![](bg3.png)
• The identification of tissue types needs expert
knowledge
This necessitates the use of algorithms incorpo-
rating a priori information for robust multiclass-
segmentation, where solely intensity-based tech-
niques are clearly unfeasible.
In the context of section imaging in (Bollenbeck
and Seiffert, 2008) we have suggested the segmen-
tation into multiple classes by intensity driven regis-
tration and deformation of reference segmentations,
performing equally accurate with image-feature based
supervised classifiers like support vector machines
and multi layer perceptrons in experiments on histo-
logical plant data, while being less computationally
costly.
Employing the well known free-form deformable reg-
istration formulation
J(u) := D(R,T ; u) + αs(u)
!
= min . (2)
of images R,T : Ω ⊂ R
2
7→ N
+
an a priori reference
segmentation S : R ⊂ Ω 7→ {1,...,M} of R is adapted
to segment T driven by an intensity based image-
metric D subject to a regularized deformation u.
By using this method we classify voxels contained in
the image stack to the respective tissue or material
based on a small set of expert created reference seg-
mentations.
These tissue mappings can be individually visualized
by iso-surface renderings as in (Gubatz et al., 2007)
and (Dercksen et al., 2008), where for valid inter-
individual models multiple individual stacks are the
basis for a statistical three-dimensional description.
Statistical 3-D Models of Barley Grains. Whereas in
the context of histological models, works so far have
neglected biodiversity amongst specimen, the novelty
of our approach is to provide a meaningful description
of diversity amongst multiple specimen in one sin-
gle model, allowing to quantify common themes and
structures for further analysis and to provide a mean-
ingful framework for the integration of functional data
acquired from other individuals.
The quantification of inter-individual variability re-
quires the mapping of data into a common reference
frame allowing the estimation of ubiquitous tissues
and regions of varying tissue composition.
While data sets generally vary in their physical exten-
sion, the task is to capture the composition of internal
structures in terms of estimating a probability to each
spatial coordinate for prevailing tissues based on seg-
mented volume data, rather than constructing averag-
ing surfaces or deformation models.
To obtain a transformation invariant to the actual tis-
sue mapping, data sets are registered into a common
coordinate frame by standardizing first image mo-
ments of the mass-centered intensities of the respec-
tive grayscale volumes of sectioned images (Alpert
et al., 1990; Schmitt et al., 2006).
Instead of using registration approaches maximizing
the correspondence of individual label- or grayscaled
volumes directly with affine mappings, spline, or free-
form deformations, a registration based only on indi-
vidual image statistics can be considered un-biased in
terms of leaving the inter-individual variances unaf-
fected.
For each gridpoint ~x ∈ Ω ⊂ R
3
and tissue M we esti-
mate a probability for ~x belonging to tissue M empir-
ically by
p
~x,M
:=
1
|S|
|S|
∑
i=1
δ(S
i
(~x),M) (3)
from segmented data sets S
i
.
Thereby a closed description of the spatial distribu-
tion of tissues and materials amongst specimen terms
of a mapping P : Ω 7→ R
M
is obtained.
While the spatial distribution of tissue probabilities is
not based on assumptions on underlying distribution
as with statistical deformation models, it can directly
be related to underlying histological information (in-
tensity volumes) as indicated in fig. 2.
3 RESULTS
For this work four individual grains at the same de-
velopmental stage were sectioned and digitized as de-
scribed, yielding 2,128 to 2,736 slice images, each of
size 1200 × 1600 pixels (approx. 30 GB image data).
Providing the basis for further modelling, intact indi-
vidual grains were reconstructed from section images
as proposed. Fig. 1 shows a volume rendering of a
registered individual grain. By virtual lateral sections,
revealing reconstituted histological features, such as
cell walls etc., the performance of the registration ap-
proach in processing large image stacks could be ini-
tially validated, while detailed assessment is feasible,
yet beyond the scope of this paper. Employing the
described registration-segmentation algorithm, inten-
sity stacks were segmented into their respective tis-
sues based on a set of reference data defined by an
expert.
For inter-individual description we registered and
joined the segmented data in a common reference,
yielding a volume of probabilities for each tissue (see
fig. 2(a)). Using the probabilistic modelling, we ad-
dressed the biological questions (1.) how are specific
tissues and relevant materials varying and (2.) what
are ubiquitous themes amongst individuals. Thus, for
an insightful 3-D visualization of probabilistic models
FROM INDIVIDUAL INTENSITY VOXEL DATA TO INTER-INDIVIDUAL PROBABILISTIC ATLASES OF
BIOLOGICAL OBJECTS BY AN INTERLEAVED REGISTRATION-SEGMENTATION APPROACH
127