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This approximate Gaussian smoothing in two dimensions is very fast.
Only eight addsubtract pairs are required per output point,
and no multiplies at all are required except for final scaling.
The compute time is independent of the widths of the Gaussian(!).
(You should understand this if you understood
that onedimensional convolution with a rectangle
requires just one addsubtract pair per output point.)
Thus this technique should be useful in
twodimensional slant stack.
EXERCISES:

Deduce that a 2D filter based on the subroutine
triangle()
which produces the 2D quasiGaussian mound in
Figure 12
has a gain of unity at zero (twodimensional) frequency
(also known as (k_{x},k_{y})=0).

Let the 2D quasiGaussian filter be known as F.
Sketch the spectral response of F.

Sketch the spectral response of 1F and suggest a use for it.

The tent filter can be implemented by smoothing first on the 1axis
and then on the 2axis.
The conjugate operator smooths first on the 2axis
and then on the 1axis.
The tentfilter operator should be selfadjoint
(equal to its conjugate),
unless some complication arises at the sides or corners.
How can a dotproduct test be used to see
if a tentfilter program is selfadjoint?
Next: PROBABILITY AND CONVOLUTION
Up: SMOOTHING IN TWO DIMENSIONS
Previous: Gaussian mounds
Stanford Exploration Project
10/21/1998