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Shape-Preserving Half-Projective Warps for Image Stitching Che-Han Chang1, Yoichi Sato2, Yung-Yu Chuang1 1National Taiwan University 2The University of Tokyo Image stitching 2 3 4 Geometric transformation 5 Projective transformation (Homography) 6 Projective warp 7 Image compositing 8 • Misalignment (overlapping regions) • Geometric distortion (non-overlapping regions) – Stretched shapes shape distortion – Non-uniform scaling area distortion Misalignment Projective Warp 9 • Misalignment (overlapping regions) • Geometric distortion (non-overlapping regions) – Stretched shapes shape distortion – Non-uniform scaling area distortion Distortion Projective Warp 10 Globally aligned Projective Warp Distortion Locally aligned As-Projective-AsPossible Warp Distortion 11 Key idea: Replacing it by a similarity transformation. (scaling, rotation, translation) As-Projective-As-Possible Warp 12 We propose shape-preserving half-projective warp, a spatial combination of a projective transformation and a similarity transformation. Source Similarity warp Projective warp 13 Projective warp Our warp APAP warp APAP + Our warp 14 Goal Given a projective transformation, construct a warp that gradually changes from projective to similarity. 15 Analysis H Scale up Scale down Linear mapping Construction + 16 Change of coordinates 17 As , area distortion H Scale up Scale down 18 H becomes linear if u is a constant H 19 H becomes linear if u is a constant H similarity transformation 20 H S 21 H S 22 C0 continuity C1 continuity 23 Given H, l1 and l2, determine S and T such that the resulting warp is C1 continuous. 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 C1 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 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 27 Two-view stitching 28 Two-view stitching Projective warp Our warp 29 Parameters Given H, l1 and l2, determine S and T such that the total warp is C1 continuous. 30 Optimizing parameters We want that each image undergoes a similarity transformation as much as possible. 31 Multiple image stitching 32 Combining with the APAP warp Our warp Projective Refined warp APAP Refined warp Combined warp 33 Results Original Projective warp AutoStitch Our warp 34 Results Projective warp AutoStitch Our warp 35 Conclusion • A novel parametric warp for image stitching • Parameter selection could be improved Similarity warp Projective warp 36 Thank you! Any questions? 37