Savitzky - Golay filter for 2D Matrices The Next CEO of Stack OverflowLaplacian of gaussian filter useGaussian filter in MATLABsuper resolution of low resolution images using delaunay triangulation, negative pixel values for the resultant High resolution imageWhat is exact difference between mean filter and median filterMode filter for large matricesAlgorithm to group sets of points together that follow a directionSavitzky golay filter errorSavitzky-Golay filtering for large data setHow to use uncertainties to weight residuals in a Savitzky-Golay filter.Zero padding for Savitzgy Golay filter not working for C++ numerical recipe
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Savitzky - Golay filter for 2D Matrices
The Next CEO of Stack OverflowLaplacian of gaussian filter useGaussian filter in MATLABsuper resolution of low resolution images using delaunay triangulation, negative pixel values for the resultant High resolution imageWhat is exact difference between mean filter and median filterMode filter for large matricesAlgorithm to group sets of points together that follow a directionSavitzky golay filter errorSavitzky-Golay filtering for large data setHow to use uncertainties to weight residuals in a Savitzky-Golay filter.Zero padding for Savitzgy Golay filter not working for C++ numerical recipe
i am doing some research about implementing a Savitzky-Golay filter for images. As far as i have read, the main application for this filter is signal processing, e.g. for smoothing audio-files.
The idea is fitting a polynomial through a defined neighbourhood around point P(i) and setting this point P to his new value P_new(i) = polynomial(i).
The problem in 2D-space is - in my opinion - that there is not only one direction to do the fitting. You can use different "directions" to find a polynomial. Like for
[51 52 11 33 34]
[41 42 12 24 01]
[01 02 PP 03 04]
[21 23 13 43 44]
[31 32 14 53 54]
It could be:
[01 02 PP 03 04], (horizontal)
[11 12 PP 23 24], (vertical)
[51 42 PP 43 54], (diagonal)
[41 42 PP 43 44], (semi-diagonal?)
but also
[41 02 PP 03 44], (semi-diagonal as well)
(see my illustration)
So my question is: Does the Savitzky-Golay filter even make sense for 2D-space, and if yes, is there and any defined generalized form for this filter for higher dimensions and larger filter masks?
Thank you !
image-processing filtering numerical-methods
asked Mar 7 at 16:41
dog fishdog fish
413
add a comment |
i am doing some research about implementing a Savitzky-Golay filter for images. As far as i have read, the main application for this filter is signal processing, e.g. for smoothing audio-files.
The idea is fitting a polynomial through a defined neighbourhood around point P(i) and setting this point P to his new value P_new(i) = polynomial(i).
The problem in 2D-space is - in my opinion - that there is not only one direction to do the fitting. You can use different "directions" to find a polynomial. Like for
[51 52 11 33 34]
[41 42 12 24 01]
[01 02 PP 03 04]
[21 23 13 43 44]
[31 32 14 53 54]
It could be:
[01 02 PP 03 04], (horizontal)
[11 12 PP 23 24], (vertical)
[51 42 PP 43 54], (diagonal)
[41 42 PP 43 44], (semi-diagonal?)
but also
[41 02 PP 03 44], (semi-diagonal as well)
(see my illustration)
So my question is: Does the Savitzky-Golay filter even make sense for 2D-space, and if yes, is there and any defined generalized form for this filter for higher dimensions and larger filter masks?
Thank you !
image-processing filtering numerical-methods
asked Mar 7 at 16:41
dog fishdog fish
413
add a comment |
i am doing some research about implementing a Savitzky-Golay filter for images. As far as i have read, the main application for this filter is signal processing, e.g. for smoothing audio-files.
The idea is fitting a polynomial through a defined neighbourhood around point P(i) and setting this point P to his new value P_new(i) = polynomial(i).
The problem in 2D-space is - in my opinion - that there is not only one direction to do the fitting. You can use different "directions" to find a polynomial. Like for
[51 52 11 33 34]
[41 42 12 24 01]
[01 02 PP 03 04]
[21 23 13 43 44]
[31 32 14 53 54]
It could be:
[01 02 PP 03 04], (horizontal)
[11 12 PP 23 24], (vertical)
[51 42 PP 43 54], (diagonal)
[41 42 PP 43 44], (semi-diagonal?)
but also
[41 02 PP 03 44], (semi-diagonal as well)
(see my illustration)
So my question is: Does the Savitzky-Golay filter even make sense for 2D-space, and if yes, is there and any defined generalized form for this filter for higher dimensions and larger filter masks?
Thank you !
image-processing filtering numerical-methods
asked Mar 7 at 16:41
dog fishdog fish
413
i am doing some research about implementing a Savitzky-Golay filter for images. As far as i have read, the main application for this filter is signal processing, e.g. for smoothing audio-files.
The idea is fitting a polynomial through a defined neighbourhood around point P(i) and setting this point P to his new value P_new(i) = polynomial(i).
The problem in 2D-space is - in my opinion - that there is not only one direction to do the fitting. You can use different "directions" to find a polynomial. Like for
[51 52 11 33 34]
[41 42 12 24 01]
[01 02 PP 03 04]
[21 23 13 43 44]
[31 32 14 53 54]
It could be:
[01 02 PP 03 04], (horizontal)
[11 12 PP 23 24], (vertical)
[51 42 PP 43 54], (diagonal)
[41 42 PP 43 44], (semi-diagonal?)
but also
[41 02 PP 03 44], (semi-diagonal as well)
(see my illustration)
So my question is: Does the Savitzky-Golay filter even make sense for 2D-space, and if yes, is there and any defined generalized form for this filter for higher dimensions and larger filter masks?
Thank you !
image-processing filtering numerical-methods
image-processing filtering numerical-methods
asked Mar 7 at 16:41
dog fishdog fish
413
asked Mar 7 at 16:41
dog fishdog fish
413
asked Mar 7 at 16:41
dog fishdog fish
413
asked Mar 7 at 16:41
dog fishdog fish
413
asked Mar 7 at 16:41
dog fishdog fish
413
413
add a comment |
add a comment |
1 Answer
1
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A first option is to use SG filtering in a separable way, i.e. filtering once on the horizontal rows, then a second time on the vertical rows.
A second option is to rewrite the equations with a bivariate polynomial (bicubic f.i.) and solve for the coefficients by least-squares.
answered Mar 7 at 16:56
Yves DaoustYves Daoust
38.3k72760
add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
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oldest
votes
active
oldest
votes
A first option is to use SG filtering in a separable way, i.e. filtering once on the horizontal rows, then a second time on the vertical rows.
A second option is to rewrite the equations with a bivariate polynomial (bicubic f.i.) and solve for the coefficients by least-squares.
answered Mar 7 at 16:56
Yves DaoustYves Daoust
38.3k72760
add a comment |
A first option is to use SG filtering in a separable way, i.e. filtering once on the horizontal rows, then a second time on the vertical rows.
A second option is to rewrite the equations with a bivariate polynomial (bicubic f.i.) and solve for the coefficients by least-squares.
answered Mar 7 at 16:56
Yves DaoustYves Daoust
38.3k72760
add a comment |
A first option is to use SG filtering in a separable way, i.e. filtering once on the horizontal rows, then a second time on the vertical rows.
A second option is to rewrite the equations with a bivariate polynomial (bicubic f.i.) and solve for the coefficients by least-squares.
answered Mar 7 at 16:56
Yves DaoustYves Daoust
38.3k72760
A first option is to use SG filtering in a separable way, i.e. filtering once on the horizontal rows, then a second time on the vertical rows.
A second option is to rewrite the equations with a bivariate polynomial (bicubic f.i.) and solve for the coefficients by least-squares.
answered Mar 7 at 16:56
Yves DaoustYves Daoust
38.3k72760
answered Mar 7 at 16:56
Yves DaoustYves Daoust
38.3k72760
answered Mar 7 at 16:56
Yves DaoustYves Daoust
38.3k72760
answered Mar 7 at 16:56
Yves DaoustYves Daoust
38.3k72760
38.3k72760
add a comment |
add a comment |
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