🚀 go-pugleaf

I am having difficulty reconciling two separate resources'
treatment of image correlation models.  My two references
are "Digital Pictures: Representation and Compression"
by Netravali and Haskell  (c. 1988) and "Information Preserving
Image Compression for Archiving NMR Images" from Computerized Medical
Imaging and Graphics vol 15 no 4 (c. 1991).

Digital Pictures defines the image autocorrelation function

R(x,y) = E(b b')   where the distance between pixels b and b' 
                   horizontally is x and vertically is y.  

Then the normalized autocovariance function is defined 

rho(x,y) = R(x,y) - E(b)^2
           ---------------
           E(b^2) - E(b)^2    <----- var(b)       

The NMR article defines the correlation coefficient between pels as

rho(x,y) = E(b_ij b_i-x,j-y) 
           -----------------
              E(b^2)

which is not the same.  I cannot figure out why one model
subtracts the square of the first moment from numerator and
denominator and the other does not.  My reason for wanting
to understand the model is that I am trying to determine 
correlation coefficients for DPCM coding using 2d linear 
adaptive prediction.

If anyone can help me, I would appreciate it.
Please send email if possible.      

Thanks,
Susan
--
Susan E. Margulies       
HP Imaging Systems         
susanm@hp-and.an.hp.com