### 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
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
```