pgaussianfilter

Synopsis

Description

pgaussianfilter designs either a lowpass, highpass, bandpass or bandreject Gaussian filter. If ndep<2 the filter im_out is a 2D float image with size nrow*ncol otherwise the filter im_out is a 3D float image with size ndep*nrow*ncol.

The Gaussian lowpass filter cuts off high-frequency components of the Fourier transform that are at a distance greater than a specified distance D0 (the cutoff value) from the origin of the centered transform.

The transfer function for a 2D Gaussian lowpass filter and with cutoff frequency at distance D0 from the origin is defined as:

   Hlp(u,v) = exp(-D2(u,v)/2D02)

where D(u,v) is the distance of point (u,v) from the origin:

   D(u,v)=sqrt((u-M/2)2 + (v-N/2)2)

where N the number of rows and M the number of columns.

The transfert function for a Gaussian highpass is defined as:

   H(u,v) =  1- Hlp(u,v)

The transfer function for a band reject is:

   H(u,v) = Hhp(u,v) - Hlp(u,v)

where Hhp(u,v) is the highpass filter with cutoff parameter and Hlp(u,v) is the lowpass filter with cutin parameter.

Parameters

• ncol, nrow, ndep specify the size of the output image. If ndep<1 then the output image im_out is a 2D image otherwise a 3D image.
• highpass is used in conjunction with the cutin parameter. It specifies the type fo the filter:
  • highpass=0 and cutin=0 : lowpass filter
  • highpass=1 and cutin=0 : highpass filter
  • highpass=0 and cutin=1 : bandreject filter
  • highpass=1 and cutin=1 : bandpass filter
• cutin is the cut in frequency of the filter D0 in case of bandreject or bandpass filter. In this case, the band width=cutoff-cutin and D0=(cutoff+cutin)/2.
• cutoff is the cutoff frequency of the filter D0. It must be a positive real value in the interval ] 0.. sqrt(M*m+N*n)/2]. It corresponds to an euclidean distance from the center of the image. The higher cutoff is, the lower is the lowpass or the higher is the highpass.

Outputs

• im_out: a float 2D image (Img2dsf).

Result

Returns SUCCESS or FAILURE in case of bad parameter values.

Examples

Performs Gaussian lowpass filtering:

   psetcst 0 tangram.pan i1.pan
   pfft tangram.pan i1.pan i2.pan i3.pan
   pgaussianfilter 256 256 0 0 0 100 i4.pan
   pmult i2.pan i4.pan i5.pan
   pmult i3.pan i4.pan i6.pan
   pifft i5.pan i6.pan out.pan i8.pan

Performs Gaussian highpass filtering:

   psetcst 0 tangram.pan i1.pan
   pfft tangram.pan i1.pan i2.pan i3.pan
   pgaussianfilter 256 256 0 1 0 50 i4.pan
   pmult i2.pan i4.pan i5.pan
   pmult i3.pan i4.pan i6.pan
   pifft i5.pan i6.pan out.pan i8.pan

   psetcst 0 tangram.pan i1.pan
   pfft tangram.pan i1.pan i2.pan i3.pan
   pgaussianfilter 256 256 0 0 25 50 i4.pan
   pmult i2.pan i4.pan i5.pan
   pmult i3.pan i4.pan i6.pan
   pifft i5.pan i6.pan out.pan i8.pan

   psetcst 0 tangram.pan i1.pan
   pfft tangram.pan i1.pan i2.pan i3.pan
   pgaussianfilter 256 256 0 1 25 50 i4.pan
   pmult i2.pan i4.pan i5.pan
   pmult i3.pan i4.pan i6.pan
   pifft i5.pan i6.pan out.pan i8.pan