1. Introduction 3D scene flow is the 3D motion field of points in the world. Structure is the depth of the scene. Motivation of our work: Numerous applications including intelligent robots, human-computer interfaces, surveillance systems, dynamic rendering, dynamic scene interpretation, etc. Challenges: Absence of correspondences, image noises, structure ambiguities, occlusion, etc.

2. System Block Diagram Image Sequence 1 Optical Flow 3D Affine ModelStereo ConstraintsRegularization Constraints 3D Scene Flow 3D Correspondences Dense Scene Structure Image Sequence 2Image Sequence N Camera 1Camera 2Camera N

3. Multiple Camera Geometry A set of cameras provide N images. A 3D point in the world can be transformed to point by the relation, Normally, one pair is used as basic stereo pair. All cameras are pre-calibrated. Given an image point and its disparity, we can back-project it to the 3D world.

4. Local Motion Model Selection Frame t Frame t +1 3D affine motion Camera i :

5. Local Motion Model Selection To avoid overfitting and ensure convergence in each local region, we can assume the motion in consecutive S frames is similar over time. The difference is only a scaling factor. Then,

6. Motion Model Fitting Eliminate translation unknowns to avoid trivial solutions. For remaining unknowns in each local region: Non-linear model fitting by using Levenberg-Marquardt (LM) algorithm.

7. Available Local Constraints

8. Constraint Discussion The EOF function is defined based on all the available constraints. – Optical flow constraints: The projected 2D motion of 3D affine motion should be compatible with optical flow. – Stereo constraints: The projected image location on different image planes of the same 3D scene point should have similar intensity patterns. Cross- correlation is used to measure this similarity.

9. EOF Function A 3D scene point is projected to different image planes of N cameras. The intensity patterns around the projective location should be similar. So,

10. EOF Function The EOF in local model fitting can be denoted as, LM algorithm is then used to minimize the EOF function.

11. Regularization Constraints To avoid overfitting, penalty constraint is added to large motion. This constraint is added to EOF function and used in every iteration.

12. Initial Guesses The unknown vector need to be initialized. By assuming small motion between two adjacent frames, we have The initial structure (depth) value can be computed by a stereo algorithm. The unknown vector need to be initialized. By assuming small motion between two adjacent frames, we have The initial structure (depth) value can be computed by a stereo algorithm.

13. Complete Recursive Algorithm 1. Initialize unknown vector. Set. 2. If, carry out affine model fitting in each local region using LM algorithm. Smoothness constraint is not used. Set ; Else, add smoothness constraint into EOF function, then carry out affine model fitting in each local region. 3. If regularization constraints are less than a threshold or maximum number of iteration has been exceeded, end the algorithm. Else go to 2.

14. Integrated 3D Scene Flow and Structure Recovery Experiments on Synthetic Data

15. Integrated 3D Scene Flow and Structure Recovered Motion Fields

16. Integrated 3D Scene Flow and Structure Ground Truth Validation

17. Integrated 3D Scene Flow and Structure Experiments on Real Data

18. Integrated 3D Scene Flow and Structure Recovered Motion Fields

19. Experimental Results of Rule- Based Stereo Top View Right View Left View Segmentation Map

20. Experimental Results of Rule- Based Stereo Initial Sparse Disparity MapResult After Applied Rule 1 and 2

21. Experimental Results of Rule- Based Stereo Result by Using A Direct Method Result by Using Our Method

22. Experimental Results of Rule- Based Stereo Occlusion Map Confidence Map

23. Experimental Results of Sequential Formulation Sample input images (only reference views are shown). Time tTime t+1

24. Experimental Results of Sequential Formulation Disparity results. Reference ViewDisparity Result

25. Experimental Results of Sequential Formulation Scene flow results. X-y projection of scene flow z motion of scene flow

26. Experimental Results of Integrated Formulation Disparity results. Reference ViewDisparity Result

27. Experimental Results of Integrated Formulation Scene flow results. X-y projection of scene flow z motion of scene flow

28. Local Nonrigid Motion Tracking Structure Nonrigid motion 3D correspon- dences Global Regulari- zation Local Nonrigid Motion Tracking Local Nonrigid Motion Tracking Scheme Overview Global Constraints 2D Image Sequence Even Segmentation Local motion analysis module Global motion analysis module

29. Local Affine Motion Model Affine motion model assumed to remain the same for a short period of time; A scaling factor,, is incorporated in order to compensate for possible temporal deviations.

30. Local EOF Function Levenberg-Marquardt method is used to perform the EOF minimization. Unknowns include affine parameters and the scaling factors. Frame (i) Frame (i+1) (R) (M)

31. GOES-8 and GOES-9 are focused on clouds; GOES-9 provides one view at approximately every minute. GOES-8 provides one view at approximately every 15 minutes; Both GOES-8 and GOES-9 have five multi-spectral channels. Cloud Image Acquisition

32. Experiments have been performed on the GOES image sequences of Hurricane Luis, start from 09-06-95 at 1023 UTC to 09-06-95 at 2226 UTC. Experiments

33. Experiments (cont.) Although the initial mean errors are very large, they decrease very quickly after the global fluid constraints are applied. Stable results are achieved at the end of the iterations.

34. Experiments on Simulation Images

35. Results Validation

36. Experiments on Real Images

37. Reconstruction Results JeabJeab Min_TrackingMin_Tracking Jeab_render Lin Lin_render Qian Qian_render Ye Ye_render

38. Results Validation Mean Error: 0.47006Mean Error: 0.527872

39. Wave Tank Experiment Experimental Setup Stereoscopic camera used to record video sequences of ice forming in the CRREL wave tank. Camera details: 15 fps B/W images at 320x240 pixel resolution 12 cm baseline with 255 pixel focal length Camera mounted on platform ~0.8 m above surface Multiple film segments captured at various stages of ice formation Several marker types (buoys, sprinkles) placed on the surface at various times

40. Wave Tank Results Experiments Performed Visualization via Anaglyphs Ice Bucket – 3D images of small ice surfaces Wave Tank - 3D images of ice in CRREL wave tank Analysis Ice Bucket - Surface reconstruction of bench-top ice Wave Tank - Surface reconstruction of ice in CRREL wave tank

41. 1. Separate the color channels (RGB) 2. For each pixel in the anaglyph: 1.Take the Red value from the left image 2. Take the Green and Blue values from the right image 3. View the constructed image with filtered glasses. Visualizations Steps to Creating an Anaglyph L image R1R1 G1G1 B1B1 R image R2R2 G2G2 B2B2 R1R1 G2G2 B2B2 Anaglyph

42. Visualizations Ice Bucket Anaglyphs Ice pieces in small bucket Camera ~0.4 m from surface

43. Visualizations Wave Tank Anaglyphs ● Wave tank motion ● Surface mostly solid ● Frames pre-aligned

44. Pre-study Examples With calibration balls Without calibration balls

45. Stereo Analysis Ice Bucket Experiment Photographs taken in lab of ice in shallow bucket Ambient lighting Stereo camera Correspondences determined manually Matching points hand selected Determining matches in specular areas still difficult

46. Stereo Results Nearest Neighbor Surface Depths calculated at given correspondence points All other points assigned the depth of nearest known point

47. Stereo Results Thin Plate Spline Surface Depths calculated at given correspondence points All other points assigned the depth of nearest known point

48. Current Results: Wave Tank Wave Tank Results Photographs taken at CRREL wave tank No special lighting used Camera mounted above tank, facing down Initial correspondences determined manually Matching points hand selected Tank walls and camera support provide context

49. Current Results: Wave Tank Thin Plate Spline Surface Depths calculated at given correspondence points All other points interpolated from smoothing spline

50. Stereo Analysis Algorithm Thin Plate Spline Surface With Iterative Warping 1. Manually determine a set of correspondences 2. Generate disparity surface using thin plate splines 3. Warp the left image to the right image via the disparity surface 4. Fill in any gaps in warped image 5. Obtain dense stereo between the right and warped left images 6. Update the disparity surface from the calculated dense stereo 7. Iterate back to step 3 until the two images converge

51. Stereo Analysis Algorithm Thin Plate Spline Surface With Iterative Warping 1. Fit surface 2. Warp the left image to the right

52. Stereo Analysis Algorithm Thin Plate Spline Surface With Iterative Warping

53. Current Results: Wave Tank

54. Visualizations

55. Deformable Dual Mesh -- application to stereo(cont.) A 3D array is formed by the correlation values between the stereo pair. (a)A stereo pair (b)Three cross sections of a 3D array filled with the correlation values (red represents higher correlation areas) NM starts deforming from the camera-side end of the volume V FM starts deforming from the far-side of the volume V

56. Deformable Dual Mesh -- application to stereo(cont.) Coarse to Fine Scheme: A coarsely initialized 3D array V. The blue plane shows the initial position of the near mesh and the red plane shows the initial position of the far mesh

57. Deformable Dual Mesh -- application to stereo(cont.)