Photo Stitching Panoramas from Multiple Images

1. 04/05/11 Photo StitchingPanoramas from Multiple Images Computer Vision CS 543 / ECE 549 University of Illinois Derek Hoiem

2. So far, we’ve looked at what can be done with one image • Recover basic geometry using vanishing points • Find image boundaries and segment objects • Categorize images • Find specific objects and detect objects that are part of some category

3. What can we get from multiple images?

4. What can we get from multiple images? • Bigger, Better, Brighter, Sharper images • Panoramas • Increased dynamic range • Super-resolution • Reduced noise/blur Product example: http://www.vreveal.com/

5. What can we get from multiple images? • Bigger, Better, Brighter, Sharper images • Panoramas • Increased dynamic range • Super-resolution • Reduced noise/blur today Product example: http://www.vreveal.com/

6. What can we get from multiple images? • Motion • Tracking • Optical flow • Action/activity recognition Tracking (from Deva Ramanan) Optical flow (source: http://www.borisfx.com/avid/bccavx/classic_features.php)

7. What can we get from multiple images? • Motion • Tracking • Optical flow • Action/activity recognition Thursday Tracking (from Deva Ramanan) Optical flow (source: http://www.borisfx.com/avid/bccavx/classic_features.php)

8. What can we get from multiple images? • Motion • Tracking • Optical flow • Action/activity recognition April 19 Tracking (from Deva Ramanan) Optical flow (source: http://www.borisfx.com/avid/bccavx/classic_features.php)

9. What can we get from multiple images? • Motion • Tracking • Optical flow • Action/activity recognition April 21 Tracking (from Deva Ramanan) Optical flow (source: http://www.borisfx.com/avid/bccavx/classic_features.php)

10. What can we get from multiple images? • Depth and 3D structure • Two-view stereo • Multi-view stereo • Shape carving • Structure from motion Next week

11. Key ideas • Correspondence • Detect interest points • Match two patches • Alignment and model fitting • Solve for motion or depth or camera movement from multiple matched points

12. Today: Image Stitching • Combine two or more overlapping images to make one larger image Add example Slide credit: Vaibhav Vaish

13. Example Camera Center

14. Review of projective geometry

15. Problem set-up • x = K [R t] X • x' = K' [R' t'] X • t=t'=0 • x'=Hxwhere H = K' R' R-1 K-1 • Typically only R and f will change (4 parameters), but, in general, H has 8 parameters . X x x' f f'

16. Image Stitching Algorithm Overview • Detect keypoints • Match keypoints • Estimate homography with four matched keypoints (using RANSAC) • Combine images

17. Computing homography Assume we have four matched points: How do we compute homographyH? Direct Linear Transformation (DLT)

18. Computing homography Direct Linear Transform • Apply SVD: UDVT= A • h = Vsmallest (column of V corr. to smallest singular value) Matlab [U, S, V] = svd(A); h = V(:, end); Explanations of SVD and solving homogeneous linear systems

19. Computing homography • Assume we have four matched points: How do we compute homographyH? Normalized DLT • Normalize coordinates for each image • Translate for zero mean • Scale so that average distance to origin is sqrt(2) • This makes problem better behaved numerically (see HZ p. 107-108) • Compute using DLT in normalized coordinates • Unnormalize:

20. Computing homography • Assume we have matched points with outliers: How do we compute homographyH? Automatic Homography Estimation with RANSAC • Choose number of samples N HZ Tutorial ‘99

21. Computing homography • Assume we have matched points with outliers: How do we compute homographyH? Automatic Homography Estimation with RANSAC • Choose number of samples N • Choose 4 random potential matches • Compute H using normalized DLT • Project points from x to x’ for each potentially matching pair: • Count points with projected distance < t • E.g., t = 5 pixels • Repeat steps 2-5 N times • Choose H with most inliers HZ Tutorial ‘99

22. Automatic Image Stitching • Compute interest points on each image • Find candidate matches • Estimate homographyH using matched points and RANSAC with normalized DLT • Transform second image and blend the two images • Matlab: maketform, imtransform

23. RANSAC for Homography Initial Matched Points

24. RANSAC for Homography Final Matched Points

25. Verification

26. RANSAC for Homography

27. Choosing a Projection Surface Many to choose: planar, cylindrical, spherical, cubic, etc.

28. Planar vs. Cylindrical Projection Planar Photos by Russ Hewett

29. Planar vs. Cylindrical Projection Planar

30. Planar vs. Cylindrical Projection Cylindrical

31. Planar vs. Cylindrical Projection Cylindrical

32. Planar Cylindrical

33. Simple gain adjustment

34. Recognizing Panoramas Brown and Lowe 2003, 2007 Some of following material from Brown and Lowe 2003 talk

35. Recognizing Panoramas Input: N images • Extract SIFT points, descriptors from all images • Find K-nearest neighbors for each point (K=4) • For each image • Select M candidate matching images by counting matched keypoints (m=6) • Solve homographyHij for each matched image

36. Recognizing Panoramas Input: N images • Extract SIFT points, descriptors from all images • Find K-nearest neighbors for each point (K=4) • For each image • Select M candidate matching images by counting matched keypoints (m=6) • Solve homographyHij for each matched image • Decide if match is valid (ni > 8 + 0.3 nf ) # keypoints in overlapping area # inliers

37. Recognizing Panoramas (cont.) (now we have matched pairs of images) • Find connected components

38. Finding the panoramas

39. Finding the panoramas

40. Recognizing Panoramas (cont.) (now we have matched pairs of images) • Find connected components • For each connected component • Perform bundle adjustment to solve for rotation (θ1, θ2, θ3) and focal length f of all cameras • Project to a surface (plane, cylinder, or sphere) • Render with multiband blending

41. Bundle adjustment for stitching • Non-linear minimization of re-projection error • whereH = K’ R’ R-1K-1 • Solve non-linear least squares (Levenberg-Marquardt algorithm) • See paper for details

42. Bundle Adjustment • New images initialised with rotation, focal length of best matching image

43. Bundle Adjustment • New images initialised with rotation, focal length of best matching image

44. Blending • Gain compensation: minimize intensity difference of overlapping pixels • Blending • Pixels near center of image get more weight • Multiband blending to prevent blurring

45. Multi-band Blending • Burt & Adelson 1983 • Blend frequency bands over range l

46. Multiband blending

47. Blending comparison (IJCV 2007)

48. Blending Comparison

49. Further reading • DLT algorithm: HZ p. 91 (alg 4.2), p. 585 • Normalization: HZ p. 107-109 (alg 4.2) • RANSAC: HZ Sec 4.7, p. 123, alg 4.6 • Recognising Panoramas: Brown and Lowe, IJCV 2007 (also bundle adjustment)

50. Things to remember • Homography relates rotating cameras • Recover homography using RANSAC and normalized DLT • Bundle adjustment minimizes reprojection error for set of related images • Details to make it look nice (e.g., blending)