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Che-Han Chang 1 , Yoichi Sato 2 , Yung-Yu Chuang 1

Shape-Preserving Half-Projective Warps for Image Stitching. Che-Han Chang 1 , Yoichi Sato 2 , Yung-Yu Chuang 1 1 National Taiwan University 2 The University of Tokyo. Image stitching. Geometric transformation. Projective transformation (Homography). Projective warp. Image compositing.

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Che-Han Chang 1 , Yoichi Sato 2 , Yung-Yu Chuang 1

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  1. Shape-Preserving Half-Projective Warps for Image Stitching Che-Han Chang1, Yoichi Sato2, Yung-Yu Chuang1 1National Taiwan University 2The University of Tokyo

  2. Image stitching

  3. Geometric transformation

  4. Projective transformation (Homography)

  5. Projective warp

  6. Image compositing

  7. Misalignment Projective Warp • Misalignment (overlapping regions) • Geometric distortion (non-overlapping regions) • Stretched shapes  shape distortion • Non-uniform scaling  area distortion

  8. Distortion Projective Warp • Misalignment (overlapping regions) • Geometric distortion (non-overlapping regions) • Stretched shapes  shape distortion • Non-uniform scaling  area distortion

  9. Globally aligned Projective Warp Distortion Locally aligned As-Projective-As-Possible Warp Distortion

  10. Key idea: Replacing it by a similarity transformation. (scaling, rotation, translation) As-Projective-As-Possible Warp

  11. We propose shape-preserving half-projective warp, a spatial combination of a projective transformation and a similarity transformation. Source Our warp Similarity warp Projective warp

  12. Projective warp Our warp APAP warp APAP + Our warp

  13. Goal Given a projective transformation, construct a warp that gradually changes from projective to similarity.

  14. Analysis Construction +  H Scale up Scale down Linear mapping

  15. Change of coordinates

  16. As , area distortion H Scale up Scale down

  17. H becomes linear if u is a constant H

  18. H becomes linear if u is a constant H similarity transformation

  19. H S

  20. H S

  21. C0 continuity C1 continuity

  22. Given H, l1 and l2, determine S and T such that the resulting warp is C1 continuous.

  23. Given H, l1 and l2, determine S and T such that the resulting warp is C1 continuous. Boundary constraints C1 C1 C1 continuity on l1 C1 continuity on l2

  24. Given H, l1 and l2, determine S and T such that the resulting warp is C1 continuous. Boundary constraints C1 continuity on l1 C1 continuity on l2

  25. Given H, l1 and l2, determine S and T such that the resulting warp is C1 continuous. Boundary constraints C1 continuity on l1 C1 continuity on l2

  26. Two-view stitching

  27. Two-view stitching Projective warp Our warp

  28. Parameters Given H, l1 and l2, determine S and T such that the total warp is C1 continuous.

  29. Optimizing parameters We want that each image undergoes a similarity transformation as much as possible.

  30. Multiple image stitching

  31. Combining with the APAP warp Our warp Projective Refined warp APAP Refined warp Combined warp

  32. Results Original AutoStitch Projective warp Our warp

  33. Results Projective warp AutoStitch Our warp

  34. Conclusion Our warp Similarity warp Projective warp • A novel parametric warp for image stitching • Parameter selection could be improved

  35. Thank you! Any questions?

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