Respiratory Motion Estimation with Hybrid Implementation - Prediction and Classification of Respiratory Motion - page 74

Fig. 4.5 Hybrid motion estimation based on EKF (HEKF) for RNN. Each group is
corresponding to an individual channel that is composed of (x, y, z) position sequence with
respect to the time step k

X

n i

m i ¼ 1
n i

P i ð j Þ;

ð 4 : 12 Þ

j ¼ 1

where n i is the component number of group i. To obtain the optimization objective
function, we define the scatter values S i and S W by
S i ¼ X
P 2 P i

ð P m i Þ 2 ; ð 4 : 13 Þ

and

S W ¼ X

g

S k ; ð 4 : 14 Þ

k ¼ 1

where g is the number of group in the given samples. We define the between-class
scatter value S B as follows [ 56 ]:
S B ¼ X

g

X

g

2

m i m j ð i 6¼ j Þ; ð 4 : 15 Þ

i ¼ 1 j ¼ 1