IntroductionEdge DetectionDiscontinuitiesIllusory EdgesAnother OneGoalEdgelsOutlineLocating EdgelsRealityProperties of an EdgeQuantitative Edge DescriptorsEdge Degradation in NoiseReal ImageEdge Detection: TypicalEdge Detection MethodsGradient MethodsGradient of a FunctionGeometric InterpretationDiscrete ApproximationsIn Two Dimensions1x2 ExampleSmoothing and Edge DetectionEffect of BlurringCombining the TwoMany Different KernelsRoberts Cross OperatorSobel OperatorAnatomy of the SobelPrewitt OperatorLarge MasksLarge KernelsCompass MasksSlide 34Robinson Compass MasksAnalysis of Edge KernelsDemo in PhotoshopPrewitt ExampleEdge ThresholdingNon-Maximal SuppressionSlide 41Slide 42Slide 43Slide 44Canny Edge DetectorBasic AlgorithmHysteresis ThresholdingCanny ResultsSlide 49PowerPoint PresentationEdges from Second DerivativesSecond DerivativesLaplacian OperatorExample Laplacian KernelsExample ApplicationDetailed View of ResultsInterpretation of the LaplacianEnhancement using the LaplacianLaplacian EnhancementNoise2D Gaussian Distributions Defines Kernel ‘Width’Creating Gaussian KernelsExampleSlide 65Kernel ApplicationWhy Gaussian for SmoothingSlide 68Why Gaussian for Smoothing – cont.Ñ2G FilterMexican Hat Filters2 Controls SizeKernelsSlide 74Slide 75Scale SpaceSlide 77Multi-Resolution Scale SpaceColor Edge DetectionHierarchical Feature ExtractionFrom Edgels to LinesEdgels to LinesSlide 83Parameter SpaceGeneral IdeaHough TransformQuantized Parameter SpaceSlide 88ProblemsWhy?Alternate RepresentationSlide 92Real ExampleModificationsGradient DataSlide 96Post HoughHough FittingGeneralizationsExample: Finding a CircleFinding a CircleFinding Circles3D Computer Visionand Video ComputingIntroductionIntroductionTOPIC 4Feature ExtractionPart 2. Edge Detection3D Computer Visionand Video ComputingEdge DetectionEdge DetectionWhat’s an edge?“He was sitting on the Edge of his seat.”“She paints with a hard Edge.”“I almost ran off the Edge of the road.”“She was standing by the Edge of the woods.”“Film negatives should only be handled by their Edges.”“We are on the Edge of tomorrow.”“He likes to live life on the Edge.”“She is feeling rather Edgy.”The definition of Edge is not always clear.In Computer Vision, Edge is usually related to a discontinuity within a local set of pixels.3D Computer Visionand Video ComputingDiscontinuitiesDiscontinuitiesA: Depth discontinuity: abrupt depth change in the worldB: Surface normal discontinuity: change in surface orientationC: Illumination discontinuity: shadows, lighting changesD: Reflectance discontinuity: surface properties, markingsACBD3D Computer Visionand Video ComputingIllusory EdgesIllusory EdgesIllusory edges will not be detectable by the algorithms that we will discussNo change in image irradiance - no image processing algorithm can directly address these situationsComputer vision can deal with these sorts of things by drawing on information external to the image (perceptual grouping techniques)Kanizsa Triangles3D Computer Visionand Video ComputingAnother OneAnother One3D Computer Visionand Video ComputingGoalGoalDevise computational algorithms for the extraction of significant edges from the image.What is meant by significant is unclear.Partly defined by the context in which the edge detector is being applied3D Computer Visionand Video ComputingEdgelsEdgelsDefine a local edge or edgel to be a rapid change in the image function over a small areaimplies that edgels should be detectable over a local neighborhoodEdgels are NOT contours, boundaries, or linesedgels may lend support to the existence of those structuresthese structures are typically constructed from edgelsEdgels have propertiesOrientationMagnitudePosition3D Computer Visionand Video ComputingOutlineOutlineFirst order edge detectors (lecture - required)Mathematics1x2, Roberts, Sobel, PrewittCanny edge detector (after-class reading)Second order edge detector (after-class reading)Laplacian, LOG / DOGHough Transform – detect by votingLinesCirclesOther shapes3D Computer Visionand Video ComputingLocating EdgelsLocating EdgelsRapid change in image => high local gradient => differentiationf(x) = step edge1st Derivative f ’(x)2nd Derivative -f ’’(x)maximumzero crossing3D Computer Visionand Video ComputingRealityReality3D Computer Visionand Video ComputingProperties of an EdgeProperties of an EdgeOriginalOrientationMagnitudeOrientationPosition3D Computer Visionand Video ComputingQuantitative Edge DescriptorsQuantitative Edge DescriptorsEdge OrientationEdge Normal - unit vector in the direction of maximum intensity change (maximum intensity gradient)Edge Direction - unit vector perpendicular to the edge normalEdge Position or Centerimage position at which edge is located (usually saved as binary image)Edge Strength / Magnituderelated to local contrast or gradient - how rapid is the intensity variation across the edge along the edge normal.3D Computer Visionand Video ComputingEdge Degradation in NoiseEdge Degradation in NoiseIdeal step edge Step edge + noiseIncreasing noise3D Computer Visionand Video ComputingReal ImageReal Image3D Computer Visionand Video ComputingEdge Detection: TypicalEdge Detection: TypicalNoise SmoothingSuppress as much noise as possible while retaining ‘true’ edgesIn the absence of other information, assume ‘white’ noise with a Gaussian distributionEdge EnhancementDesign a filter that responds to edges; filter output high are edge pixels and low elsewhereEdge LocalizationDetermine which edge pixels should be discarded as noise and which should be retainedthin wide edges to 1-pixel width (nonmaximum suppression)establish minimum value to declare a local maximum from edge filter to be an edge (thresholding)3D Computer Visionand Video ComputingEdge Detection MethodsEdge Detection Methods1st Derivative EstimateGradient edge detectionCompass edge detectionCanny edge detector (*)2nd Derivative EstimateLaplacianDifference of GaussiansParametric Edge Models (*)3D Computer Visionand Video ComputingGradient MethodsGradient MethodsF(x)xF’(x)xEdge= sharp variationLarge first derivative3D Computer Visionand Video ComputingGradient of a FunctionGradient of a FunctionAssume f is a continuous function in (x,y). Thenare the rates of change of the
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