Respect for Tissue Representation Using Photoelastic Stress Analysis for Endovascular Surgery Simulation - Microsurgery: Advances, Simulations, and Applications - page 153

recognition, and catheter tip detection in the XY-plane and the XZ-
plane cameras. A point belonging to a source trajectory is deined
as

T T

Lccc

, (,

, , , G , , G ) (4.44)

ik x y z XY XY XZ XZ

where c x , c y , and c z are the catheter tip locations,

T XY and T XZ are the
stress levels, and G XY and G XZ are the deformation levels at frame k
for the source trajectory i . These parameters are calculated from the
video frames L XY,i,k and L XZ,i,k . In this study, ive source trajectories ( L 1 -
L 5 ) between the start point and the target were registered; they have
different duration and include the rotation of the catheter to select
the target branch. They were built using a standard 5F catheter.
Let us name T Li the amount of frames captured between the
catheter tip detection at the start point until it reaches the target for
trajectory L i . To be compared, these trajectories must be normalized
in time; the normalized frame rate for each trajectory is obtained
from the inverse of T Li and named SR Li . And for all trajectories to be
represented at least with a point during a reference trajectory point
construction, the reference trajectory normalized frame rate SR R is
obtained from

I

2

SR

Li

i 1

SR (4.44)

R

I

where I is the number of studied trajectories. The number of points
composing the reference trajectory T R is given by rounding to the
next natural number the inverse of SR R . The reference trajectory is
constructed using the following equation:

T T

Rcc c (, , , , G , , G )

n x y z XY XY XZ XZ

¤

t

¤

5

n

(4.45)

T T

Lccc (, , , , G , , G )

i t , xyz Y Y Y Y

tt i 1

n 1

p

n

where n is reference trajectory frame number (between zero and
the number of frames of the reference trajectory T R ) that occurs
at normalized time t n , and p n is the number of points belonging
to L i occurring after t n- 1 and before t n . Figures 4.28-4.30 show the
variation in normalized time for the components of the trajectories
L 1 - L 5 and the resulting reference trajectory R obtained by applying
equation (4.45) to these components.