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Automatic Image Stitching using Invariant Features

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Automatic Image Stitching using Invariant Features. Matthew Brown and David Lowe, University of British Columbia. 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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Automatic Image Stitching using Invariant Features

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  1. Automatic Image Stitching using Invariant Features Matthew Brown and David Lowe, University of British Columbia

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

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

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

  5. Recognising Panoramas

  6. Recognising Panoramas • 1D Rotations (q) • Ordering  matching images

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

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

  9. 2D Rotations (q, f) • Ordering  matching images Recognising Panoramas • 1D Rotations (q) • Ordering  matching images

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

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

  12. Recognising Panoramas

  13. Overview • Feature Matching • Image Matching • Bundle Adjustment • Multi-band Blending • Results • Conclusions

  14. Overview • Feature Matching • Image Matching • Bundle Adjustment • Multi-band Blending • Results • Conclusions

  15. Overview • Feature Matching • SIFT Features • Nearest Neighbour Matching • Image Matching • Bundle Adjustment • Multi-band Blending • Results • Conclusions

  16. Overview • Feature Matching • SIFT Features • Nearest Neighbour Matching • Image Matching • Bundle Adjustment • Multi-band Blending • Results • Conclusions

  17. Invariant Features • Schmid & Mohr 1997, Lowe 1999, Baumberg 2000, Tuytelaars & Van Gool 2000, Mikolajczyk & Schmid 2001, Brown & Lowe 2002, Matas et. al. 2002, Schaffalitzky & Zisserman 2002

  18. SIFT Features • Invariant Features • Establish invariant frame • Maxima/minima of scale-space DOG  x, y, s • Maximum of distribution of local gradients q • Form descriptor vector • Histogram of smoothed local gradients • 128 dimensions • SIFT features are… • Geometrically invariant to similarity transforms, • some robustness to affine change • Photometrically invariant to affine changes in intensity

  19. Overview • Feature Matching • SIFT Features • Nearest Neighbour Matching • Image Matching • Bundle Adjustment • Multi-band Blending • Results • Conclusions

  20. Nearest Neighbour Matching • Nearest neighbour matching • Use k-d tree • k-d tree recursively bi-partitions data at mean in the dimension of maximum variance • Approximate nearest neighbours found in O(n log n) • Find k-NN for each feature • k  number of overlapping images (we use k = 4) [ Beis Lowe 1997, Nene Nayar 1997, Gray Moore 2000, Shakhnarovich 2003 ]

  21. K-d tree

  22. K-d tree

  23. Overview • Feature Matching • SIFT Features • Nearest Neighbour Matching • Image Matching • Bundle Adjustment • Multi-band Blending • Results • Conclusions

  24. Overview • Feature Matching • Image Matching • Bundle Adjustment • Multi-band Blending • Results • Conclusions

  25. Overview • Feature Matching • Image Matching • Bundle Adjustment • Multi-band Blending • Results • Conclusions

  26. Overview • Feature Matching • Image Matching • RANSAC for Homography • Bundle Adjustment • Multi-band Blending • Results • Conclusions

  27. Overview • Feature Matching • Image Matching • RANSAC for Homography • Bundle Adjustment • Multi-band Blending • Results • Conclusions

  28. RANSAC for Homography

  29. RANSAC for Homography

  30. RANSAC for Homography

  31. least squares line RANSAC: 1D Line Fitting

  32. RANSAC: 1D Line Fitting

  33. RANSAC line RANSAC: 1D Line Fitting

  34. The RANSAC Algorithm function H = RANSAC(points, nIterations) { bestInliers = 0; bestH = zeros(3, 3); for (i = 0; i < nIterations; i++) { samplePoints = RandomSample(points); H = ComputeTransform(samplePoints); nInliers = Consistent(H); if (nInliers > bestInliers) { bestInliers = nInliers; bestH = H; } // end if } // end for } // end RANSAC

  35. 2D Transforms • Linear (affine) • Homography

  36. Finding the panoramas

  37. Finding the panoramas

  38. Finding the panoramas

  39. Finding the panoramas

  40. Connected Components

  41. Overview • Feature Matching • Image Matching • Bundle Adjustment • Multi-band Blending • Results • Conclusions

  42. Bundle Adjustment • Adjust rotation, focal length of each image to minimise error in matched features

  43. Bundle Adjustment • Adjust rotation, focal length of each image to minimise error in matched features

  44. Overview • Feature Matching • Image Matching • Bundle Adjustment • Multi-band Blending • Results • Conclusions

  45. Overview • Feature Matching • Image Matching • Bundle Adjustment • Multi-band Blending • Results • Conclusions

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

  47. 2-band Blending Low frequency (l > 2 pixels) High frequency (l < 2 pixels)

  48. Linear Blending

  49. 2-band Blending

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