13D from multiple views15-463: Rendering and Image ProcessingAlexei Efros…with a lot of slides stolen from Steve Seitz and Jianbo Shi Our Goal2Stereo ReconstructionThe Stereo Problem• Shape from two (or more) images• Biological motivationknownknowncameracameraviewpointsviewpointsWhy do we have two eyes?Cyclope vs. TA31. Two is better than one2. Depth from ConvergenceHuman performance: up to 6-8 feet43. Depth from binocular disparitySign and magnitude of disparityP: converging pointC: object nearer projects to the outside of the P, disparity = +F: object farther projects to the inside of the P, disparity = -5Stereoscene pointscene pointoptical centeroptical centerimage planeimage planeStereoBasic Principle: Triangulation• Gives reconstruction as intersection of two rays• Requires – calibration– point correspondence6Stereo correspondenceDetermine Pixel Correspondence• Pairs of points that correspond to same scene pointEpipolar Constraint• Reduces correspondence problem to 1D search along conjugateepipolar lines• Java demo: http://www.ai.sri.com/~luong/research/Meta3DViewer/EpipolarGeo.htmlepipolar planeepipolar lineepipolar lineepipolar lineepipolar lineStereo image rectification7Stereo image rectificationImage Reprojection• reproject image planes onto common plane parallel to line between optical centers• a homography (3x3 transform)applied to both input images• pixel motion is horizontal after this transformation• C. Loop and Z. Zhang. Computing Rectifying Homographies for Stereo Vision. IEEE Conf. Computer Vision and Pattern Recognition, 1999.Your basic stereo algorithmFor each epipolar lineFor each pixel in the left image• compare with every pixel on same epipolar line in right image• pick pixel with minimum match costImprovement: match windows• This should look familar...• Can use Lukas-Kanade or discrete search (latter more common)8Window size• Smaller window+–• Larger window+–W = 3 W = 20Effect of window sizeStereo resultsGround truthScene• Data from University of Tsukuba• Similar results on other images without ground truth9Results with window searchWindow-based matching(best window size)Ground truthBetter methods exist...State of the art methodBoykov et al., Fast Approximate Energy Minimization via Graph Cuts, International Conference on Computer Vision, September 1999.Ground truth10Depth from disparityfx x’baselinezC C’Xfinput image (1 of 2)[Szeliski & Kang ‘95]depth map 3D rendering• Camera calibration errors• Poor image resolution• Occlusions• Violations of brightness constancy (specular reflections)• Large motions• Low-contrast image regionsStereo reconstruction pipelineSteps• Calibrate cameras• Rectify images• Compute disparity• Estimate depthWhat will cause errors?11Stereo matchingNeed texture for matchingJulesz-style Random Dot StereogramActive stereo with structured lightProject “structured” light patterns onto the object• simplifies the correspondence problemcamera 2camera 1projectorcamera 1projectorLi Zhang’s one-shot stereo12Active stereo with structured lightLaser scanningOptical triangulation• Project a single stripe of laser light• Scan it across the surface of the object• This is a very precise version of structured light scanningDirectionoftravelObjectCCDCCDimageplaneLaserCylindricallensLasersheetDigital Michelangelo Projecthttp://graphics.stanford.edu/projects/mich/13Portable 3D laser scanner (this one by Minolta)Real-time stereoUsed for robot navigation (and other tasks)• Several software-based real-time stereo techniques have been developed (most based on simple discrete search)Nomad robot searches for meteorites in Antarticahttp://www.frc.ri.cmu.edu/projects/meteorobot/index.html14Structure from MotionReconstruct • Scene geometry• Camera motionUnknownUnknowncameracameraviewpointsviewpointsThree approachesThree approaches15Outline of a simple algorithm (1)Outline of a simple algorithm (1)• Based on constraints• Input to the algorithm (1): two imagesOutline of a simple algorithm (2)Outline of a simple algorithm (2)• Input to the algorithm (2): User select edges and corners16Outline of a simple algorithm (3)Outline of a simple algorithm (3)• Camera Position and OrientationDetermine the position and orientation of cameraOutline of a simple algorithm (4)Outline of a simple algorithm (4)• Computing projection matrix and Reconstruction17Outline of a simple algorithm (5)Outline of a simple algorithm (5)• Compute 3D textured trianglesView-Dependant Texture Mapping18Facade Facade SFMOMA (San Francisco Museum of Modern Art) by Yizhou Yu, Façade (Debevec et al) inputs19Façade (Debevec et al)Wrap-Up1. Why we were here?2. What did we learn?3. How is this useful?20Our Goal: The Plenoptic FunctionFigure by Leonard McMillanOur Tools: The “Theatre Workshop” Metaphordesired image(Adelson & Pentland,1996)Painter Lighting DesignerSheet-metalworker21Painter (images)Lighting Designer (environment maps)22Sheet-metal Worker (geometry)… working togetherWant to minimize costEach one does what’s easiest for him• Geometry – big things• Images – detail• Lighting – illumination effects23How is this useful?1. You learned a basic set of image-based techniques• All quite simple• All can be done “at home”2. You have your digital camera3. You have your imaginationGo off and explore!That’s all, folks!THANK
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