Removing motion blur Removing motion blur from a single imagefrom a single image

Sources of blurSources of blur

• Object motion

Sources of blurSources of blur

• Object motion

• Translation of camera

Sources of blurSources of blur

• Object motion

• Translation of camera

• Rotation of camera

• Defocus

• Internal camera distortions

Sources of blurSources of blur

• Object motion

• Translation of camera

• Rotation of camera

Point Spread Function (PSF)Point Spread Function (PSF)

Assume:• Point light source

PSFPSF ==

Convolution model motivationConvolution model motivation• Assume:

– No image plane rotation– No object motion during the exposure– No significant parallax (depth variation)

• Violation of assumption:

Camera motion isCamera motion is

Pure Translation!!!Pure Translation!!!

Convolution model motivationConvolution model motivation• Assume:

– No image plane rotation– No object motion during the exposure– No significant parallax (depth variation)

Camera motion isCamera motion is

Pure Translation!!!Pure Translation!!!

Close-up of dots

8 subjects handholding DSLR with 1 sec exposure

• Experimental validation:

Convolution ModelConvolution Model• Notations

– L: original image

– K: the blur kernel (PSF)

– N: sensor noise (white)

– BB: input blurred image

Generation rule: B B = K L + N

+

How can the image be How can the image be recovered?recovered?

Assumptions:• Known kernel (PSF)• Constant kernel for the

whole image• No noise

Goal:• Recover L s.t.:

Fourier Fourier Convolution Convolution Theorem!Theorem!

B B = K L

De-blur using Convolution De-blur using Convolution Theorem Theorem

B KL KB L

/BL K

Convolution Theorem: f g f g

1 /BL K

LB K

Example:Example:

PSFPSF BlurredBlurredImageImage

RecoveredRecovered

Noisy case:Noisy case:

1 /BL K

Example:Example: 0, 0.001

DeconvolutionDeconvolutionis unstableis unstable

1 / /K KL B N

1D 1D example:example:

Regularization is requiredRegularization is required

Original signalOriginal signalFT of original signalFT of original signal

Convolved signals w/w noiseConvolved signals w/w noiseFT of convolved signalsFT of convolved signals

Reconstructed FT of the Reconstructed FT of the signalsignal

RegularizinRegularizing g by window by window

Window size:

51 151 191