1	Announcements Project 3 extension: Wednesday at noon Final project proposal extension: Friday at noon consult with Steve, Rick, and/or Ian now! Project 2 artifact winners...
2	Active stereo with structured light Project “structured” light patterns onto the object simplifies the correspondence problem
3	Active stereo with structured light
4	Laser scanning Optical 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 scanning
5	3D cameras
6	Multiview stereo
7	Choosing the stereo baseline What’s the optimal baseline? Too small: large depth error Too large: difficult search problem
8	The Effect of Baseline on Depth Estimation
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11	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
12	The visibility problem
13	Volumetric stereo
14	Discrete formulation: Voxel Coloring
15	Complexity and computability
16	Issues Theoretical Questions Identify class of all photo-consistent scenes Practical Questions How do we compute photo-consistent models?
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18	Reconstruction from Silhouettes (C = 2)
19	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
20	Voxel algorithm for volume intersection Color voxel black if on silhouette in every image for M images, N³ voxels Don’t have to search 2^N³ possible scenes!
21	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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23	Voxel Coloring Approach
24	Depth Ordering: visit occluders first!
25	Panoramic Depth Ordering Cameras oriented in many different directions Planar depth ordering does not apply
26	Panoramic Depth Ordering
27	Panoramic Layering
28	Panoramic Layering
29	Compatible Camera Configurations
30	Calibrated Image Acquisition Calibrated Turntable 360° rotation (21 images)
31	Voxel Coloring Results (Video)
32	Limitations of Depth Ordering A view-independent depth order may not exist
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34	Space Carving Algorithm Space Carving Algorithm
35	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
36	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
37	Multi-Pass Plane Sweep Sweep plane in each of 6 principle directions Consider cameras on only one side of plane Repeat until convergence
38	Multi-Pass Plane Sweep Sweep plane in each of 6 principle directions Consider cameras on only one side of plane Repeat until convergence
39	Multi-Pass Plane Sweep Sweep plane in each of 6 principle directions Consider cameras on only one side of plane Repeat until convergence
40	Multi-Pass Plane Sweep Sweep plane in each of 6 principle directions Consider cameras on only one side of plane Repeat until convergence
41	Multi-Pass Plane Sweep Sweep plane in each of 6 principle directions Consider cameras on only one side of plane Repeat until convergence
42	Multi-Pass Plane Sweep Sweep plane in each of 6 principle directions Consider cameras on only one side of plane Repeat until convergence
43	Space Carving Results: African Violet
44	Space Carving Results: Hand
45	Properties of Space Carving Pros Voxel coloring version is easy to implement, fast Photo-consistent results No smoothness prior Cons Bulging No smoothness prior
46	Alternatives to space carving Optimizing space carving recent surveys Slabaugh et al., 2001 Dyer et al., 2001 many others... Graph cuts Kolmogorov & Zabih Level sets introduce smoothness term surface represented as an implicit function in 3D volume optimize by solving PDE’s
47	Alternatives to space carving Optimizing space carving recent surveys Slabaugh et al., 2001 Dyer et al., 2001 many others... Graph cuts Ramin Zabih’s lecture Level sets introduce smoothness term surface represented as an implicit function in 3D volume optimize by solving PDE’s
48	Level sets vs. space carving Advantages of level sets optimizes consistency with images + smoothness term excellent results for smooth things does not require as many images Advantages of space carving much simpler to implement runs faster (orders of magnitude) works better for thin structures, discontinuities For more info on level set stereo: Renaud Keriven’s page: http://cermics.enpc.fr/~keriven/stereo.html
49	Current/Future Trends Optimizing with visibility Kolmogorov & Zabih
50	Current/Future Trends Real-time algorithms e.g., Buehler et al., image-based visual hulls, SIGGRAPH 2000
51	Current/Future Trends Modeling shiny things (BRDF’s and materials) e.g., Zickler et al., Helmholtz Stereopsis
52	References 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. Matusik, Buehler, Raskar, McMillan, and Gortler , “Image-Based Visual Hulls”, Proc. SIGGRAPH 2000, pp. 369-374. Voxel Coloring and Space Carving Seitz & Dyer, “Photorealistic Scene Reconstruction by Voxel Coloring”, Intl. Journal of Computer Vision (IJCV), 1999, 35(2), pp. 151-173. Kutulakos & Seitz, “A Theory of Shape by Space Carving”, International Journal of Computer Vision, 2000, 38(3), pp. 199-218. Recent surveys Slabaugh, Culbertson, Malzbender, & Schafer, “A Survey of Volumetric Scene Reconstruction Methods from Photographs”, Proc. workshop on Volume Graphics 2001, pp. 81-100. http://users.ece.gatech.edu/~slabaugh/personal/publications/vg01.pdf Dyer, “Volumetric Scene Reconstruction from Multiple Views”, Foundations of Image Understanding, L. S. Davis, ed., Kluwer, Boston, 2001, 469-489. ftp://ftp.cs.wisc.edu/computer-vision/repository/PDF/dyer.2001.fia.pdf
53	References Other references from this talk Multibaseline Stereo: Masatoshi Okutomi and Takeo Kanade. A multiple-baseline stereo. IEEE Trans. on Pattern Analysis and Machine Intelligence (PAMI), 15(4), 1993, pp. 353--363. Level sets: 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. Mesh based: Fua & Leclerc, “Object-centered surface reconstruction: Combining multi-image stereo and shading", IJCV, 16, 1995, pp. 35-56. 3D Room: Narayanan, Rander, & Kanade, “Constructing Virtual Worlds Using Dense Stereo”, Proc. ICCV, 1998, pp. 3-10. Graph-based: Kolmogorov & Zabih, “Multi-Camera Scene Reconstruction via Graph Cuts”, Proc. European Conf. on Computer Vision (ECCV), 2002. Helmholtz Stereo: Zickler, Belhumeur, & Kriegman, “Helmholtz Stereopsis: Exploiting Reciprocity for Surface Reconstruction”, IJCV, 49(2-3), 2002, pp. 215-227.