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