1. CSCE 641 Computer Graphics: Image-based Modeling Jinxiang Chai

2. Outline • Stereo matching • - Traditional stereo • - Multi-baseline stereo • - Active stereo • Volumetric stereo • - Visual hull • - Voxel coloring • - Space carving

3. Multi-baseline stereo reconstruction Need to choose reference frames! Does not fully utilize pixel information across all images

4. Volumetric stereo Scene Volume V Input Images (Calibrated) Goal: Determine occupancy, “color” of points in V

5. Discrete formulation: Voxel Coloring Discretized Scene Volume Input Images (Calibrated) • Goal: Assign RGBA values to voxels in V • photo-consistent with images

6. True Scene All Scenes (CN3) Photo-Consistent Scenes Complexity and computability Discretized Scene Volume 3 N voxels C colors

7. Issues • Theoretical Questions • Identify class of all photo-consistent scenes • Practical Questions • How do we compute photo-consistent models?

8. Voxel coloring solutions • 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]

9. background + foreground background foreground - = Why use silhouettes? • Can be computed robustly • Can be computed efficiently

10. Reconstruction from silhouettes (C = 2) Binary Images • How to construct 3D volume?

11. Reconstruction from silhouettes (C = 2) Binary Images • Approach: • Backproject each silhouette • Intersect backprojected volumes

12. 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

13. 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( ? ),

14. Visual Hull Results • Download data and results from http://www-cvr.ai.uiuc.edu/ponce_grp/data/visual_hull/

15. 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

16. 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]

17. 1. Choose voxel • Color if consistent • (standard deviation of pixel • colors below threshold) 2. Project and correlate Voxel coloring approach Visibility Problem: in which images is each voxel visible?

18. Known Scene Unknown Scene • Forward Visibility • - Z-buffer • - Painter’s algorithm • known scene • Inverse Visibility?known images The visibility problem • Which points are visible in which images?

19. Layers Depth ordering: visit occluders first! Scene Traversal Condition: depth order is the same for all input views

20. Panoramic depth ordering • Cameras oriented in many different directions • Planar depth ordering does not apply

21. Panoramic depth ordering Layers radiate outwards from cameras

22. Panoramic layering Layers radiate outwards from cameras

23. Panoramic layering Layers radiate outwards from cameras

24. Inward-Looking • cameras above scene • Outward-Looking • cameras inside scene Compatible camera configurations • Depth-Order Constraint • Scene outside convex hull of camera centers

25. Calibrated image acquisition • Calibrated Turntable • 360° rotation (21 images) Selected Dinosaur Images Selected Flower Images

26. Voxel coloring results Dinosaur Reconstruction 72 K voxels colored 7.6 M voxels tested 7 min. to compute on a 250MHz SGI Flower Reconstruction 70 K voxels colored 7.6 M voxels tested 7 min. to compute on a 250MHz SGI

27. 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

28. 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

29. Initialize to a volume V containing the true scene • Choose a voxel on the current surface • Project to visible input images • Carve if not photo-consistent • Repeat until convergence Space carving algorithm • Space Carving Algorithm Image 1 Image N …...

30. V Photo Hull 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 V True Scene

31. 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

32. 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

33. Multi-pass plane sweep • Sweep plane in each of 6 principle directions • Consider cameras on only one side of plane • Repeat until convergence

34. Multi-pass plane sweep • Sweep plane in each of 6 principle directions • Consider cameras on only one side of plane • Repeat until convergence

35. Multi-pass plane sweep • Sweep plane in each of 6 principle directions • Consider cameras on only one side of plane • Repeat until convergence

36. Multi-pass plane sweep • Sweep plane in each of 6 principle directions • Consider cameras on only one side of plane • Repeat until convergence

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. Space carving results: african violet Input Image (1 of 45) Reconstruction Reconstruction Reconstruction

39. Space carving results: hand Input Image (1 of 100) Views of Reconstruction

40. Properties of space carving • Pros • Voxel coloring version is easy to implement, fast • Photo-consistent results • No smoothness prior • Cons • Bulging • No smoothness prior

41. Next lecture Model Panoroma Image-based rendering Image based modeling Images + Depth Geometry+ Images Camera + geometry Imagesuser input range scans Images Geometry+ Materials Light field Kinematics Dynamics Etc.

42. Stereo reconstruction • Given two or more images of the same scene or object, compute a representation of its shape known camera viewpoints

43. Stereo reconstruction • Given two or more images of the same scene or object, compute a representation of its shape known camera viewpoints How to estimate camera parameters? - where is the camera? - where is it pointing? - what are internal parameters, e.g. focal length?

44. Spectrum of IBMR Model Panoroma Image-based rendering Image based modeling Images + Depth Geometry+ Images Camera + geometry Imagesuser input range scans Images Geometry+ Materials Light field Kinematics Dynamics Etc.

45. How can we estimate the camera parameters?

46. Camera calibration • Augmented pin-hole camera • - focal point, orientation • - focal length, aspect ratio, center, lens distortion Known 3D • Classical calibration • - 3D 2D • - correspondence Camera calibration online resources

47. Camera and calibration target

48. Classical camera calibration • Known 3D coordinates and 2D coordinates • - known 3D points on calibration targets • - find corresponding 2D points in image using feature detection • algorithm

49. Camera parameters Known 3D coords and 2D coords sx а u0 u 0 -sy v0 v 0 0 1 1 Viewport proj. Perspective proj. View trans.

50. Camera parameters Known 3D coords and 2D coords sx а u0 u 0 -sy v0 v 0 0 1 1 Viewport proj. Perspective proj. View trans. Intrinsic camera parameters (5 parameters) extrinsic camera parameters (6 parameters)