Errata for Dr. Gopal Surya's Thesis:

1.  In Eq. 4.11 on page 47,  h20 and h02 should be replaced
    by  h20/2 and h02/2 based on Eq. 4.8 on page 46.

 2.  When the PSF is a Gaussian as in Eq. 6.6 on page 122,
 the thesis says that the blur parameter is the same as the Gausssian
 parameter sigma (standard deviation or std of the Gaussian distribution).
 This is wrong. Instead of sigma, we should have used a different symbol to denote the
 Gaussian parameter as std.  The relation between the
 blur parameter  sigma defined in Eq. 6.3 and the Gaussian std parameter is
 sigma2 = 2 (std)2. This error and confusion occurs only for the case of
 the Gaussian PSF.  This error  happened as
 we were a little careless when we first derived the S-transform for the 1-dimensional
 case and then generalized it to the 2D case. For the 1D case,
 you get sigma2 = (std)2. But for the 2D case, it is sigma2 = 2 (std)2.

 However, what  we can assure you is that the more important relation that
 the blur parameter sigma = R/sqrt(2) is correct where R is the radius of the
 blur circle according to geometric optics model of image formation.
 Therefore, other derivations in the thesis such as Eqs. 2.15 to 2.17 on page 14
 and other subsequent derivations are correct. We want our blur parameter
 sigma to be the "square root of the second central moment as defined by Eq. 6.3"
 ( actually, to be more precise, x should be replaced by (x-h10) and y by (y-h01),
 but for circularly symmetric PSFs,  h10=h01=0).

 In summary, please take Eq. (6.3) to be a definition and therefore correct,
 and also Eq. 6.5 and Eq. 4.22  are correct as all the derivation steps are
 correct (after correcting Eq. 4.11).
 But,  in the case of a Gaussian PSF, please take sigma2 =  2 (std)2.


We regret any inconvenience caused by these errors and mistakes.


 Thank you.
 Murali Subbarao and the CVL group