Appeal No. 1999-2069
Application 08/397,639
step vi) of carrying out the affine transformation. An "affine
transformation" is a special transformation that involves only
rotation, scaling, and translation, and does not contain any
terms greater than first order (e.g., x 2) or any cross-product
terms (e.g., xy). For example, to translate a point (x,y) to a
new point (u,v) by a combination of rotation, translation, and
scaling, an affine transformation has the general form:
u = ax + by + e
v = cx + dy + f
The "nonlinear warping transformation" of Kano (col. 12,
lines 18-24; note that "i)0" should be "i=0") includes the terms
above in addition to other terms and does not put any limitations
on the terms a, b, c, and d.2 Kano involves a more complex
transformation than an affine transformation and can correct for
greater distortion. Kano discloses that there are many sources
of misregistration between image pairs due to movements of the
2 An affine transformation constrains a=S xcos2, b=-Sxsin2,
c=Sysin2, d=Sycos2, where Sx and Sy are scaling factors in the x
and y direction, respectively. This means that the values of a,
b, c, and d are not completely independent. Therefore, the
Examiner's statement that "equation 4 of [sic, unnumbered
equations at col. 12, lines 18-24] Kano et al. not only provides
for the translation term 'a1' and the two first order terms that
belong to the affine transformation, but also for higher terms as
well for 'accuracy'" (EA11), is not strictly correct. The
nonlinear transformation in Kano is of the form "u = ax + by + e
+ cross-product and higher order terms, "v = cx + dy + f +
cross-product and higher order terms," but the coefficients a, b,
c, and d do not necessarily define an affine transformation.
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