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PSU CSE/EE 486 - Harris Corner Detector

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CSE486, Penn StateRobert CollinsLecture 06:Harris Corner DetectorReading: T&V Section 4.3CSE486, Penn StateRobert CollinsMotivation: Matchng ProblemVision tasks such as stereo and motion estimation requirefinding corresponding features across two or more views.CSE486, Penn StateRobert CollinsMotivation: Patch MatchingCamps, PSU==??Task: find the best (most similar) patch in a second imageElements to be matched are image patches of fixed sizeCSE486, Penn StateRobert CollinsNot all Patches are Created Equal!Camps, PSU==??Inituition: this would be a good patch for matching, sinceit is very distinctive (there is only one patch in the secondframe that looks similar).CSE486, Penn StateRobert Collins==??Not all Patches are Created Equal!Camps, PSUInituition: this would be a BAD patch for matching, sinceit is not very distinctive (there are many similar patchesin the second frame)CSE486, Penn StateRobert CollinsWhat are Corners?M.Hebert, CMU• They are good features to match!CSE486, Penn StateRobert CollinsCorner Points: Basic IdeaC.Dyer, UWisc• We should easily recognize the point by looking at intensity values within a small window • Shifting the window in any direction should yield a large change in appearance.CSE486, Penn StateRobert CollinsAppearance Change inNeighborhood of a PatchInteractive“demo”CSE486, Penn StateRobert CollinsHarris Corner Detector: Basic IdeaC.Dyer, UWiscHarris corner detector gives a mathematicalapproach for determining which case holds.CSE486, Penn StateRobert CollinsHarris Detector: MathematicsC.Dyer, UWiscCSE486, Penn StateRobert CollinsHarris Detector: IntuitionC.Dyer, UWiscFor nearly constant patches, this will be near 0.For very distinctive patches, this will be larger.Hence... we want patches where E(u,v) is LARGE.CSE486, Penn StateRobert CollinsTaylor Series for 2D Functions(Higher order terms)First partial derivativesSecond partial derivativesThird partial derivativesFirst order approxCSE486, Penn StateRobert CollinsHarris Corner DerivationFirst order approxRewrite as matrix equationCSE486, Penn StateRobert CollinsHarris Detector: MathematicsC.Dyer, UWiscNote: these are just products ofcomponents of the gradient, Ix, IyWindowing function - computing aweighted sum (simplest case, w=1)CSE486, Penn StateRobert CollinsIntuitive Way to Understand HarrisTreat gradient vectors as a set of (dx,dy) pointswith a center of mass defined as being at (0,0).Fit an ellipse to that set of points via scatter matrixAnalyze ellipse parameters for varying cases…CSE486, Penn StateRobert CollinsExample: Cases and 2D DerivativesM.Hebert, CMUCSE486, Penn StateRobert CollinsPlotting Derivatives as 2D PointsM.Hebert, CMUCSE486, Penn StateRobert CollinsFitting Ellipse to each Set of PointsM.Hebert, CMUλ1~λ2 = smallλ1 large; λ2 = smallλ1~λ2 = largeCSE486, Penn StateRobert CollinsClassification via EigenvaluesC.Dyer, UWiscCSE486, Penn StateRobert CollinsCorner Response MeasureC.Dyer, UWiscCSE486, Penn StateRobert CollinsCorner Response MapR=0R=28R=65R=104R=142lambda1lambda2(0,0)CSE486, Penn StateRobert CollinsCorner Response MapR=0R=28R=65R=104R=142lambda1lambda2|R| small“Flat”R < 0 “Edge”R < 0 “Edge”R large“Corner”CSE486, Penn StateRobert CollinsCorner Response ExampleHarris R score. Ix, Iy computed using Sobel operator Windowing function w = Gaussian, sigma=1CSE486, Penn StateRobert CollinsCorner Response Example Threshold: R < -10000(edges)CSE486, Penn StateRobert CollinsCorner Response Example Threshold: > 10000(corners)CSE486, Penn StateRobert CollinsCorner Response Example Threshold: -10000 < R < 10000(neither edges nor corners)CSE486, Penn StateRobert CollinsHarris Corner Detection AlgorithmM.Hebert, CMU6. Threshold on value of R. Compute nonmax


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