduction toComputer VisionPoint Transforms: BrightnessPoint Transforms: Brightness0 0.5 100.510 0.5 100.510 0.5 100.510 100 2000200040000 0.5 10200040000 0.5 1020004000Introduction toComputer VisionPoint Transforms:ThresholdingPoint Transforms:ThresholdingT is a point-to-point transformationonly information at I(x,y) used to generate I’(x,y)ThresholdingImax if I(x,y) > tImin if I(x,y) ≤ t I’(x,y) =t=89t 25500255Introduction toComputer VisionPoint Transforms: Linear StretchPoint Transforms: Linear Stretch0255255INPUTOUTPUTIntroduction toComputer VisionLinear ScalingLinear ScalingConsider the case where the original image only utilizes a small subset of the full range of gray values:New image uses full range of gray values.What's F? {just the equation of the straight line}I'(x,y)I(x,y) ImaxImin00KKOutput image I'(x,y) = F [ I(x,y)] Desired gray scale range: [0 , K]Input image I(x,y) Gray scale range: [I , I ]min maxIntroduction toComputer VisionLinear ScalingLinear ScalingF is the equation of the straight line going through the point (Imin , 0) and (Imax , K)useful when the image gray values do not fill the available range.Implement via lookup tablesI' = mI + bI'(x,y) = I(x,y) -minIKImax min- IKImax min- IIntroduction toComputer VisionScaling Discrete ImagesScaling Discrete ImagesHave assumed a continuous grayscale.What happens in the case of a discrete grayscale with K levels??Empty!1 2 3 4 5 6 7001235467Input Gray LevelOutput Gray LevelIntroduction toComputer VisionExamplesExamplesLightenDarkenEmphasize Dark Pixels Like Photographic SolarizationIntroduction toComputer VisionNon-Linear Scaling: Power LawNon-Linear Scaling: Power Law < 1 to enhance contrast in dark regions > 1 to enhance contrast in bright regions.O = I0 0.5 100.51Introduction toComputer VisionSquare Root Transfer: =.5Square Root Transfer: =.50 0.5 100.51Introduction toComputer Vision=3.0=3.00 50 100 150 200 250050010001500200025003000350040000 50 100 150 200 250050010001500200025003000350040000 0.5 100.51Introduction toComputer VisionExamplesExamplesTechnique can be applied to color imagessame curve to all color bandsdifferent curves to separate color bands:Introduction toComputer VisionPoint Transforms:ThresholdingPoint Transforms:ThresholdingT is a point-to-point transformationonly information at I(x,y) used to generate I’(x,y)ThresholdingImax if I(x,y) > tImin if I(x,y) ≤ t I’(x,y) =t=89t 25500255Introduction toComputer VisionThreshold SelectionThreshold SelectionArbitrary selectionselect visuallyUse image histogramThresholdIntroduction toComputer VisionHistogramsHistogramsThe image shows the spatial distribution of gray values.The image histogram discards the spatial information and shows the relative frequency of occurrence of the gray values.0 3 3 2 5 5 1 1 0 3 4 5 2 2 2 4 4 4 3 3 4 4 5 5 3 4 5 5 6 6 7 6 6 6 6 50 2 .05 1 2 .05 2 4 .11 3 6 .17 4 7 .20 5 8 .22 6 6 .17 7 1 .03 ImageCountGray ValueRel. Freq.Sum= 36 1.00Introduction toComputer VisionImage HistogramImage HistogramThe histogram typically plots the absolute pixel count as a function of gray value:0 1 2 3 4 5 6 7012345678Pixel CountGray ValueFor an image with dimensions M by NMNiHIIiminmin)(Introduction toComputer