1. Removing motion blur from a single image

2. Sources of blur
Object motion

3. Sources of blur
Object motion
Translation of camera

4. Sources of blur
Object motion
Translation of camera
Rotation of camera

5. Sources of blur Object motion Translation of camera Rotation of camera
Defocus
Internal camera distortions

6. Point Spread Function (PSF)
Assume:
Point light source
PSF =

7. Convolution model motivation
B = K  L + N
Convolution model motivation
Assume:
No image plane rotation
No object motion during the exposure
No significant parallax (depth variation)
Camera motion is
Pure Translation!!!
Violation of assumption:

8. Convolution model motivation
B = K  L + N
Convolution model motivation
Assume:
No image plane rotation
No object motion during the exposure
No significant parallax (depth variation)
Camera motion is
Pure Translation!!!
Experimental validation:
8 subjects handholding DSLR
with 1 sec exposure
Close-up of dots

9. Convolution Model  + Notations Generation rule: B = K  L + N
L: original image
K: the blur kernel (PSF)
N: sensor noise (white)
B: input blurred image  +
Generation rule: B = K  L + N

10. How can the image be recovered?
Assumptions:
Known kernel (PSF)
Constant kernel for the whole image
No noise
Goal:
Recover L s.t.:
B = K  L
Fourier Convolution Theorem!

11. De-blur using Convolution Theorem

12. Example:
PSF
Blurred
Image
Recovered

13. Noisy case:
Example:
Deconvolution
is unstable

14. Regularization is required
1D example:
FT of original signal
Original signal
Reconstructed FT of the signal
Convolved signals w/w noise
FT of convolved signals
Regularization is required

15. Regularizing by window
Window size: 51
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