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CSCE 641 Computer Graphics: Image-based ModelingOutlineVolumetric stereoDiscrete formulation: Voxel ColoringComplexity and computabilityIssuesSlide 7Why use silhouettes?Reconstruction from silhouettes (C = 2)Slide 10Volume intersectionVoxel algorithm for volume intersectionVisual Hull ResultsProperties of volume intersectionSlide 15Voxel coloring approachThe visibility problemSlide 18Depth ordering: visit occluders first!Panoramic depth orderingSlide 21Panoramic layeringSlide 23Compatible camera configurationsCalibrated image acquisitionVoxel coloring resultsLimitations of depth orderingSlide 28Space carving algorithmWhich shape do you get?Slide 31Multi-pass plane sweepSlide 33Slide 34Slide 35Slide 36Slide 37Space carving results: african violetSpace carving results: handProperties of Space CarvingExtensions: Modeling Dynamic ObjectsRecent Development: Modeling Dynamic ObjectsCSCE 641 Computer Graphics: Image-based ModelingJinxiang ChaiOutlineStereo matching - Traditional stereo - Active stereoVolumetric stereo - Visual hull - Voxel coloring - Space carvingVolumetric stereoScene VolumeScene VolumeVVInput ImagesInput Images(Calibrated)(Calibrated)Goal: Goal: Determine occupancy, “color” of points in VDetermine occupancy, “color” of points in VDiscrete formulation: Voxel ColoringDiscretized Discretized Scene VolumeScene VolumeInput ImagesInput Images(Calibrated)(Calibrated)Goal: Assign RGBA values to voxels in Vphoto-consistent with imagesComplexity and computabilityDiscretized Discretized Scene VolumeScene VolumeN voxelsN voxelsC colorsC colors33All Scenes (CN3)Photo-ConsistentScenesTrueSceneIssuesTheoretical Questions•Identify class of all photo-consistent scenesPractical Questions•How do we compute photo-consistent models?1. C=2 (shape from silhouettes)•Volume intersection [Baumgart 1974]>For more info: Rapid octree construction from image sequences. R. Szeliski, CVGIP: Image Understanding, 58(1):23-32, July 1993. (this paper is apparently not available online) or>W. Matusik, C. Buehler, R. Raskar, L. McMillan, and S. J. Gortler, Image-Based Visual Hulls, SIGGRAPH 2000 ( pdf 1.6 MB )2. C unconstrained, viewpoint constraints•Voxel coloring algorithm [Seitz & Dyer 97]3. General Case•Space carving [Kutulakos & Seitz 98]Voxel coloring solutionsWhy use silhouettes?Can be computed robustlyCan be computed efficiently-=background background + + foregroundforegroundbackgroundbackground foreground foregroundReconstruction from silhouettes (C = 2)Binary ImagesBinary ImagesHow to construct 3D volume?Reconstruction from silhouettes (C = 2)Binary ImagesBinary ImagesApproach: •Backproject each silhouette•Intersect backprojected volumesVolume intersectionReconstruction Contains the True Scene•But is generally not the same •In the limit (all views) get visual hull >Complement of all lines that don’t intersect SVoxel algorithm for volume intersectionColor voxel black if on silhouette in every image• for M images, N3 voxels•Don’t have to search 2N3 possible scenes!O( ? ),Visual Hull ResultsDownload data and results fromhttp://www-cvr.ai.uiuc.edu/ponce_grp/data/visual_hull/Properties of volume intersectionPros•Easy to implement, fast•Accelerated via octrees [Szeliski 1993] or interval techniques [Matusik 2000]Cons•No concavities•Reconstruction is not photo-consistent•Requires identification of silhouettesVoxel coloring solutions1. C=2 (silhouettes)•Volume intersection [Baumgart 1974]2. C unconstrained, viewpoint constraints•Voxel coloring algorithm [Seitz & Dyer 97]>For more info: http://www.cs.washington.edu/homes/seitz/papers/ijcv99.pdf3. General Case•Space carving [Kutulakos & Seitz 98]1. Choose voxel1. Choose voxel2. Project and correlate2. Project and correlate3.3.Color if consistentColor if consistent(standard deviation of pixel colors below threshold)Voxel coloring approachVisibility Problem: Visibility Problem: in which images is each voxel visible?in which images is each voxel visible?The visibility problemInverse Visibility?known imagesUnknown SceneUnknown SceneWhich points are visible in which images?Known SceneKnown SceneForward Visibility - Z-buffer - Painter’s algorithmknown sceneThe visibility problemInverse Visibility? - visit occluders first!Unknown SceneUnknown SceneWhich points are visible in which images?Known SceneKnown SceneForward Visibility - Z-buffer - Painter’s algorithmknown sceneLayersLayersDepth ordering: visit occluders first!SceneSceneTraversalTraversalCondition: Condition: depth order is the depth order is the same for all input viewssame for all input viewsPanoramic depth ordering•Cameras oriented in many different directions•Planar depth ordering does not applyPanoramic depth orderingLayers radiate outwards from camerasLayers radiate outwards from camerasPanoramic layeringLayers radiate outwards from camerasLayers radiate outwards from camerasPanoramic layeringLayers radiate outwards from camerasLayers radiate outwards from camerasCompatible camera configurationsDepth-Order Constraint•Scene outside convex hull of camera centersOutward-Lookingcameras inside sceneInward-Lookingcameras above sceneCalibrated image acquisitionCalibrated Turntable360° rotation (21 images)Selected Dinosaur ImagesSelected Dinosaur ImagesSelected Flower ImagesSelected Flower ImagesVoxel coloring resultsDinosaur ReconstructionDinosaur Reconstruction72 K voxels colored72 K voxels colored7.6 M voxels tested7.6 M voxels tested7 min. to compute 7 min. to compute on a 250MHz SGIon a 250MHz SGIFlower ReconstructionFlower Reconstruction70 K voxels colored70 K voxels colored7.6 M voxels tested7.6 M voxels tested7 min. to compute 7 min. to compute on a 250MHz SGIon a 250MHz SGILimitations of depth orderingA view-independent depth order may not existp qNeed more powerful general-case algorithms•Unconstrained camera positions•Unconstrained scene geometry/topologyVoxel coloring solutions1. C=2 (silhouettes)•Volume intersection [Baumgart 1974]2. C unconstrained, viewpoint constraints•Voxel coloring algorithm [Seitz & Dyer 97]3. General Case•Space carving [Kutulakos & Seitz 98]>For more info: http://www.cs.washington.edu/homes/seitz/papers/kutu-ijcv00.pdfSpace carving algorithmSpace Carving AlgorithmImage 1Image N…...•Initialize to a volume V containing the true scene•Repeat until convergence•Choose a voxel on the current surface•Carve if not


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