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Image Stitching

Image Stitching. Shangliang Jiang Kate Harrison. What is image stitching?. What is image stitching?. Introduction. Are you getting the whole picture? Compact Camera FOV = 50 x 35°. Introduction. Are you getting the whole picture? Compact Camera FOV = 50 x 35°

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Image Stitching

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  1. Image Stitching Shangliang Jiang Kate Harrison

  2. What is image stitching?

  3. What is image stitching?

  4. Introduction • Are you getting the whole picture? • Compact Camera FOV = 50 x 35°

  5. Introduction • Are you getting the whole picture? • Compact Camera FOV = 50 x 35° • Human FOV = 200 x 135°

  6. Introduction • Are you getting the whole picture? • Compact Camera FOV = 50 x 35° • Human FOV = 200 x 135° • Panoramic Mosaic = 360 x 180°

  7. Recognizing Panoramas • 1D Rotations (q) • Ordering  matching images

  8. Recognizing Panoramas • 1D Rotations (q) • Ordering  matching images

  9. Recognizing Panoramas • 1D Rotations (q) • Ordering  matching images

  10. 2D Rotations (q, f) • Ordering  matching images Recognizing Panoramas • 1D Rotations (q) • Ordering  matching images

  11. 2D Rotations (q, f) • Ordering  matching images Recognizing Panoramas • 1D Rotations (q) • Ordering  matching images

  12. 2D Rotations (q, f) • Ordering  matching images Recognizing Panoramas • 1D Rotations (q) • Ordering  matching images

  13. Recognizing Panoramas

  14. Overview • Feature Matching • Image Matching • Bundle Adjustment • Image Compositing • Conclusions

  15. Overview • Feature Matching • Image Matching • Bundle Adjustment • Image Compositing • Conclusions

  16. Overview • Feature Matching • SIFT Features • Nearest Neighbor Matching • Image Matching • Bundle Adjustment • Image Compositing • Conclusions

  17. SIFT Features • SIFT features are… • Geometrically invariant to similarity transforms, • some robustness to affine change • Photometrically invariant to affine changes in intensity

  18. Overview • Feature Matching • SIFT Features • Nearest Neighbor Matching • Image Matching • Bundle Adjustment • Image Compositing • Conclusions

  19. Nearest Neighbor Matching • Find k nearest neighbors for each feature • k  number of overlapping images (we use k = 4) • Use k-d tree • k-d tree recursively bi-partitions data at mean in the dimension of maximum variance • Approximate nearest neighbors found in O(nlogn)

  20. Overview • Feature Matching • SIFT Features • Nearest Neighbor Matching • Image Matching • Bundle Adjustment • Image Compositing • Conclusions

  21. Overview • Feature Matching • Image Matching • Bundle Adjustment • Image Compositing • Conclusions

  22. Overview • Feature Matching • Image Matching • Bundle Adjustment • Image Compositing • Conclusions

  23. Overview • Feature Matching • Image Matching • Random Sample Consensus (RANSAC) for Homography • Probabilistic model for verification • Bundle Adjustment • Image Compositing • Conclusions

  24. Overview • Feature Matching • Image Matching • Random Sample Consensus (RANSAC) for Homography • Probabilistic model for verification • Bundle Adjustment • Image Compositing • Conclusions

  25. RANSAC for Homography

  26. RANSAC for Homography • SIFT features of two similar images

  27. RANSAC for Homography • SIFT features common to both images

  28. RANSAC for Homography • Select random subset of features (e.g. 6) • Compute motion estimate • Apply motion estimate to all SIFT features • Compute error: feature pairs not described by motion estimate • Repeat many times (e.g. 500) • Keep estimate with best error

  29. RANSAC for Homography

  30. Overview • Feature Matching • Image Matching • Random Sample Consensus (RANSAC) for Homography • Probabilistic model for verification • Bundle Adjustment • Image Compositing • Conclusions

  31. Probabilistic model for verification • Potential problem: • Two images don’t match… • … but RANSAC found a motion estimate • Do a quick check to make sure the images do match • MAP for inliers vs. outliers

  32. Finding the panoramas

  33. Finding the panoramas

  34. Finding the panoramas

  35. Overview • Feature Matching • Image Matching • RANSAC for Homography • Probabilistic model for verification • Bundle Adjustment • Image Compositing • Conclusions

  36. Overview • Feature Matching • Image Matching • Bundle Adjustment • Image Compositing • Conclusions

  37. Overview • Feature Matching • Image Matching • Bundle Adjustment • Image Compositing • Conclusions

  38. Overview • Feature Matching • Image Matching • Bundle Adjustment • Error function • Image Compositing • Conclusions

  39. Overview • Feature Matching • Image Matching • Bundle Adjustment • Error function • Image Compositing • Conclusions

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

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

  42. Error function • Sum of squared projection errors • n = #images • I(i) = set of image matches to image i • F(i, j) = set of feature matches between images i,j • rijk = residual of kth feature match between images i,j • Robust error function

  43. Overview • Feature Matching • Image Matching • Bundle Adjustment • Error function • Image Compositing • Conclusions

  44. Overview • Feature Matching • Image Matching • Bundle Adjustment • Image Compositing • Conclusions

  45. Overview • Feature Matching • Image Matching • Bundle Adjustment • Image Compositing • Conclusions

  46. Blending

  47. Gain compensation

  48. How do we blend? Linear blending Multi-band blending

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

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