cpsc 643 aligning windows of live video from an imprecise pan-tilt-zoom robotic camera into a remote...
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CPSC 643
Aligning Windows of Live Video from an Imprecise Pan-Tilt-Zoom Robotic Camera
into a Remote Panoramic Display
Dezhen SongDepartment of
Computer Science and Engineering
Texas A&M University
Supported in part by
2
Network PTZ Robotic Camera for Nature Observation
Panosonic HCM 280
– PTZ Robotic Camera:
• 350° Pan, 120° Tilt, 42x Zoom
• 200° per second servo speed
– Network Video Camera:
• Built-in streaming server
• 640x480 pixels video
• >30 frames per second
– Low power consumption: <5
Watt
– Affordable price: $ 1.2 K
3
Real Time Panoramic Video
Tilt
Pan
Frame sequence
Panorama
Tilt
Time
Panorama
Live frame sequence
Updated Part in
Panorama
4
5
Related Work
– Multiple fixed cameras• [Swaminathan and Nayar
2000]
• [Tan et al. 2004]
• [Foote et al. 2000, 2001]
– Single wide angle camera• [Baker and Nayar 1999]
• [Nayar 1997]
• [Xing and Turkowski 1997]
6
Related Work: Image Alignment
– Direct Method• Use pixel intensity value
• Sensitive to luminance change
• Need good guess for initial parameters input
• Existing work– [Shum and Szeliski 1997] [Szeliski 1994, 1996]
– [Coorg and Teller 2000] [Kang and Weiss 1997]
– Frequency Domain Registration• Existing work
– [Castro and Morandi 1987] [Reddy and Chatterji 1996]
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Related Work: Image Alignment
– Feature-based Image Registration• Use feature points: Harris corner point, SIFT
• Robust to luminance change
• Faster than direct method
• Existing work– [Torr and Zisserman 1997] [Brown and Lowe 2003]
– [Zoghlami et al. 1997] [Hu et al. 2001] [Cho et al. 2003]
– [Kanazawa and Kanatani 2002] [Zhang et al. 2002]
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Comparison: Panoramic Video
System Resolution Bandwidth Live Motion Images
Our system Excellent Low Yes
Film-based panorama
Excellent Low No
Wide-angle systems
Poor Moderate Yes
Multi-cameras
Good Moderate to High
Yes
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Assumptions
• Pan-tilt camera with a fixed base
• Known intrinsic camera parameters
– Calibrated camera before deployment
• Inaccurate pan-tilt readings
– May deteriorate over time
• Standard video camera with HFOV ≤ 45o
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QKRI Wq
Review: Perspective Projection
Intrinsic
Parameters Extrinsic
Parameters
[Tsai86,
87]
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Problem Definition
qtpMqRKKq BBB
BAB
A ),(1
Re-projection: Project image B onto image A plane:
Image alignment:
BAiBtBp
iA
AiB
BBB qqtpM2
Intensity,Intensitymin),(
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Excessive Computation in Image Alignment
Speed slow down caused by coupling re-projection and SSD:
– Extensive float point computation
– Coupled with Sum of Squared Difference (SSD) operation
– A naive search takes O(km) re-projection operations
• k: number of candidate pan/tilt pairs over feasible solution
set.
• m: number of overlapping pixels
Proposed solution: decouple re-projection and SSD– Spherical re-projection – Cell-based Alignment
• Constant time alignment
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• Project image onto a spherical surface• Image =(p, t) on local spherical coordinate system { }
Spherical Projection
22arctan
arctan
fu
vt
f
up
CY
CX
tp
u
v
)(~ ),,(
p,tq
zyxQC
),( vuq
OImage plane
f
CZ
I~
I~
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0.8
0.4
-0.4
-0.8-1.5 -0.5-1 0 0.5
p
t 0
-400
-200
0
200
400
v
200u -200-600-1000
Planar Spherical
Two poses have 30o pan difference with the same 30o tilt value
Distortion under Re-projection
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0.8
0.4
-0.4
-0.8-1.5 -0.5-1 0 0.5
p
t 0
Invariant under Spherical Re-projection
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Re-projection after Spherical Projection
Define conversion between camera coordinate system and local spherical coordinate system
Re-projection function between two local spherical coordinate system
qP
pctcf
tsf
pstcf
z
y
x
Q ~1
QP
zxy
zx
t
pq
22arctan
arctan~
qRFqRPPQRPq BAB
BAB
BAB
A ~,~~ 1
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• Rc is a 2x2 rotation matrix
• Cell distortion under re-projection is negligible.
Lemma 1: If the spherical cell is small , define
point
and its corresponding point
)5 and 5( cc tp
Cqq BBo
B ~ Aqq Ao
A ~~
qRq BC
A ~~
qqqqRF Ao
ABo
BAB
~~ ~~,
we have
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Proof for Lemma 1:
qP
pctcf
tsf
pstcf
z
y
x
Q ~1
df
dt
dp
pctcpctfspstfc
tstfc
pstcpstfspctfc
Q 0
Introduce coefficient matrix HRadius f remains
same
f
f
f
H
00
00
00
0
0
33
23
13
p
p
mpctspstc
mtc
mpstspctc
H
z
y
x
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Continue: Proof for Lemma 1
HFOV≤45o and VFOV ≤34o
0.956 ≤ cos(t) ≤ 1
Dropping cos(t) introduces ≤ 5% distortion for 20x20 cell
∆f=0 substitute [m13, m23, m33]T
0
0
33
23
13
p
p
mtspcps
mtc
mtspspc
H
z
y
x
tRpR
tcpctspcps
tstc
tcpstspspc
XY
0
20
Continue: Proof for Lemma 1
0
~
0
~ qR
q BA
oB
XoB
YABo
AYo
AX tRpRRpRtRR
10
0
21
12cRR
qtRpHRQ XY~ QRQ BA
BA
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Lemma 2: Rotation angle Θ of Rc can be approximated by
where α is the dot product of Z axis of {CA} and {CB}
BoB
oA
AB
AoB
oA
AB
oB
oA
ABoB
oA
tcpspcpps
tcpcpspps
pspsppcpcpc
arccos
BAABBA tstsppctctc
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Algorithm
Cj ε(Cj )
A~
B~
ojB q~
2
1
IntensityIntensitymin),(
c
BtBp
k
jjAjcB CCR
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Cell based Image Alignment
Select kc cells from the overlapping region in O(1)
Sphere projection O(1)
Feature detection in the cell and searching regions O(1)
For each(δpB, δtB) O(1)
For each cell O(1)
Compute Cj
Compute , j=1, …, kc
Compute SSD between and
End For
Report sum of SSD across all cells
End For
Output solution with the minimum SSD
BCR jC
~
BCR jC
~1 AC j
~
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Experiment and Results
Speed test:
– 881 milliseconds to align 21 320x240 images
– 4 seconds for Autostitch program on same data set
– Up to 25fps on a laptop PC
25
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• Align video images from a camera that only differ in pan and tilt settings into a panorama at 25 frames per second.
• Alignment is performed on a spherical surface to avoid excessive distortion caused by homographic transformation.
• A constant time algorithm pre-rotates small pre-sampled squared patches on spherical surface for matching.
• Experiments show that the alignment speed is 4.5x faster than the best method available.
live video window
Thank You!