Volume 2, Algorithms - mipav - National Institutes of Health

M I P A V
M e d i c a l I m a g e P r o c e s s i n g, A n a l y s i s, & V i s u a l i z a t i o n
Chapter 2, Using MIPAV Algorithms: B-Spline Automatic Registration
for coordinate k. If the problem is to register images of three dimensions,
and the B-spline bases for all three dimensions are selected to have degree 1,
then
EQUATION 11
B i0 , i 1
, i 2
=
⎛i ----- 0
----- i 1
i 2⎞
⎜ , , ----- ⎟
⎝n 0
n 1
n 2 ⎠
For a B-spline basis of degree 2 or larger, the initial placement of the control
point coordinates is computed by the method of least squares. Again
referring to Equation 1 for the definition of the B-spline mapping function,
the identity map for coordinate k is
n k
j k
⎛ j k ⎞
-------------- = N
p ∑ ik , d
⎜--------------
⎟ Bik
k – 1
k ⎝p k – 1 ⎠
i k
= 0
for any target image coordinate j k satisfying 0