Path: utzoo!utgpu!water!watmath!clyde!att!osu-cis!tut.cis.ohio-state.edu!mailrus!husc6!bbn!mit-eddie!mit-amt!turk
From: turk@mit-amt (Matthew Turk)
Newsgroups: comp.graphics
Subject: Re: Image Processing question
Summary: gaussian pyramid interpolation
Message-ID: <3179@mit-amt>
Date: 18 Oct 88 15:49:52 GMT
References: <26451@ucbvax.BERKELEY.EDU>
Organization: MIT Media Lab, Cambridge, MA
Lines: 32

In article <26451@ucbvax.BERKELEY.EDU>, nick@marvax.berkeley.edu (nicholas socci) writes:
> I have simple (I hope) image processing problem.  I am given an image
> with say 32x32 pixels (8 bits) and want to magnify the image to say
> 512x512. (Actually i need to go from MxN --> M1xN1).
> 
> I would like to know if there are any good algorithms out there to do
> this. NOTE linear interpolation is not good enough. It was suggested to
> me that I fourier transform the image and then use the transform to
> interpolate. 

This simplest way I know of doing this is described by Burt and Adelson
in April 1983 IEEE Trans. on Communications (p.534).  They give a
simple algorithm for expanding a pyramid level, which basically
preserves the band-limited spatial frequency characteristics of the
image.  In a nutshell, here it is:

	I'old - (M+1)by(N+1)
	I'new - (2M+1)by(2N+1)

                        2    2
	I'new(i,j) = 4 Sum  Sum  w(m,n) I'old( (i-m)/2, (j-n)/2 )
                       m=-2 n=-2

	where w(m,n) is the 5x5 array whose 1D separable component
	  is (0.05 0.25 0.4 0.25 0.05)
	and only terms for which (i-m)/2 and (j-n)/2 are integers
	  are included in the sum.

You could use a larger filter, but this 5x5 one is pretty good and 
rather quick.

	Matthew Turk