IntroductionWhat are Image Features?More Color WoesTopicsImage EnhancementSpatial Domain MethodsPoint Transforms: General IdeaGrayscale TransformsPoint Transforms: BrightnessPoint Transforms:ThresholdingPoint Transforms: Linear StretchLinear ScalingLinear ScalingScaling Discrete ImagesNon-Linear Scaling: Power LawSquare Root Transfer: g=.5g=3.0ExamplesPoint Transforms:ThresholdingThreshold SelectionHistogramsImage HistogramProbability InterpretationCumulative Density FunctionExamplesColor HistogramsHistogram EqualizationHistogram EqualizationDesired HistogramBrute ForceHistogram EqualizationExampleExampleComparisonWhy?Why? continuedWhy? continuedHistogram Equalization AlgorithmObservationsNoise ReductionNoiseSources of NoiseNoise ModelEffect of sTwo Dimensional GaussianNoiseNoise Reduction - 1Noise Reduction - 1Neighborhood Operations2D Analog of 1D Convolution2D Blurring KernelConvolutionExampleBorder ProblemConvolution SizeConvolutionProperties of ConvolutionNoise Reduction - 1Noise Reduction - 1Noise Reduction - 1hmmmmm…..Noise Reduction - 2: Median FilterNoise Reduction - 2Edge Preserving SmoothingNagao-Matsuyama FilterKuwahara FilterKuwahara Filter ExampleAnisotropic Diffusion FilteringExample: Perona-MalikObservations on EnhancementSummaryIntroduction toComputer VisionIntroductionIntroductionZhigang Zhu, City College of New York [email protected] I6716Spring 2011Image EnhancementPart IFeature Extraction (1)Introduction toComputer VisionWhat are Image Features?What are Image Features?nLocal, meaningful, detectable parts of the image.Introduction toComputer VisionMore Color WoesMore Color WoesSquares with dots in them are the same colorIntroduction toComputer VisionTopicsTopicsnImage EnhancementlBrightness mappinglContrast stretching/enhancementlHistogram modificationlNoise Reductionl……...nMathematical TechniqueslConvolutionlGaussian FilteringnEdge and Line Detection and ExtractionnRegion SegmentationnContour ExtractionnCorner DetectionIntroduction toComputer VisionImage EnhancementImage EnhancementnGoal: improve the ‘visual quality’ of the imagelfor human viewinglfor subsequent processingnTwo typical methodslspatial domain techniques....uoperate directly on image pixelslfrequency domain techniques....uoperate on the Fourier transform of the imagenNo general theory of ‘visual quality’lGeneral assumption: if it looks better, it is betterlOften not a good assumptionIntroduction toComputer VisionSpatial Domain MethodsSpatial Domain MethodsnTransformation Tlpoint - pixel to pixellarea - local area to pixellglobal - entire image to pixelnNeighborhoods ltypically rectangularltypically an odd size: 3x3, 5x5, etclcentered on pixel I(x,y)nMany 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 TransformsnPhotoshop ‘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:ThresholdingnT is a point-to-point transformationlonly information at I(x,y) used to generate I’(x,y)nThresholdingImax 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 ScalingnConsider the case where the original image only utilizes a small subset of the full range of gray values:nNew image uses full range of gray values.nWhat'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 ScalingnF is the equation of the straight line going through the point (Imin , 0) and (Imax , K)nuseful when the image gray values do not fill the available range.nImplement via lookup tablesI' = mI + bI'(x,y) = I(x,y) -minIKImax min- IKImax min- IIntroduction toComputer VisionScaling Discrete ImagesScaling Discrete ImagesnHave assumed a continuous grayscale.nWhat happens in the case of a discrete grayscale with K levels??Empty!1 2 3 4 5 6 7001235467Input Gray LevelOutput Gray LevelIntroduction toComputer VisionNon-Linear Scaling: Power LawNon-Linear Scaling: Power Lawn < 1 to enhance contrast in dark regionsn > 1 to enhance contrast in bright regions.O = Ig0 0.5 100.51g=1g<1g>1Introduction toComputer VisionSquare Root Transfer: g=.5Square Root Transfer: g=.50 0.5 100.51Introduction toComputer Visiong=3.0g=3.00 50 100 150 200 250050010001500200025003000350040000 50 100 150 200 250050010001500200025003000350040000 0.5 100.51Introduction toComputer VisionExamplesExamplesnTechnique can be applied to color imageslsame curve to all color bandsldifferent curves to separate color bands:Introduction toComputer VisionPoint Transforms:ThresholdingPoint Transforms:ThresholdingnT is a point-to-point transformationlonly information at I(x,y) used to generate I’(x,y)nThresholdingImax if I(x,y) > tImin if I(x,y) ≤ t I’(x,y) =t=89t 25500255Introduction toComputer VisionThreshold SelectionThreshold SelectionnArbitrary selectionlselect visuallynUse image histogramThresholdIntroduction toComputer VisionHistogramsHistogramsnThe image shows the spatial distribution of gray values.nThe 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 HistogramnThe 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 VisionProbability InterpretationProbability InterpretationnThe graph of relative