Image FeaturesCSE 576, Spring 20053/31/2005CSE 576: Computer Vision2About me Ph. D., Carnegie Mellon, 1988 Researcher, Cambridge Research Lab at DEC, 1990-1995 Senior Researcher, Interactive Visual Media Group, Microsoft, 1995- Research interests: computer vision (stereo, motion), computer graphics (image-based rendering), data-parallel programming3/31/2005CSE 576: Computer Vision3Todays lecture What is computer vision? Scale-space and pyramids What are good features? Feature detection Feature descriptors (Next lecture: feature matching) Project 1description and demo Ian SimonWhat is Computer Vision?3/31/2005CSE 576: Computer Vision5What is Computer Vision? Image Understanding (AI, behavior) A sensor modality for robotics Computer emulation of human vision Inverse of Computer GraphicsComputer visionWorld modelComputer graphicsWorld model3/31/2005CSE 576: Computer Vision6Intersection of Vision and Graphicsmodeling - shape - light - motion - optics - imagesIPanimationrenderinguser-interfacessurface designComputer Graphicsshape estimationmotion estimationrecognition2D modelingmodeling - shape - light - motion - optics - imagesIPComputer Vision3/31/2005CSE 576: Computer Vision7Computer Vision Trucco Mitsunaga E increases in all directions1 and 2 are small; E is almost constant in all directions“Edge” 1 2“Edge” 2 1“Flat” regionClassification of image points using eigenvalues of M:3/31/2005CSE 576: Computer Vision47Harris Detector: MathematicsMeasure of corner response:(k empirical经验的 constant, k = 0.04-0.06)3/31/2005CSE 576: Computer Vision48Harris Detector: Mathematics12“Corner”“Edge” “Edge” “Flat” R depends only on eigenvalues of M R is large for a corner R is negative with large magnitude for an edge |R| is small for a flat regionR 0R threshold) Take the points of local maxima of R3/31/2005CSE 576: Computer Vision50Harris Detector: Workflow3/31/2005CSE 576: Computer Vision51Harris Detector: WorkflowCompute corner response R3/31/2005CSE 576: Computer Vision52Harris Detector: WorkflowFind points with large corner response: Rthreshold3/31/2005CSE 576: Computer Vision53Harris Detector: WorkflowTake only the points of local maxima of R3/31/2005CSE 576: Computer Vision54Harris Detector: Workflow3/31/2005CSE 576: Computer Vision55Harris Detector: SummaryAverage intensity change in direction u,v can be expressed as a bilinear form: Describe a point in terms of eigenvalues of M: measure of corner responseA good (corner) point should have a large intensity change in all directions, i.e. R should be large positive3/31/2005CSE 576: Computer Vision56Harris Detector: Some PropertiesRotation invarianceEllipse rotates but its shape (i.e. eigenvalues) remains the sameCorner response R is invariant to image rotation3/31/2005CSE 576: Computer Vision57Harris Detector: Some PropertiesPartial invariance to affine intensity change Only derivatives are used = invariance to intensity shift I I + b Intensity scale: I a IRx (image coordinate)thresholdRx (image coordinate)3/31/2005CSE 576: Computer Vision58Harris Detector: Some PropertiesBut: non-invariant to image scale!All points will be classified as edgesCorner !3/31/2005CSE 576: Computer Vision59Harris Detector: Some PropertiesQuality of Harris detector for different scale changesRepeatability rate:# correspondences # possible correspondencesC.Schmid et.al. “Evaluation of Interest Point Detectors”. IJCV 20003/31/2005CSE 576: Computer Vision60Models of Image ChangeGeometry Rotation Similarity (rotation + uniform scale) Affine (scale dependent on direction) valid for: orthographic camera, locally planar object Photometry光度 Affine intensity change (I a I + b)3/31/2005CSE 576: Computer Vision61Rotation Invariant DetectionHarris Corner DetectorC.Schmid et.al. “Evaluation of Interest Point Detectors”. IJCV 20003/31/2005CSE 576: Computer Vision62Scale Invariant DetectionConsider regions (e.g. circles) of different sizes around a point Regions of corresponding sizes will look the same in both images3/31/2005CSE 576: Computer Vision63Scale Invariant DetectionThe problem: how do we choose corresponding circles independently in each image?3/31/2005CSE 576: Computer Vision64Scale invarianceRequires a method to repeatably select points in location and scale: The only reasonable scale-space kernel is a Gaussian (Koenderink, 1984; Lindeberg, 1994) An efficient choice is to detect peaks in the difference of Gaussian pyramid (Burt Crowley & Parker, 1984 but examining more scales) Difference-of-Gaussian with constant ratio of scales is a close approximation to Lindebergs scale-normalized Laplacian (can be shown from the heat diffusion扩散 equation)3/31/2005CSE 576: Computer Vision65Scale Invariant DetectionSolution: Design a function on the region (circle), which is “scale invariant” (the same for corresponding regions, even if they are at different scales)Example: average intensity. For corresponding regions (even of differen