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