Removing motion blur from a single image

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

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

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

11. De-blur using Convolution Theorem Convolution Theorem:

12. Recovered Example: Blurred Image PSF

13. Deconvolution is unstable Example: Noisy case:

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

15. 51 151 191 Regularizing by window Window size: