Model based approach for Improved 3-D Segmentation of Aggregated-Nuclei in Confocal Image Stacks

1
Model based approach for Improved 3-D
Segmentation of Aggregated-Nuclei in Confocal
Image Stacks
Nicolas Roussel1,James. A. Tyrell2, Qin Shen3,
Sally Temple3, Badrinath Roysam1 1Department of
Electrical, Computer and Systems Engineering,
Rensselaer Polytechnic Institute, Troy, NY
12180 2Massachusetts General Hospital, Boston, MA
02114 3Albany Medical Center, Albany, NY 12208
This work was supported in part by CenSSIS, the
Center for Subsurface Sensing and Imaging
Systems, under the Engineering Research Centers
Program of the National Science Foundation (Award
Number EEC-9986821)
Introduction
Problem illustration
Results
We present a study on a new modeling based
approach to cell segmentation and its application
to cell detection in 3D space. As a model, we use
an ellipsoid to which three types of deformation
can be applied, namely translation, rotation and
scaling. The geometric and intensity parameters
of the models are optimized independently at each
iteration step. The purpose of this approach is
to derive a virtual fitting Pseudo-Force that
drives the ellipsoid to the apparent boundaries
of the cell. In an environment where a number of
cells can coexist and partially overlap, it is
also necessary to model the inter-object
constraints that limit the extent to which
overlap is possible. We propose to implement this
constraint as an interaction force that will
counteract the fitting Force and prevent two
objects from occupying the same space.
Model Description
Geometric descriptor
Illustration of the segmentation problem. In the
field of view, a number of ellipsoidally shaped
cells coexist and partially overlap. The presence
of cell aggregates combined with the
inconsistency of their appearance model makes for
a challenging segmentation task
We define as B the ellipsoid Surface and R its
volume
Model based segmentation Framework
Model Fitting
Fitting the region based active contour model as
defined in the previous section can be seen as an
optimization process whereas the quantity J(ß) is
to be minimized with respect the geometric
parameters ß. For the sake of clarity, the
objective function can be seen as the weighted
sum from a level based factor Ja(ß) and an edge
based factor Je(ß) . The weighting coefficients
can be used to balance the appearance and edge
energy terms.
Our modeling approach is based on a common
template is used for all objects in the field of
view. In 3D space, this geometric template is
defined over a 3D mesh, each facet defined by its
center Xe() and normal Ne() . Essentially, every
object in the field of view is considered a
deformed version of this template. Actual object
structure if thus captured by the deformation
T(X,ß). This formalism allows for the use of a
wide range of shape families.
Gradient search which requires the derivative of
L with respect to the deformation of the ellipsoid
Illustration of our fitting framework Ellipsoid
model for each cell are overlaid on the image
projection (left) and iso-surface (right). Using
this modeling approach, it is feasible to detect
specific objects based on their assumed shape and
appearance model.
A parameterized object surface can be implicitly
formulated in term of an inside/outside function
that allows us to define the volume occupied by a
given shape
Interaction model
Conclusion
In the case where multiple object are to occupy
the same field of view and possibly demonstrate
partial overlap pattern, it can be useful to
incorporate a non overlap constraint that limits
the extent to which overlap is possible. To that
end, we are going to introduce an additional set
of interaction pseudo-forces created by
neighboring objects that will counteract the
fitting Force and prevent two objects from
occupying the same space.
Where R is the region of space occupied by the
object, C its surface and the domain. For a
given template Su(X) and deformation parameter
T(X,ß), the object is defined by
Using a model based approach to 3D cell
segmentation has proven successful in a number of
test cases. Overall the results are encouraging
and suggest that such an approach would prove
useful in dealing with situation involving dense
cell population with irregular appearance.
One of the main advantage of this algorithm is
its modularity as it can be easily generalized
using alternative template and interaction models
in application involving the segmentation of
different anatomical structure.
In this paper, our focus is on the segmentation
of brain cells. On a first level of
approximation, those cells can be considered to
be of ellipsoidal shape. As a result and under
the formalism described above, they can be
modeled as a unit sphere Su(X) defined as
Neighboring inside outside function
to which the transformation T(x, ß)R(F)D(s)xµ
is applied. The Matrix D(s) is a 3x3 matrix with
positive scale parameters on the diagonal, the
rotation R(F) matrix and a translation factor.
Interraction force from Neighbooring function
Modular object representation
Highly parallelizable Segmentation scheme
Appearance model
Segmentation Framework
References
As an appearance model we assume uniform
intensity IB and IF inside and outside the
ellipsoid boundaries respectively.
J. Tyrrell, V. Mahadevan, R. Tong, B. Roysam, E.
Brown, and R. Jain, \3-d model-based complexity
analysis of tumor microvasculature from in
vivo multiphoton confocal images," J. of
Microvascular Research, vol. 70, pp. 165178,
2005. S. Jehan-Besson, M. Barlaud, and G.
Aubert, \Dreams Deformable regions driven by an
eulerian accurate minimization method for image
and video segmentation Application to face
detection in color video sequences." Online.
Available citeseer.ist.psu.edu/558842.html Harri
s, J. W. and Stocker, H. "Ellipsoid." 4.10.1 in
Handbook of Mathematics and Computational
Science. New York Springer-Verlag, p. 111, 1998.

2D illustration of the appearance model
Pixel appearance within a geometric model can be
defined in term of a homogeneity estimator ki()
for the pixels within R and ko() within O\(RUC)
. For instance, in the case where we assume
uniform intensity distribution within and outside
the object model, the homogeneity estimator could
be defined as
Edge homogeneity estimator kb() can be defined
for the pixel on the object boundaries from a
separate edge detection channel Ib(). In snake
literature, commonly used edge channel called
external energy, include