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From Images to Voxels

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From Images to Voxels3D Reconstruction from Calibrated ImagesDiscrete Formulation: Voxel ColoringComplexity and ComputabilityIssuesPowerPoint PresentationReconstruction from Silhouettes (C = 2)Volume IntersectionVoxel Algorithm for Volume IntersectionProperties of Volume IntersectionSlide 11Voxel Coloring ApproachThe Global Visibility ProblemDepth Ordering: visit occluders first!Panoramic Depth OrderingSlide 16Panoramic LayeringSlide 18Compatible Camera ConfigurationsCalibrated Image AcquisitionVoxel Coloring Results (Video)Limitations of Depth OrderingSlide 24Space Carving AlgorithmConvergenceWhat is Computable?Slide 28Slide 29Multi-Pass Plane SweepSlide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Slide 51Other ApproachesConclusionsBibliographySlide 62From Images to VoxelsFrom Images to VoxelsSteve SeitzSteve SeitzCarnegie Mellon UniversityCarnegie Mellon UniversityUniversity of WashingtonUniversity of Washingtonhttp://www.cs.cmu.edu/~seitzhttp://www.cs.cmu.edu/~seitzSIGGRAPH 2000 Course onSIGGRAPH 2000 Course on3D Photography3D Photography3D Reconstruction from Calibrated Images3D Reconstruction from Calibrated ImagesScene VolumeScene VolumeVVInput ImagesInput Images(Calibrated)(Calibrated)Goal: Goal: Determine transparency, radiance of points in VDetermine transparency, radiance of points in VDiscrete Formulation: Voxel ColoringDiscrete Formulation: Voxel ColoringDiscretized Discretized Scene VolumeScene VolumeInput ImagesInput Images(Calibrated)(Calibrated)Goal: Goal: Assign RGBA values to voxels in VAssign RGBA values to voxels in Vphoto-consistentphoto-consistent with images with imagesComplexity and ComputabilityComplexity and ComputabilityDiscretized Discretized Scene VolumeScene VolumeN voxelsN voxelsC colorsC colors33All Scenes (CN3)Photo-ConsistentScenesTrueSceneIssuesIssuesTheoretical QuestionsTheoretical Questions•Identify class of Identify class of allall photo-consistent scenes photo-consistent scenesPractical QuestionsPractical Questions•How do we compute photo-consistent models?How do we compute photo-consistent models?1. C=2 (silhouettes)1. C=2 (silhouettes)•Volume intersection [Martin 81, Szeliski 93]Volume intersection [Martin 81, Szeliski 93]2. C unconstrained, viewpoint constraints2. C unconstrained, viewpoint constraints•Voxel coloring algorithm [Seitz & Dyer 97]Voxel coloring algorithm [Seitz & Dyer 97]3. General Case3. General Case•Space carving [Kutulakos & Seitz 98]Space carving [Kutulakos & Seitz 98]Voxel Coloring SolutionsVoxel Coloring SolutionsReconstruction from Silhouettes (C = 2)Reconstruction from Silhouettes (C = 2)BinaryBinary ImagesImagesApproach: Approach: •BackprojectBackproject each silhouette each silhouette•Intersect backprojected volumesIntersect backprojected volumesVolume IntersectionVolume IntersectionReconstruction Contains the True SceneReconstruction Contains the True Scene•But is generally not the same But is generally not the same •In the limit get In the limit get visual hullvisual hull >Complement of all lines that don’t intersect SComplement of all lines that don’t intersect SVoxel Algorithm for Volume IntersectionVoxel Algorithm for Volume IntersectionColor voxel black if on silhouette in every imageColor voxel black if on silhouette in every image•O(MNO(MN33), for M images, N), for M images, N33 voxels voxels•Don’t have to search 2Don’t have to search 2NN33 possible scenes! possible scenes!Properties of Volume IntersectionProperties of Volume IntersectionProsPros•Easy to implement, fastEasy to implement, fast•Accelerated via octrees [Szeliski 1993]Accelerated via octrees [Szeliski 1993]ConsCons•No concavitiesNo concavities•Reconstruction is not photo-consistentReconstruction is not photo-consistent•Requires identification of silhouettesRequires identification of silhouettes1. C=2 (silhouettes)1. C=2 (silhouettes)•Volume intersection [Martin 81, Szeliski 93]Volume intersection [Martin 81, Szeliski 93]2. C unconstrained, viewpoint constraints2. C unconstrained, viewpoint constraints•Voxel coloring algorithm [Seitz & Dyer 97]Voxel coloring algorithm [Seitz & Dyer 97]3. General Case3. General Case•Space carving [Kutulakos & Seitz 98]Space carving [Kutulakos & Seitz 98]Voxel Coloring SolutionsVoxel Coloring Solutions1. Choose voxel1. Choose voxel2. Project and correlate2. Project and correlate3. Color if consistent3. Color if consistentVoxel Coloring ApproachVoxel Coloring ApproachVisibility Problem: Visibility Problem: in which images is each voxel visible?in which images is each voxel visible?The Global Visibility ProblemThe Global Visibility ProblemInverse VisibilityInverse Visibilityknown imagesknown imagesUnknown SceneUnknown SceneWhich points are visible in which images?Which points are visible in which images?Known SceneKnown SceneForward VisibilityForward Visibilityknown sceneknown sceneLayersLayersDepth Ordering: visit occluders first!Depth Ordering: visit occluders first!SceneSceneTraversalTraversalCondition: Condition: depth order is depth order is view-independentview-independentPanoramic Depth OrderingPanoramic Depth Ordering•Cameras oriented in many different directionsCameras oriented in many different directions•Planar depth ordering does not applyPlanar depth ordering does not applyPanoramic Depth OrderingPanoramic Depth OrderingLayers radiate outwards from camerasLayers radiate outwards from camerasPanoramic LayeringPanoramic LayeringLayers radiate outwards from camerasLayers radiate outwards from camerasPanoramic LayeringPanoramic LayeringLayers radiate outwards from camerasLayers radiate outwards from camerasCompatible Camera ConfigurationsCompatible Camera ConfigurationsDepth-Order ConstraintDepth-Order Constraint•Scene outside convex hull of camera centersScene outside convex hull of camera centersOutward-LookingOutward-Lookingcameras inside scenecameras inside sceneInward-LookingInward-Lookingcameras above scenecameras above sceneCalibrated Image AcquisitionCalibrated Image AcquisitionCalibrated TurntableCalibrated Turntable360° rotation (21 images)360° rotation (21 images)Selected Dinosaur ImagesSelected Dinosaur ImagesSelected Flower ImagesSelected Flower ImagesVoxel Coloring Results (Video)Voxel Coloring Results (Video)Dinosaur ReconstructionDinosaur Reconstruction72 K 72 K voxels coloredvoxels


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