Transcript slides (PowerPoint)

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
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Projective transformation
(Homography)
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Projective warp
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Image
compositing
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• Misalignment (overlapping regions)
• Geometric distortion (non-overlapping regions)
– Stretched shapes  shape distortion
– Non-uniform scaling  area distortion
Misalignment
Projective Warp
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• 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
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Key idea: Replacing it by
a similarity transformation.
(scaling, rotation, translation)
As-Projective-As-Possible Warp
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We propose shape-preserving half-projective warp,
a spatial combination of a
projective transformation
and a similarity transformation.
Source
Similarity warp
Projective warp
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Projective warp
Our warp
APAP warp
APAP + Our warp
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Goal
Given a projective transformation, construct a
warp that gradually changes from projective to
similarity.
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Analysis
H
Scale
up
Scale
down
Linear mapping
Construction
+

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Change of coordinates
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As
, area distortion
H
Scale
up
Scale
down
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H becomes linear if u is a constant
H
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H becomes linear if u is a constant
H
similarity
transformation
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H
S
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H
S
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C0 continuity
C1 continuity
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Given H, l1 and l2,
determine S and T such
that the resulting warp is
C1 continuous.
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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
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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
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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
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Two-view stitching
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Two-view stitching
Projective warp
Our warp
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Parameters
Given H, l1 and l2,
determine S and T such
that the total warp is C1
continuous.
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Optimizing parameters
We want that each image undergoes a similarity
transformation as much as possible.
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Multiple image stitching
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Combining with the APAP warp
Our warp
Projective
Refined
warp
APAP
Refined
warp
Combined warp
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Results
Original
Projective warp
AutoStitch
Our warp
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Results
Projective warp
AutoStitch
Our warp
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Conclusion
• A novel parametric warp for image stitching
• Parameter selection could be improved
Similarity warp
Projective warp
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Thank you!
Any questions?
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