Forums

About Notch Filtering in the Frequency Domain (2D images)

Started by Javier Montoya May 17, 2007
Dear all:

I was studying the notch filter. As far as I understood, there are 2
possible ways to accomplish this task:
1) Set the DC component of the spectrum to be equal to zero, i.e:
F(0,0) =0. To obtain the filtered image, apply the IDFT.
2) Create a kernel (k) having the same size as the filtered image. Set
all the kernel values equal to 1, except for the pixel in position (M/
2,N/2), which will be equal to 0. Note that M,N represent respectively
the width and height of the filtered image. Compute the DFT of the
kernel (k) obtaining a kernel K in the frequency domain. Convolve the
spectrum with the kernel K in the frequency domain, and apply the IDFT
to the convolved image in order to obtain the filtered image in the
spacial domain.

I would like to know, if those 2 operations are equivalent, because
the obtained filtered images in method 1, and 2 differ from each
other.

Best regards,

Javier

--
=================================================
Javier A. Montoya Zegarra - http://www.lis.ic.unicamp.br/~jmontoya
Institute of Computing, State University of Campinas, SP - Brazil
=================================================

"Set all Afire" - St. Ignatius of Loyola

On 17 May, 17:04, Javier Montoya <jmonto...@gmail.com> wrote:
> Dear all: > > I was studying the notch filter. As far as I understood, there are 2 > possible ways to accomplish this task: > 1) Set the DC component of the spectrum to be equal to zero, i.e: > F(0,0) =0. To obtain the filtered image, apply the IDFT. > 2) Create a kernel (k) having the same size as the filtered image. Set > all the kernel values equal to 1, except for the pixel in position (M/ > 2,N/2), which will be equal to 0. Note that M,N represent respectively > the width and height of the filtered image. Compute the DFT of the > kernel (k) obtaining a kernel K in the frequency domain. Convolve the > spectrum with the kernel K in the frequency domain, and apply the IDFT > to the convolved image in order to obtain the filtered image in the > spacial domain. > > I would like to know, if those 2 operations are equivalent, because > the obtained filtered images in method 1, and 2 differ from each > other.
Formally, they are equivalent, except for wrap-around effects. If, for the sake of argument, your image is of size 2N+1 x 2N+1, then the resulting image after convolition (your approach #2) is of size 4N+1 x 4N+1. Your approach #1 is formally equal to your approach #2 PROVIDED both the image and the mask, which are of size 2N+1 x 2N+1, are zero-padded to size 4N+1 x 4N+1 prior to computing the 2D DFTs. Since you haven't done that, the "overshoot" wraps around the edges and start messing up your image. Rune
Please tell me you would not do 1) in this way!

Dirk

On May 17, 11:04 am, Javier Montoya <jmonto...@gmail.com> wrote:
> Dear all: > > I was studying the notch filter. As far as I understood, there are 2 > possible ways to accomplish this task: > 1) Set the DC component of the spectrum to be equal to zero, i.e: > F(0,0) =0. To obtain the filtered image, apply the IDFT.
<xnipped>
> Javier > > -- > ================================================= > Javier A. Montoya Zegarra -http://www.lis.ic.unicamp.br/~jmontoya > Institute of Computing, State University of Campinas, SP - Brazil > ================================================= > > "Set all Afire" - St. Ignatius of Loyola