Removing Camera Shake from a Single Photograph
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Removing Camera Shake from a Single Photograph
报告人:牟加俊 日期: 2013-12-13
In ACM SIGGRAPH, 2006.
Content
(1) Introduction Image Restoration
(2) Introduction the method in this paper
(3) Experiments
Image RestorationRestoration
客观过程 (an objective process)
“ 图像恢复”是根据某最优准则,使得恢复后的图像是对理想图像的最佳逼近。
WHAT?
Image blurs and PSF
Global blurs: camera shake
Local blurs: object moving
What ‘s motion blur?Motion blur results from relatively large motion between the
camera and the object. 相对运动
WHY?
Image blurs and PSF
Total exposure= (instantaneous exposure)
模糊图像=理想的局部积分
0 00( , ) ( ), ( )
Tg x y f x x t y y t dt
Point Spread Function:If the ideal image would consist of a single
intensity point or point source (x,y)=1, this point would be recorded as
a spread-out intensity pattern 。
THEN ?
Model of the Image Degradation
( , ) ( , ) ( , ) ( , ) g x y h x y f x y x y
( , ) ( , ) ( , ) ( , )G u v H u v F u v N u v
g Hf n
SO
Image Restoration
Blind image deconvolution ( BID 盲去卷积):在模糊核未知的条件下恢复出清晰的图像。Non-blind image deconvolution ( NBID 非盲去卷积): inverse filtering ( 逆滤波 ) 、 Wiener filtering
( 维纳滤波 ) 、 Richardson-Lucy 方法等。
Image restoration
Image deblurring
Image deconvolution
==
HOW?
Inverse Filtering
( , ) ( , ) ( , ) ( , )G u v H u v F u v N u v Ignore noise N(u,v)
( , ) ( , ) ( , )G u v H u v F u v( , )ˆ ( , )( , )
G u vF u vH u v
( , )( , )
N u vH u v
( , )( , )
N u vH u v
Drawback :
Wiener filtering
求 Wopt(u,v) 使得均方差 =min
Wiener filtering ( 维纳滤波 )= 最小均方差滤波( , ) ( , ) ( , ) ( , )G u v H u v F u v N u v
2ˆ( , ) ( , )
F u v F u v dudv
已知
Wiener 给出的解是 :2
2
| ( , ) || ( , ) | ( , ) / (
1(, )
, )( , )
of
ptH u v
H u v S u v SW u v
v uu vH
退化函数 噪声功率谱 理想图像功率谱
ˆ ( , ) ( , )G( , ) optF u v W u v u v*
2
( , ) ( , )( , )
( , ) | ( , ) | ( , )
fopt
f
H u v S u vW u v
S u v H u v S u v
Example
Inverse filtering Inverse filtering with cut-off frequency 70 Wiener filtering
Image model
B : blurred input image
K : blur kernel
L : latent image
N : sensor noise Two main steps:
1: estimate blur kernel;
2:deblur.
B K L N
estimate blur kernel
The distribution over gradient magnitudes
obey heavy-tailed distributions;
The distribution can be represented with
a zero mean mixture-of-Gaussians model
ONE CONTRIBUTION!!
estimate blur kernel
Given the grayscale blurred patch , estimate K and the latent patch
image
PLP
(K, | ) ( | , ) ( ) ( )P P Pp L P p P K L p L p K
2
1 1
( (i) | (K L (i)), )
( L (i) | 0, v ) (K | )
pi
C D
c p c d j dc di j
N P
N E
N and E denote Gaussian and Exponential distributions
respectively
estimate blur kernel
maximum a-posteriori (MAP) solution:finds the kernel
and latent image gradients that maximizes
KL (K, L | P)pp
THE SECOND CONTRIBUTION!!Using Miskin and MacKay's algorithm :
Minimizes the distance between the approximating
distribution and the true posterior.2(q(K, L , ) || p(K, L | P))p pKL
Multi-scale approach
perform estimation by varying image resolution in a
coarse-to-fine manner
Multi-scale approach
At last, reconstruct
the latent color image
L
with the Richardson-
Lucy (RL) algorithm
Experiments
Conclusion
There are many improvements spaces:
1) ringing artifacts occur near saturated regions and regions of
significant object motion.
2) There are a number of common photographic effects that we do not
explicitly model, including saturation, object motion, and compression artifacts.
3) this method requires some manual intervention.
Conclusion
Solution:
1) Make use of more advanced natural image statistics
2) applying modern statistical methods to the non-blind
deconvolution problem.
3) employing more exhaustive search procedures, or
heuristics to guess the relevant parameters
Thank you
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