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Seminar
A Digital Image Stabilization Method Based
on the Hilbert–Huang Transform
Konstantinos Ioannidis and Ioannis AndreadisIEEE TRANSACTIONS on Instrumentation And Measurement,
VOL. 61, NO. 9, SEPTEMBER 2012
Presented by
Shibudas K Subhashdas
1/22
Introduction
An innovative technique for digital image stabilization
(DIS) based on the Hilbert Huang transform (HHT)
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
2/22
Proposed method in a Nutshell
Local Motion Vector (LMV) Estimation
Hilbert Huang Transform ( HHT)
Empirical Mode Decomposition (EMD) process
Hilbert Transform
Detect the unwanted Camera Motion
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
3/22
Local Motion Vector (LMV) Estimation
LMV represents the offset of specific image regions be-
tween two consecutive images (displacement vector)
LMV includes intentional and unwanted motion of the
camera
Block based motion estimation used in LMV
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
4/22
Local Motion Vector (LMV) Estimation
The criteria for selecting the best match is sum of absolute
difference (SAD)
1 1
21 0 2 0
1( , ) [ ( 1, 2, ) ( 1 , 2 , 1)]
N N
n n
SAD i j s n n k s n i n j kN
S(0,0)S(0,1)S(1,0)S(1,1)
Current Frame
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
5/22
Previous Frame
Local Motion Vector (LMV) Estimation
Minimum SAD value defines the displacement vector
Full search (FS) algorithm is used in this method
[ 1, 2] arg min[ ( , )]d d SAD i j
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
6/22
Local Motion Vector (LMV) Estimation
Comparison of Full search (FS) algorithm with other
search method
three step search algorithm
Four step search algorithm
Diamond search algorithm
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
7/22
Local Motion Vector (LMV) Estimation
Using LMV estimation - x(t) (displacement vector)
[ 1, 2] arg min[ ( , )]d d SAD i j
1 1
21 0 2 0
1( , ) [ ( 1, 2, ) ( 1 , 2 , 1)]
N N
n n
SAD i j s n n k s n i n j kN
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
8/22
Hilbert Huang Transform ( HHT)
Empirical Mode Decomposition (EMD) process • Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
9/22
Hilbert Huang Transform ( HHT)
Empirical Mode Decomposition (EMD) process
11
( ) ( )( )
2
U t L tm t
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
10/22
Hilbert Huang Transform ( HHT)
Empirical Mode Decomposition (EMD) process Shifting Process
This will continue until value sum of difference (SD)
reaches between 0.2 and 0.3
1 1( ) ( ) ( )h t x t m t
11 1 11( ) ( ) ( )h t h t m t
12 11 12( ) ( ) ( )h t h t m t
1 1( 1) 1( ) ( ) ( )k k kh t h t m t
21
0
21
0
| ( ) ( ) |
( )
T
k kt
T
kt
h t h tSD
h t
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
11/22
Hilbert Huang Transform ( HHT)
Empirical Mode Decomposition (EMD) process If 0.2<= SD <=0.3
c1= h1k be the first IMF (Intrinsic Mode function)
c1 (t) is removed from the image to get residue
r1 is the residue
Residue is treated as the new data and subjected to same shifting process to give c2(t)
1 1( ) ( ) ( )r t x t c t
2 1 2( ) ( ) ( )r t r t c t
1( ) ( ) ( )w w wr t r t c t Cw(t) is the wth
IMF
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
12/22
Hilbert Huang Transform ( HHT)
Empirical Mode Decomposition (EMD) process
When the residue rw becomes a monotonic function
from which no IMF can be extracted.
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
13/22
Hilbert Huang Transform ( HHT)
Empirical Mode Decomposition (EMD) process
Sum of the IMFs and the residue recovers the original
signal.
1
( )w
j wj
x t c r
1 1
11 1
( )w w
j w w j wj j
x t c c r c r
2 1
1 1 21 1
w w
j w w j wj j
c c r c r
1
2 2 1 11
( )jj
c c r c r x t
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
14/22
Hilbert Huang Transform ( HHT)
Hilbert Transform
It is used to compute instantaneous frequencies and
amplitudes
Where P denotes Cauchy principal value
z(t) analytical signal is given by
Where α(t) – Instantaneous Amplitude
θ(t) – Instantaneous Phase
1 ( )( ( )) ( )
xH x t y t P d
t
( )( ) ( ) ( ) ( ) i tz t x t iy t t e
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
15/22
Hilbert Huang Transform ( HHT)
Hilbert Transform
Instantaneous Amplitude
Instantaneous Phase
Instantaneous Frequency
2 2( ) ( ) ( )t x t y t
1 ( )( ) tan
( )
y tt
x t
1 ( )( )
2
d tf t
dt
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
16/22
Hilbert Huang Transform ( HHT)
Detect the unwanted Camera Motion
EMD process divides the initial signal into finite
number of sub signals based on their frequencies
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
17/22
Hilbert Huang Transform ( HHT)
Detect the unwanted Camera Motion
The power of each IMF is proportional to the ampli-
tude of its sample.
Where αi – amplitude of a IMF’s
i = 1,2 ….. w+1
t – frame number
2
0
( )K
it
Pi t
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
18/22
Hilbert Huang Transform ( HHT)
Detect the unwanted Camera Motion
IMF with lower indices include high frequency com-
ponent (jitter)
From lower to higher IMFs , the energy content is re-
duced
After a certain IMF , a sharp increase of the energy
occur due to intentional camera motion
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
19/22
Hilbert Huang Transform ( HHT)
Detect the unwanted Camera Motion
IMF with higher index and lower energy content to
the last IMF which includes jitter components
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
20/22
Hilbert Huang Transform ( HHT)
Detect the unwanted Camera Motion
Jitter and intentional camera motion
where
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
21/22
1
( ) ( )d
J ii
X t c t
( ) ( )w
G i wi d
X t c t r
arg min[ ]id P
Experimental Results
2 2
1
1( ) ( )
N
rms n n n nn
e x x y yN
Where N is the number of frames
Optimal camera motion
Resulting camera motion,( )n nx y
( , )n nx y
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
22/22
Conclusion
DIS method based on HHT has been presented
Jitter signal is defined based on its two principle feature
High frequency
Low energy
Experimental results have proven that the proposed
method can successfully decompose two camera motions
• Introduction
• Proposed method in a Nutshell
• Local Motion Vector (LMV) Es-
timation
• Hilbert Huang Transform( HHT)
• Empirical Mode Decomposi-
tion (EMD) process
• Hilbert Transform
• Detect the unwanted Camera
Motion
• Experimental Results
• Conclusion
23/22
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