Biomedical Engineering Reference
In-Depth Information
Table 11.1:
Anatomical structures of the bee brain with abbreviations used in
this chapter
Abbreviation
Structure
Abbreviation
Structure
PL-SOG
protocerebral lobes
r-medBR
right medial basal ring
CB
central body
l-latBR
left lateral basal ring
l-Med
left medulla
r-latBR
right lateral basal ring
r-Med
right medulla
l-medColl
left medial collar
l-Lob
left lobula
r-medColl
right medial collar
r-Lob
right lobula
l-latColl
left lateral collar
l-AL
left antennal lobe
r-latColl
right lateral collar
r-AL
right antennal lobe
l-medLip
left medial lip
l-vMB
left mushroom body
r-medLip
right medial lip
r-vMB
right mushroom body
l-latLip
left lateral lip
l-medBR
left medial basal ring
r-latLip
right lateral lip
conceptually very similar to an image in the same coordinate space, which is a
mapping from
R
n
to the space of gray values, a subset of
R
. An atlas can therefore
itself be considered as a special type of image, that is, a label image. In order to
segment a new image
R
using an atlas
A
, we need to compute a coordinate map-
ping between them, that is, we need to register one image to the other. The coordi-
nate mapping must be anatomically correct for the segmentation to be accurate.
An atlas is often generated by (manually) segmenting an actual image, say
F
. Therefore, we typically have access not only to a spatial map of labels, the
actual atlas, but also to a corresponding realization using at least one particular
imaging modality. In case multiple co-registered images from different modal-
ities form the basis of the atlas, there may even be multiple instances of ac-
tual images. An example of an atlas and a corresponding microscopy image
is shown in Fig. 11.1. This dual character is relevant insofar as, while funda-
mentally possible, registration of an image to the label representation of an
atlas is a much harder problem than registration to the corresponding original
image.
Let us consider two 3D scalar images,
R
:
R
→ R
.Weas-
sume that each point in one image has a corresponding equivalent in the other.
For any two images, this correspondence is mathematically represented as a co-
ordinate transformation
T
that maps the image coordinates of
R
onto those of
F
. For a given location
x
in the domain of
R
, we find the corresponding location
in the domain of
F
as
T
(
x
). If
F
is associated with an atlas
A
, then we can find
3
→ R
and
F
:
R
3
