why is an image non-stationary?

Gordon Sande <g.sande@worldnet.att.net> wrote 

> Position invariance would mean that a seascape would have the same
> properties as an urban image. If you think not then you have given
> up the Fourier assumptions. The things folks will agree on tend to
> suggest Haar analysis or perhaps wavelets.

I actually think it's a little different from the way you say it.  I
don't think it's that the stationarity problem occurs between
different images, it's that the statistics of an image change _within_
a given image.

For example, the pixel values of the sea in a seascape would have
different mean and standard deviation from the pixel values of the
beach in the same seascape.

That's why images can be thought of as non-stationary.

For what it's worth, I really don't think that stationarity says
anything about whether the Fourier transform can or can't be used.  Of
course it can be used; how you interpret it might be a problem, but
many non-stationary problems (e.g. speech, sonar) have used the
Fourier transform to good effect.

Ciao,

Peter K.