1 Removing Camera Shake from a Single Photograph Rob Fergus, Barun Singh, Aaron Hertzmann, Sam T. Roweis and William T. Freeman ACM SIGGRAPH 2006, Boston, USA

2 Outline Overview Proposed method for camera shake removing Simulation results

3 Image blur due to camera shake Desired imageDegraded image

4 Image formation process =  Blurry imageSharp imageBlur kernel Input to algorithm Desired output Convolution operator + Gaussian noise

5 Image formation process A linear imaging model is assumed in this paper, that is: Prior for blur kernel Prior for image Observation model

6 Prior model for nature image (1) Characteristic distribution of sharp image with heavy tails Histogram of image gradient

7 Prior model for nature image (2) Use parametric model for sharp image statistics

8 Prior model for blur kernel (1) The characteristics of blur kernel are positive and sparse =  Blurry image Sharp image Blur kernel

9 Prior model for blur kernel (2) Assume the probability distribution of the element of blur kernel is the mixture of exponential distributions Exponential distribution

10 Model transformation The imaging model need to be transformed before we using the image gradient prior, that is:

11 Variational Baye (1) Illustration for Bayesian mean squared error estimator (Minimum mean squared error estimator, MMSE) Ө1Ө1 Ө2Ө2 Ө3Ө3 Process Parameter space Ө d Observed data

12 Variational Baye (2) Apply MMSE estimator for blur kernel estimation It may be difficult to find the integration result of the posterior probability

13 Variational Baye (3) Factorize the previous posterior probability for blur kernel inference operation

14 Variational Baye (4) The factorization of the posterior probability could be modeled as an optimization problem

15 Original photograph

16 Blur kernel Proposed method

17 Original photograph Matlab’s deconvblind

18 Original photograph

19 Matlab’s deconvblind

20 Proposed method Blur kernel

21 Original photograph

22 Proposed method Blur kernel

23 Original photographProposed method