announcements
DESCRIPTION
Announcements. Midterm due now Project 2 artifacts: vote today! Project 3. Multiview stereo. Readings S. M. Seitz and C. R. Dyer, Photorealistic Scene Reconstruction by Voxel Coloring , International Journal of Computer Vision , 35(2), 1999, pp. 151-173. - PowerPoint PPT PresentationTRANSCRIPT
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• Midterm due now• Project 2 artifacts: vote today!• Project 3
Announcements
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Multiview stereo
Readings• S. M. Seitz and C. R. Dyer,
Photorealistic Scene Reconstruction by Voxel Coloring, International Journal of Computer Vision, 35(2), 1999, pp. 151-173.
> http://www.cs.washington.edu/homes/seitz/papers/ijcv99.pdf
CMU’s 3D Room
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width of a pixel
Choosing the Baseline
What’s the optimal baseline?• Too small: large depth error• Too large: difficult search problem
Large BaselineLarge Baseline Small BaselineSmall Baseline
all of thesepoints projectto the same pair of pixels
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The Effect of Baseline on Depth Estimation
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1/z
width of a pixel
width of a pixel
1/z
pixel matching score
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Multibaseline Stereo
Basic Approach• Choose a reference view• Use your favorite stereo algorithm BUT
> replace two-view SSD with SSD over all baselines
Limitations• Must choose a reference view (bad)• Visibility!
CMU’s 3D Room Video
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The visibility problem
Inverse Visibilityknown images
Unknown SceneUnknown Scene
Which points are visible in which images?
Known SceneKnown Scene
Forward Visibilityknown scene
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Volumetric stereo
Scene VolumeScene VolumeVV
Input ImagesInput Images(Calibrated)(Calibrated)
Goal: Goal: Determine occupancy, “color” of points in VDetermine occupancy, “color” of points in V
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Discrete formulation: Voxel Coloring
Discretized Discretized Scene VolumeScene Volume
Input ImagesInput Images(Calibrated)(Calibrated)
Goal: Assign RGBA values to voxels in Vphoto-consistent with images
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Complexity and computability
Discretized Discretized Scene VolumeScene Volume
N voxelsN voxelsC colorsC colors
33
All Scenes (CN3)Photo-ConsistentScenes
TrueScene
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Issues
Theoretical Questions• Identify class of all photo-consistent scenes
Practical Questions• How do we compute photo-consistent models?
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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 solutions
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Reconstruction from Silhouettes (C = 2)
Binary ImagesBinary Images
Approach: • Backproject each silhouette• Intersect backprojected volumes
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Volume intersection
Reconstruction 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 S
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Voxel algorithm for volume intersection
Color voxel black if on silhouette in every image• for M images, N3 voxels• Don’t have to search 2N3 possible scenes!
O( ? ),
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Properties of Volume Intersection
Pros• 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 silhouettes
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Voxel Coloring Solutions
1. 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.pdf
3. General Case• Space carving [Kutulakos & Seitz 98]
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1. Choose voxel1. Choose voxel2. Project and correlate2. Project and correlate
3.3. Color if consistentColor if consistent(standard deviation of pixel colors below threshold)
Voxel Coloring Approach
Visibility Problem: Visibility Problem: in which images is each voxel visible?in which images is each voxel visible?
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LayersLayers
Depth Ordering: visit occluders first!
SceneSceneTraversalTraversal
Condition: Condition: depth order is the depth order is the same for all input viewssame for all input views
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Panoramic Depth Ordering
• Cameras oriented in many different directions• Planar depth ordering does not apply
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Panoramic Depth Ordering
Layers radiate outwards from camerasLayers radiate outwards from cameras
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Panoramic Layering
Layers radiate outwards from camerasLayers radiate outwards from cameras
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Panoramic Layering
Layers radiate outwards from camerasLayers radiate outwards from cameras
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Compatible Camera Configurations
Depth-Order Constraint• Scene outside convex hull of camera centers
Outward-Lookingcameras inside scene
Inward-Lookingcameras above scene
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Calibrated Image Acquisition
Calibrated Turntable360° rotation (21 images)
Selected Dinosaur ImagesSelected Dinosaur Images
Selected Flower ImagesSelected Flower Images
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Voxel Coloring Results (Video)
Dinosaur 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 SGI
Flower 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 SGI
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Limitations of Depth Ordering
A view-independent depth order may not exist
p q
Need more powerful general-case algorithms• Unconstrained camera positions• Unconstrained scene geometry/topology
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Voxel Coloring Solutions
1. 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.pdf
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Space Carving Algorithm
Space Carving Algorithm
Image 1 Image N
…...
• Initialize to a volume V containing the true scene
• Repeat until convergence
• Choose a voxel on the current surface
• Carve if not photo-consistent• Project to visible input images
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Convergence
Consistency Property• The resulting shape is photo-consistent
> all inconsistent points are removed
Convergence Property• Carving converges to a non-empty shape
> a point on the true scene is never removed
p
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Which shape do you get?
The Photo Hull is the UNION of all photo-consistent scenes in V• It is a photo-consistent scene reconstruction• Tightest possible bound on the true scene
True SceneTrue Scene
VV
Photo HullPhoto Hull
VV
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Space Carving Algorithm
The Basic Algorithm is Unwieldy• Complex update procedure
Alternative: Multi-Pass Plane Sweep• Efficient, can use texture-mapping hardware• Converges quickly in practice• Easy to implement
Results Algorithm
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Multi-Pass Plane Sweep• Sweep plane in each of 6 principle directions• Consider cameras on only one side of plane• Repeat until convergence
True Scene Reconstruction
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Multi-Pass Plane Sweep• Sweep plane in each of 6 principle directions• Consider cameras on only one side of plane• Repeat until convergence
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Multi-Pass Plane Sweep• Sweep plane in each of 6 principle directions• Consider cameras on only one side of plane• Repeat until convergence
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Multi-Pass Plane Sweep• Sweep plane in each of 6 principle directions• Consider cameras on only one side of plane• Repeat until convergence
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Multi-Pass Plane Sweep• Sweep plane in each of 6 principle directions• Consider cameras on only one side of plane• Repeat until convergence
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Multi-Pass Plane Sweep• Sweep plane in each of 6 principle directions• Consider cameras on only one side of plane• Repeat until convergence
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Space Carving Results: African Violet
Input Image (1 of 45) Reconstruction
ReconstructionReconstruction
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Space Carving Results: Hand
Input Image(1 of 100)
Views of Reconstruction
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Other Approaches
Level-Set Methods [Faugeras & Keriven 1998]• Evolve implicit function by solving PDE’s
Probabilistic Voxel Reconstruction [DeBonet & Viola 1999], [Broadhurst et al. 2001]
• Solve for voxel uncertainty (also transparency)
Transparency and Matting [Szeliski & Golland 1998]• Compute voxels with alpha-channel
Max Flow/Min Cut [Roy & Cox 1998]• Graph theoretic formulation
Mesh-Based Stereo [Fua & Leclerc 1995], [Zhang & Seitz 2001]• Mesh-based but similar consistency formulation
Virtualized Reality [Narayan, Rander, Kanade 1998]• Perform stereo 3 images at a time, merge results
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Volume Intersection• Martin & Aggarwal, “Volumetric description of objects from multiple views”, Trans. Pattern
Analysis and Machine Intelligence, 5(2), 1991, pp. 150-158.• Szeliski, “Rapid Octree Construction from Image Sequences”, Computer Vision, Graphics,
and Image Processing: Image Understanding, 58(1), 1993, pp. 23-32.
Voxel Coloring and Space Carving• Seitz & Dyer, “Photorealistic Scene Reconstruction by Voxel Coloring”, Proc. Computer
Vision and Pattern Recognition (CVPR), 1997, pp. 1067-1073.• Seitz & Kutulakos, “Plenoptic Image Editing”, Proc. Int. Conf. on Computer Vision (ICCV),
1998, pp. 17-24.• Kutulakos & Seitz, “A Theory of Shape by Space Carving”, Proc. ICCV, 1998, pp. 307-314.
Bibliography
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Related References• Bolles, Baker, and Marimont, “Epipolar-Plane Image Analysis: An Approach to Determining
Structure from Motion”, International Journal of Computer Vision, vol 1, no 1, 1987, pp. 7-55.• DeBonet & Viola, “Poxels: Probabilistic Voxelized Volume Reconstruction”, Proc. Int. Conf. on
Computer Vision (ICCV) 1999.• Broadhurst, Drummond, and Cipolla, "A Probabilistic Framework for Space Carving“,
International Conference of Computer Vision (ICCV), 2001, pp. 388-393. • Faugeras & Keriven, “Variational principles, surface evolution, PDE's, level set methods and the
stereo problem", IEEE Trans. on Image Processing, 7(3), 1998, pp. 336-344.• Szeliski & Golland, “Stereo Matching with Transparency and Matting”, Proc. Int. Conf. on
Computer Vision (ICCV), 1998, 517-524.• Roy & Cox, “A Maximum-Flow Formulation of the N-camera Stereo Correspondence Problem”,
Proc. ICCV, 1998, pp. 492-499.• Fua & Leclerc, “Object-centered surface reconstruction: Combining multi-image stereo and
shading", International Journal of Computer Vision, 16, 1995, pp. 35-56.• Narayanan, Rander, & Kanade, “Constructing Virtual Worlds Using Dense Stereo”, Proc. ICCV,
1998, pp. 3-10.
Bibliography