Real-time video deblurring
A method of reducing blurring in an image of size greater than M columns by N rows of pixels, comprises deriving a blur kernel k representing the blur in the image, and deriving an inverse blur kernel k −1 . The inverse blur kernel is given by (I) where h(m) is the sum of the first m terms of the series (II) δ is the Dirac delta, m is greater than 1, and h(m) is a two dimensional matrix of size M×N. The two dimensional matrix h(m) is convolved with the image over the whole image in the image pixel domain to produce an image with reduced blur. The method may be applied to a video sequence allowing the sequence of images to be deblurred in real time.
1. A method of reducing blurring in an image of size greater than M columns by N rows of pixels, comprising
deriving a blur kernel k representing the blur in the image,
deriving an inverse blur kernel k −1 where
k
-
1
=
h
(
m
)
=
∑
n
=
0
m
(
δ
-
k
)
n
where h(m) is the sum of the first m terms of the series
∑
n
=
0
m
(
∂
-
k
)
n
δ is the Dirac delta, 2<m<20, and h(m) is a two dimensional matrix of size M×N, and
convolving the two dimensional matrix h(m) over the whole image in the image spatial domain to produce an image with reduced blur.
2. A method according to claim 1 , wherein the matrix is convolved with the image as two one dimensional matrices.
3. A method according to claim 1 , wherein m=3 and h( 3 )=4δ−6k+4k 2 −k 3 .
4. A method according to claim 1 , comprising:
reducing blurring of a video sequence of images, each of size greater than M×N; and
convolving each image with the said two dimensional matrix h(m) in the image spatial domain.
5. A method according to claim 1 , further comprising applying a spatial filter to the image to reduce spatial noise in the image prior to convolving the image with the said matrix h(m).
6. A method according to claim 1 , further comprising applying a temporal filter to the image to reduce temporal noise in the image after convolving the image with the said matrix h(m).
7. A method according to claim 1 , comprising:
reducing blurring of a video sequence; and
applying a temporal filter to images in the sequence image to reduce temporal noise in the images prior to convolving the images with the said matrix h(m).
8. A method according to claim 1 , wherein the blur kernel is derived from a single image.
9. A system for reducing blur in an image of size greater than M columns by N rows of pixels, comprising a convolution processor arranged to convolve the image with a two dimensional matrix h(m) over the whole image in the image spatial domain to produce an image with reduced blur,
wherein the matrix h(m) is derived from a blur kernel k representing the blur in the image as an inverse blur kernel k −1 where
k
-
1
=
h
(
m
)
=
∑
n
=
0
m
(
δ
-
k
)
n
where h(m) is the sum of the first m terms of the series
∑
n
=
0
m
(
∂
-
k
)
n
,
δ is the Dirac delta, m is greater than 1, and h(m) is a two dimensional matrix of size M×N.
10. A system according to claim 9 , further comprising a spatial filter arranged to reduce spatial noise in the image prior to convolving the image with the said matrix h(m).
11. A system according to claim 9 , further comprising a temporal filter arranged to reduce temporal noise in the image after convolving the image with the said matrix h(m).
12. A system according to claim 9 , wherein the convolution processor comprises a graphics processor.
13. A system according to claim 9 , reducing blur in a video sequence and, further comprising a temporal filter arranged to reduce temporal noise in the sequence prior to convolving the sequence with the said matrix h(m).
14. A non-transitory computer readable medium including machine readable instructions that when executed by a processor reduce blurring in an image of size greater than M columns by N rows of pixels, wherein the instructions comprise instructions to:
derive a blur kernel k representing the blur in the image,
deriving an inverse blur kernel k −1 where
k
-
1
=
h
(
m
)
=
∑
n
=
0
m
(
δ
-
k
)
n
where h(m) is the sum of the first m terms of the series
∑
n
=
0
m
(
∂
-
k
)
n
δ is the Dirac delta, 2≦m≦20, and h(m) is a two dimensional matrix of size M×N; and
convolve the two dimensional matrix h(m) over the whole image in the image spatial domain to produce an image with reduced blur.
15. A non-transitory computer readable medium according to claim 14 , wherein the matrix is convolved with the image as two one dimensional matrices.