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UCSD CSE 152 - Lecture 16

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1CSE152, Spr 04 Intro Computer VisionContinuous MotionIntroduction to Computer VisionCSE 152Lecture 16CSE152, Spr 04 Intro Computer VisionAnnouncements• Assignment 3: Due Today.• Assignment 4: To be posted shortly, Due next thursday• Read: Trucco & Verri, Chapter 8CSE152, Spr 04 Intro Computer VisionSome countingConsider M images of N points, how many unknowns?1. Affix coordinate system to location of first camera location: (M-1)*6 Unknowns2. 3-D Structure: 3*N Unknowns3. Can only recover structure and motion up to scale. Why?Total number of unknowns: (M-1)*6+3N-1CSE152, Spr 04 Intro Computer VisionThe Eight-Point Algorithm (Longuet-Higgins, 1981)Set F33to 1SolveFor FCSE152, Spr 04 Intro Computer Visionhomogeneousedgecorner[]()dxdyyxwyIxIWyIxI,∂∂∂∂∂∂∂∂∫∫=MM should have large eigenvalues(e.g.Harris&Stephens´88; Shi&Tomasi´94)∆∆≈ MTSSDFind points that differ as much as possible from all neighboring pointsFeature = local maxima (subpixel) of F(λ1, λ2)Detecting Feature pointsCSE152, Spr 04 Intro Computer VisionDetection of Corner Features• Need two strong edges:• Example:Create the following matrix:Create the following matrix:If min(If min(λλ11,,λλ22) > T) > TThere is a corner!There is a corner!Eigenvalues of C(Or create an matrix with the same dimension as an image with value of min(λ1, λ2) at each location–Find local maximum2CSE152, Spr 04 Intro Computer VisionEvaluate normalized cross correlation (or sum of squared differences) for all features with similar coordinatesKeep mutual best matchesKeep mutual best matchesStill many wrong matches!Still many wrong matches!()[][]10101010,,´´, e.g.hhwwyyxxyx+−×+−∈?Feature matchingCSE152, Spr 04 Intro Computer VisionReconstruction Results (Tomasi and Kanade, 1992)Reprinted from “Factoring Image Sequences into Shape and Motion,” by C. Tomasi andT. Kanade, Proc. IEEE Workshop on Visual Motion (1991).  1991 IEEE.CSE152, Spr 04 Intro Computer VisionFiat Lux:An Application of Discrete SFMCSE152, Spr 04 Intro Computer VisionBuilding Blocks• For more info, see http://www.cs.berkeley.edu/~debevec/http://www.cs.berkeley.edu/~debevec/Items/NewScientist/• Structure and Motion from Line Segments in Multiple Images, C. J. Taylor, D. Kriegman, IEEE PAMI, 1995• Reconstructing Polyhedral Models of Architectural Scenes from Photographs, C.J. Taylor, P. Debevec, J. Malik, ECCV96• Facade: Modeling and Rendering Architecture from Photographs, P. Debevec, C.J. Taylor, J. Malik, SIGGRAPH 96• Recovering High Dynamic Range Radiance Maps from Photographs, P. Debevec, J. Malik SIGGRAPH 97• Rendering Synthetic Objects into Real Scenes, P. Debevec, SIGGRAPH 98CSE152, Spr 04 Intro Computer VisionSt. Peter’s PlanCSE152, Spr 04 Intro Computer VisionModel of St. Peters constructed with Facade3CSE152, Spr 04 Intro Computer Vision CSE152, Spr 04 Intro Computer VisionStructure-from-motion from Line SegmentsCSE152, Spr 04 Intro Computer VisionComparison of measured segment to projected lineCSE152, Spr 04 Intro Computer VisionImages with marked featuresCSE152, Spr 04 Intro Computer VisionRecovered Recovered model edges reprojected through recovered camera positions into the three original imagesCSE152, Spr 04 Intro Computer VisionResulting model & Camera Positions4CSE152, Spr 04 Intro Computer VisionView-Dependent texture mappingCSE152, Spr 04 Intro Computer VisionComposite of all texture mapsCSE152, Spr 04 Intro Computer VisionHigh Dynamic Range Radiance MapsCSE152, Spr 04 Intro Computer VisionSt. Peter’s PanoramaCSE152, Spr 04 Intro Computer VisionCreating the Radiance MapTwo images of a two-inch mirrored sphere placed in front of Bernini'sBaldacchino inside St. Peter'sCSE152, Spr 04 Intro Computer VisionFIAT LUX Radiance MapsSt. Peters200,000:15CSE152, Spr 04 Intro Computer VisionPanoramic environment created by taking multiple radiance images and assembling them into panoramas. Used to create the background plates for the film. Three-dimensionality was added to these backgrounds by projecting them onto a model of the corresponding environments.CSE152, Spr 04 Intro Computer VisionContinuous Motion• Consider a video camera moving continuously along a trajectory (rotating & translating). • How do points in the image move• What does that tell us about the 3-D motion & scene structure?CSE152, Spr 04 Intro Computer Vision CSE152, Spr 04 Intro Computer VisionIs motion estimation inherent in humans?DemoCSE152, Spr 04 Intro Computer VisionMotion“When objects move at equal speed,those more remote seem to movemore slowly.”- Euclid, 300 BCCSE152, Spr 04 Intro Computer VisionMotion Reveals1. Object boundaries – segmentation2. Abrupt changes to scenes – movie shot?3. Observer motion4. 3-D structure6CSE152, Spr 04 Intro Computer VisionSimplest Idea for video processingImage Differences• Given image I(u,v,t) and I(u,v, t+δt), compute I(u,v, t+δt) - I(u,v,t).• This is partial derivative: • At object boundaries, is large and is cue for segmentation• Doesn’t tell which way stuff is movingtI∂∂tI∂∂CSE152, Spr 04 Intro Computer VisionBackground Subtraction• Gather image I(x,y,t0) of background without objects of interest (perhaps computed over average over many images).• At time t, pixels where |I(x,y,t)-I(x,y,t0)| > τare labeled as coming from foreground objectsRaw Image Foreground regionCSE152, Spr 04 Intro Computer VisionThe Motion FieldWhere in the image did a point move?Down and leftCSE152, Spr 04 Intro Computer VisionThe Motion FieldCSE152, Spr 04 Intro Computer VisionTHE MOTION FIELDThe “instantaneous” velocity of points in an imageLOOMINGThe Focus of Expansion (FOE)With just this informationit is possible to calculate:1. Direction of motion2. Time to collisionIntersection of velocity vector with image planeCSE152, Spr 04 Intro Computer VisionRigid Motion: General CasePosition and orientation of a rigid bodyRotation Matrix & Translation vectorRigid Motion:Velocity Vector: TAngular Velocity Vector: ω (or Ω)PpTp ×+=ω&p&7CSE152, Spr 04 Intro Computer VisionGeneral Motion=yxzfvu−=yxzzfyxzfvu2&&&&&−=vuzzyxzf&&&pTp ×+=ω&Substitute where p=(x,y,z)TCSE152, Spr 04 Intro Computer VisionMotion Field Equation• T: Components of 3-D linear motion• ω: Angular velocity vector•


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UCSD CSE 152 - Lecture 16

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