Image Processing Reference
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Fig. 2.
The spectral matching algorithm. After preterm-specific segmentation, meshes
are defined for the 30 and 40 week timepoints. After Coherent Point Drift initialisation,
a mesh correspondence is defined by Joint-Spectral Matching (spectral matching colour-
coded anterior-posterior).
matching technique is important for data of this type due to the longitudinal
nature of the change being measured. The algorithm is summarised in Figure
2
.
Application of this technique also allows us to find correspondence between
all the 30w meshes in order to carry out a group analysis of cortical change in
this preterm period.
Measurement of Longitudinal Development.
To quantify the early cor-
tical folding we computed the principal curvatures
ʺ
1
and
ʺ
2
for each vertex
of the surface mesh from which we derived the mean and Gaussian curvatures,
M
=
1
2
(
ʺ
1
+
ʺ
2
)and
G
=
ʺ
1
ʺ
2
, respectively. Because of the uniqueness of
the application, we decided to choose well-known measures of curvature for the
measurement of longitudinal change in each individual.
Additionally, we computed the bending energy (
E
)[
15
], which is intuitively
dependent on the local surface area change. The change in the bending energy,
over time and over area, describes the energy needed to deform that area over the
corresponding period of time, thus providing information about the mechanical
properties of the underlying tissue:
∂E
∂t
∂
∂t
(
ʺ
1
2
+
ʺ
2
2
)
dA
=
(1)
To investigate the longitudinal development of the prefrontal cortex for each
subject, we mapped the 40 week PFC to the 30 week PFC using the JSM and
computed the change of the surface parameters at each vertex of the mesh.
The longitudinal change in all the parameters (
M
,
G
,
E
) can be computed by
measuring the change between the parameter value at any given point on one
surface and its corresponding point on the other surface given the local volume
and area change. The surface area of the 30 and 40 week meshes may be estimated
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