CODEWITHSUNDEEP
image-processingfilteringnumerical-methods
beinando
beinando

Reputation: 497

Savitzky - Golay filter for 2D Matrices

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)

1D-Neighbourhoods in a 2D Space

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 !

Upvotes: 0

Views: 1058

Answers (1)

user1196549
user1196549

Reputation:

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.

Upvotes: 1

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