NETWORK TOMOGRAPHY-BASED TRACKING FOR
INTRACELLULAR TRAFFIC ANALYSIS IN FLUORESCENCE
MICROSCOPY IMAGING
Thierry P´ecot
1,2
, Charles Kervrann
1,2
and Patrick Bouthemy
1
1
IRISA/INRIA, Campus universitaire de Beaulieu, F-35042 Rennes, France
2
INRA, UR341 Math´ematiques et Informatique Appliqu´ees, F-78352 Jouy-en-Josas
Keywords:
Object tracking, fluorescence microscopy, network tomography, Voronoi diagram, trafficking, membrane
transport.
Abstract:
Determination of the sub-cellular localization and dynamics of any proteins is an important step towards
the understanding of multi-molecular complexes in a cellular context. Green Fluorescent Protein (GFP)-
tagging and time-lapse fluorescence microscopy allows to acquire multidimensional data on rapid cellular
activities, and then make possible the analysis of proteins of interest. Consequently, novel techniques of
image analysis are needed to quantify dynamics of biological processes observed in such image sequences.
In biological trafficking analysis, the previous tracking methods do not manage when many small and poorly
distinguishable objects interact. Nevertheless, an another way of tracking that usually consists in determining
the full trajectories of all the objects, can be more relevant. General information about the traffic like the
regions of origin and destination of the moving objects represent interesting features for analysis. In this
paper, we propose to estimate the paths (regions of origin and destination) used by the objects of interest, and
the proportions of moving objects for each path. This can be accomplished by exploiting the recent advances
in Network Tomography (NT) commonly used in network communications. This idea is demonstrated on
real image sequences for the Rab6 protein, a GTPase involved in the regulation of intracellular membrane
trafficking.
1 INTRODUCTION
Small GTPases play a key role in many aspects of
cell biology: control of cell growth and differentia-
tion, regulation of cell adhesion and cell movement,
organization of the actin cytoskeleton, and regulation
of intracellular vesicular transport. The small GT-
Pases Rab proteins are important regulators of traf-
ficking within the membrane. Each member of this
family (60 described in human cells) exists under dif-
ferent dynamic states in the cell: i) diffusion in the
cytosol; ii) exchanges between the cytosol and the
membranes; iii) vesicular transport. The Rab protein
family plays an essential role in the dynamics of the
transport vesicles and their targeting/anchoring with
the acceptor membranes. Studying the role of Rab
proteins inside multiprotein complexes is then fun-
damental to deeply understand the molecular mecha-
nisms responsible for membrane transport and for the
maintenance of the integrity and global architecture
of the cell, in space and time.
Rab6 is located on the Golgi Apparatus mem-
branes and the trans-Golgi network membranes. It is
involved in a retrograde transport from the Golgi Ap-
paratus to the Endoplasmic Reticulum. When Rab6
proteins embedded into vesicles are marked with GFP
(Green Fluorescence Protein), they appear on the im-
age sequence as blobs heterogeneously moving along
the microtubule network. The study of the membrane
trafficking by measuring the activity of small trans-
port vesicles from donor to acceptor compartments
within the cell thanks to image analysis techniques is
challenging.
Rab6 trafficking is really hard to analyse as it is
composed of several hundreds similar objects that are
moving with variable velocities. The most commonly
used tracking concept is the connexionist approach
(Anderson et al., 1992; Sbalzarini and Koumout-
sakos, 2005; Racine et al., 2006) consisting in de-
tecting particles independently in each frame in a
first time, and then linking the detected objects over
time. But, measurements from clutter and multiple
objects make the data association problem very hard
to compute. From now, data association even com-
bined with sophisticated particle filtering techniques
(Smal et al., 2007) or graph-theory based methods
154
Pécot T., Kervrann C. and Bouthemy P. (2008).
NETWORK TOMOGRAPHY-BASED TRACKING FOR INTRACELLULAR TRAFFIC ANALYSIS IN FLUORESCENCE MICROSCOPY IMAGING.
In Proceedings of the First International Conference on Bio-inspired Systems and Signal Processing, pages 154-161
DOI: 10.5220/0001060701540161
Copyright
c
SciTePress
(Thomann et al., 2003) are problematic to track sev-
eral hundreds of similar objects with a high reliability.
Deterministic approaches have also been ex-
plored. (Sibarita et al., 2006) exploits the fact that
vesicles are moving along the microtubule network,
and thus follow the same paths. Kymograms are used
for analysing the time intensity profile of the given
paths. The main limitation of the kymogram-based
method is that each path is independently supervised.
Another line of work consists in detecting changes in
the temporal signal for a set of pixels (Bechar and
Trubuil, 2006). By grouping similar temporal pro-
files, dynamics of vesicles can be better described.
In this paper, we propose to get around the diffi-
cult problem of data association by using an original
statistical approach. The aim is to apply the Network
Tomography (NT) concept to real image sequences,
which is challenging for several reasons described be-
low. Accordingly, we need to construct a graph and
to propose a method to measure the activity on edges,
according to the NT approach (Vardi, 1996). This is
the main contribution of this paper. The NT-based ap-
proach, already applied in video surveillance (Santini,
2000; Boyd et al., 1999), allows us to track objects
but only requires the detection of the objects when
they move from one region to another. The estimated
variables give only a general aspect of the whole traf-
fic, but the data association, usually complex, is not
needed. In this paper, we propose to adapt this NT
concept to the estimation of trajectories of vesicles
since it can be motivated by biological analyses. The
number of vesicles that pass through each transition of
the graph is estimated by solving an underconstrained
optimization problem. We will demonstrate that this
method is suited for understanding membrane trans-
port. The paper is organized as follows: in Section
2, we propose to partition the image into regions of
interest, and we estimate the number of moving vesi-
cles on edges at each time step. Then, this estimation
is tested on simulations. In Section 3, we estimate the
regions of origin and destination for the vesicles, and
these estimations are tested on a real image sequence
in Section 4. Finally, we present a conclusion and the
perspectives in Section 5.
2 MEASUREMENTS ON EDGES
In (P´ecot et al., 2007), the idea was to extract the mi-
crotubule network, and to determine the origin and
destination regions for the vesicles, and the cross-
ings of different microtubules, all labeled as vertices
in the graph. Vertices and edges (links between ver-
tices) define the graph G = {E,V}, and the activ-
Figure 1: Images extracted from a microscopic sequence
using a fast 4D deconvolution (wide-field) process at two
time steps.
ity measurements on edges correspond to the ob-
servations required to apply the NT-based approach,
which amounts to estimating the origin-destination
(OD) pairs for the vesicles. In other words, our goal
is to determine the different paths used by the vesicles
from the donor compartment to the acceptor compart-
ment, and the proportions of vesicles for each path.
However, the extraction of the microtubule network is
really hard to compute, since very complex with lim-
ited spatial resolution. So we prefer to partition the
image into regions and to represent the relationships
between regions using a graph.
2.1 Image Partitionning
The Maximum Intensity Projection (MIP) map in the
direction of time axis is a precious key for the par-
titionning of a cell compartment. Indeed, the likely
regions of origin or destination appear as brighter
spots in the MIP map because vesicles are temporally
stocked in these areas. For illustration, the MIP map
extracted from the image sequence shown in Fig. 1 is
given in Fig. 2. It is established that the Golgi Appa-
ratus is the main origin region for Rab6 protein. This
region appears as a very bright region in the MIP map
as shown in Fig. 2. A possible image partitionning
consists in dividing the image into Voronoi cells as
in (Boyd et al., 1999). The Voronoi cells are further
assumed to be the OD regions observed in the MIP
map. It is also possible to compute a Voronoi dia-
gram at a finest spatial resolution including crossings
as relevant features for traffic analysis.
NETWORK TOMOGRAPHY-BASED TRACKING FOR INTRACELLULAR TRAFFIC ANALYSIS IN
FLUORESCENCE MICROSCOPY IMAGING
155
Figure 2: MIP map extracted from the image sequence
shown in Fig. 1.
In order to partition the regions of interest within
the cell, the expert can also manually define the cen-
ters of the Voronoi diagram if required. This diagram
is then computed using the qhull library (Barber et al.,
1996). A segmentation for the cell observed in the im-
age sequence of Fig. 1 is typically illustrated in Fig. 3
where the centers appear in green and the different re-
gions appear in red, while the MIP map is depicted in
the background. In this figure, the centers were fixed
to represent the Golgi Apparatus, and the three possi-
ble end-points of the cell.
The Voronoi diagram is also described by an adja-
cency graph (Fig. 3, right) and then consistent with
the NT concept used for tracking. The different
Voronoi cells represent the set of vertices V while
the boundaries between the cells represent the set of
edges E. We introduce two edges between two neigh-
bouring cells in order to analyse trafficking in both
directions.
Given the graph G , the next step consists in ex-
tracting the data to apply the NT approach, i.e. es-
timating the number of vesicles that move from one
Voronoi cell to another one during the whole image
sequence.
2.2 Temporal Estimation of the Number
of Moving Vesicles
We want to know exactly how many vesicles are mov-
ing from one Voronoi cell to another one at each time
step. Our idea is to compute the difference of the
number of vesicles observed at two consecutive time
1
2
3
2
3
4
6
4
1
5
7
8
Figure 3: Left: partition of the compartment and surround-
ings observed in the image sequence shown in Fig. 1 by us-
ing a Voronoi decomposition. The different regions appear
in red, their centers are labeled in green, and the MIP map
is in the background; right: the corresponding graph; the
vertex numbers are labeled in blue, while the edge numbers
are labeled in red.
steps in each neighbouring region, and then to infer
the exact number of vesicles that crosses each com-
mon boundary. Nevertheless, computing the differ-
ence of vesicles in each region involves image seg-
mentation, a hard task since many similar objects
overlap. By applying NT, we circumvent the problem
since a crude partition of the image is only needed.
In what follows, we assume that the level of fluores-
cence is proportional to the number of Rab6 proteins
at each pixel. So the difference of image intensity at
two time steps represents the difference of the number
of Rab6 proteins in each region. In practice, the back-
ground corresponding to the Golgi apparatus and to
the cytosol diffusion is first removed during a prepro-
cessing step (Boulanger et al., 2006) for better perfor-
mance. We illustrate this concept on a simple example
explained below.
We consider the fluorescence exchanges at the ver-
tex 1 in the graph shown in Fig. 3. Let Z
v,t
be the total
amount of fluorescence in the complete Voronoi re-
gion corresponding to the vertex v at time t, and let
Y
e,t
be the level of fluorescence to be determined on
edge e at time t:
Z
1,t+1
Z
1,t
= Y
1,t+1
Y
2,t+1
+Y
4,t+1
Y
3,t+1
+Y
6,t+1
Y
5,t+1
.
This equation can be extended to all vertices: let Z
be the n × t matrix corresponding to the difference of
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Table 1: Definition of the matrix M corresponding to the
graph shown in Fig. 3.
vertices
edges 1 2 3 4
1 1 -1 0 0
2 -1 1 0 0
3 -1 0 0 1
4 1 0 0 -1
5 -1 0 1 0
6 1 0 -1 0
fluorescence in each region between two consecutive
time steps, with n the number of regions and t the
number of images in the sequence. Let Y be the r × t
matrix representing the level of fluorescence that fluc-
tuates from one region to another at each time, with
r denoting the number of edges. We define M as the
so-called “neighbourhood n× r matrix” composed of
ternary elements m = {−1,0,1} that links the regions
according to the neighbourhoodrelationships. For ex-
ample, in Fig. 3, M is defined as shown in Tab. 1.
Then, we have:
Z = MY (1)
Our aim is to estimate Y with r > n given Z,
so to solve an under-constrained problem. Additional
constraints are necessary for solving (1). First, we as-
sume that all the components of Y are positive since
the edges are unidirectional. In addition, the Z rows
are assumed to be i.i.d., and we naturally choose the
L
2
distance. Finally, we propose to solve the follow-
ing optimization problem:
b
Y = min
Y
k Z MY k
2
subject toY 0.
This optimization problem leads to an estimation of
Y. To improve the solution, we also introduce an ad-
ditional constraint based on the idea of parsimony (see
(Tibshirani, 1996; Candes and Tao, 2007)). Actually,
each row of
b
Y corresponds to fluorescence exchanges
on edges during the whole image sequence. In what
follows, we want to check if the estimation of Y is
improved when the traffic on some edges is removed,
especially on edges for which a very low traffic is ob-
served. Accordingly, Y is split into positive rows Y
l
and rows with zero values Y
nl
. The minimization
can be then modified as follows:
(
ˆ
l,
b
Y) = min
l,Y
l
k Z M
l
Y
l
k
2
+ρl, subject toY 0,
where the second term encourages the selection of
few edges with l denoting the number of non-zero
rows in Y, ρ a balance term, Y
l
the (r l) × t matrix
corresponding to Y restricted to rows with significant
measurements (non zero), M
l
the neighbourhood ma-
trix that matches Y
l
, and Z denoting the difference
of fluorescence in each region between two consecu-
tive time steps.
In practice, we propose the following greedy al-
gorithm for minimization:
1. compute
b
Y
l
= min
Y
l
0
k Z M
l
Y
l
k
2
,
2. compute e =k Z M
l
b
Y
l
k
2
+ρl,
3. remove the row l
in
b
Y
l
that contains the higher
number of 0 values,
4. update the matrices Y
and M
with (l 1) com-
ponents,
5. compute
b
Y
= min
Y
0
k Z M
Y
k
2
,
6. compute e
=k Z M
b
Y
k
2
+ρ(l 1),
7. accept
b
Y =
b
Y
if e
< e,
8. if all rows were considered, stop the procedure,
else go back to step 2.
Finally, depending on the microtubule network
topology and the related Voronoi diagram, the expert
can also forbid the fluorescence transfer between sev-
eral regions if required. This option is explained in
the next section.
2.3 Traffic Partially Known
Biological motivations, confirmed by the MIP map,
can be exploited to prevent the displacements of vesi-
cles from one region to another one. This can be
performed by modifying the neighbourhood matrix
M. For instance, in Fig. 3, we assume that the ex-
pert knows that no vesicle is moving between region
1 and region 2. The matrix is therefore modified ac-
cordingly as
M(:,1) = 0, and
M(:,2) = 0,
with M(:,1) = {M(1,1);M(2,1);...;M(n,1)}. For
the expert, this flexibility can be appropriate for real
applications where interactions with the image is re-
quired, as demonstrated in our experiments.
2.4 Experiments
In this section, we propose a first set of experiments
to evaluate the performance of the estimation proce-
dure, to be exploited in the NT approach described in
Section 3. In this experiment, the vesicles at the ori-
gin and destination regions are stocked, to take into
account the difference of fluorescence.
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Figure 4: Network used for the first simulation. The mi-
crotubule network appears in white, the Voronoi cells are in
red, the origin regions are labeled in green, and the destina-
tion regions are labeled in blue.
Figure 5: Network used for the second simulation. The mi-
crotubule network appears in white, the Voronoi cells are in
red, the origin regions are labeled in green, and the destina-
tion regions are labeled in blue.
Table 2: Evaluation of the estimation of the traffic from the
simulated network shown in Fig. 4.
Temporal tolerances 0 1 2 3
without greedy algorithm
PFA 36% 9% 5% 4%
PFN 36% 9% 5% 4%
PGD 64% 91% 95% 96%
with greedy algorithm
PFA 34% 6% 2% 1%
PFN 34% 6% 2% 2%
PGD 65% 94% 98% 99%
Table 3: Evaluation of the estimation of the traffic from the
simulated network shown in Fig. 5.
Temporal tolerances 0 1 2 3
without greedy algorithm
PFA 39% 9% 5% 5%
PFN 39% 11% 7% 7%
PGD 61% 89% 93% 93%
with greedy algorithm
PFA 35% 5% 1% 1%
PFN 37% 8% 4% 4%
PGD 63% 92% 96% 96%
Two sequences are simulated based on the net-
works shown in Figs. 4 and 5, where the network
appears in white, the Voronoi cells in red, the origin
regions in green and the destination regions in blue.
The simulations correspond to sequences of 1000 im-
ages, showing 2000 moving vesicles.
The performance of our estimation procedure de-
scribed in Section 2.2 are measured using three cri-
teria:
PFA =
number of false detections
total real number of detections
,
PFN =
number of true detections not effected
total real number of detections
,
PGD =
number of good detections
total real number of detections
,
where PFA denotes the Probability of False
Alarms, PFN the Probability of False Negatives, and
PGD the Probability of Good Detections.
A slight temporal shifting between the estimation
results and the “ground truth” is observed. That is
why the results are presented with different temporal
tolerances. For instance, a temporal tolerance equal
to δt means that the estimation results are compared
with a shifting in [δt,.. .,δt] to the ground truth. The
temporal estimations of the number of moving vesi-
cles in the simulations based on the networks shown
in Figs. 4 and 5 are given in Tabs. 2 and 3. In these ta-
bles, the results obtainedare shown with and without
using the greedy algorithm.
Clearly, with a slight temporal tolerance, the es-
timated results are very close to the ”ground truth”.
In addition, it worth noting that we only use temporal
averages for NT, so the shifting will not be crucial for
OD pairs estimation. Moreover, it is also confirmed
that the greedy algorithm significantly improves the
estimation results.
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3 NETWORK TOMOGRAPHY
As explained in Section 2.1 and illustrated in Fig. 3,
a region within the cell (e.g. compartment) can be
represented by a graph corresponding to a Voronoi
diagram, where the centers of the Voronoi cells cor-
respond to regions of interest. The graph G (E,V) is
defined by n vertices and r edges, where E denotes the
set of edges, and V the set of vertices. A connection
between two vertices is also called a path, and each
path consists of one or more edges. In the NT-based
approach, the data is the number of objects detected as
going from one vertex to another vertex in the graph.
Based on these measurements, the new goal is to esti-
mate how many vesicles coming from an origin vertex
go to a destination vertex along a path, in the set of all
possible OD pairs in the graph, that is c = n(n 1)
OD pairs. This problem is then similar to determine
the source-destination traffick based on link measure-
ments in computer networks (Vardi, 1996). In this ap-
proach, it is not necessary to track an object through
a dynamic scene, but just to determine when an ob-
ject reaches a vertex, which is generally easier than
estimating a continuous trajectory.
3.1 Problem Solving
More formally, let X
j,t
, j = 1, ··· , c, be the quantity of
“transmitted” fluorescence on the OD pair j at time t.
The measurements Y
t
= (Y
1,t
,...,Y
r,t
)
T
are computed
as explained in Section 2. The inherent randomness
of the measurements motivates the adoption of a sta-
tistical approach. Now, we reasonably assume that
the whole traffic is temporally distributed as a Pois-
son process, X
j,t
Poisson(λ
j
). In this traffic flow
problem, we then assume the following model:
Y
t
= AX
t
, (2)
where X
t
= (X
1,t
,...,X
c,t
)
T
, and A denotes a
r× c routing matrix which binary elements A
ij
= 1 if
edge i is in the path for the OD pair j, and 0 otherwise.
For illustration, if we consider the simple example
shown in Fig. 3, some rows of the matrix A are pre-
sented in Tab. 4. Typically, the number c is greater
than r, and the problem is then under-constrained.
Additional constraints are necessary for solving this
inverse problem. First, (Vardi, 1996) proposed to
introduce constraints related to the assumption that
the traffic is temporally Poisson distributed. The
NT method amounts then to estimating the values λ
j
given the additional set of equations corresponding to
temporal averages:
Table 4: Part of the matrix A corresponding to the graph
shown in Fig. 3.
edges
OD pairs 1 2 3 4 5 6
1 2 0 1 0 0 0 0
1 3 0 0 0 0 1 0
1 4 0 0 1 0 0 0
2 1 1 0 0 0 0 0
2 3 1 0 0 0 1 0
2 4 1 0 1 0 0 0
... ...
Y
i
=
c
k=1
A
i,k
λ
k
, i = 1,.. .,r,
cov(Y
i
,Y
i
) =
c
k=1
A
i,k
A
i
,k
λ
k
, 1 i i
r.
This set of equations gives a system of r(r+ 3)/2 lin-
ear equations that forms an over-constrained problem
that can be better solved with the conditions λ
i
0.
Moreover, in this application, the aim is not to ob-
tain the number of vesicles that utilize each path, but
to estimate the proportions of vesicles on each path.
Hence, unlike previous methods (Vardi, 1996; San-
tini, 2000; Boyd et al., 1999), we impose the condi-
tion
c
i=1
λ
i
= 1 as an additional constraint. The pre-
vious system can be written more compactly as:
Y
S
=
A
B
Λ, (3)
where Λ = (λ
1
,...,λ
c
)
T
contains the temporal mean
of the traffic flow, S = {cov(Y
i
,Y
i
)} is the sample
covariance matrix rewritten as a vector of length
r(r + 1)/2, and B is an (r(r+ 1) /2) ×c matrix with
the (i, i
)th row of B being the element-wise product
of row i and row i
of the matrix A.
The system can be solved using the estimation-
maximization (EM) method (Vardi, 1996; Santini,
2000) or the convex-projection algorithms (Boyd
et al., 1999). In our case, we adapt a non negative
mean square estimation which also provides a simple
and reliable way to estimate the OD traffic
b
Λ. For the
implementation, our method is based on the lsqnonlin
function from the Matlab Optimization toolbox. Note
that a review of existing methods is also proposed in
(Medina et al., 2002).
3.2 Origin-destination Regions Partially
Known
When the expert specifies the origin or destination re-
gions, the problem is better constrained and the solu-
NETWORK TOMOGRAPHY-BASED TRACKING FOR INTRACELLULAR TRAFFIC ANALYSIS IN
FLUORESCENCE MICROSCOPY IMAGING
159
tion is expected to be more relevant.
Typically, if we assume that the origins or destina-
tions for the regions are known, this can be casted into
additional hard constraints. If the Voronoi cell r is the
single origin region, then all the OD pairs that have
another Voronoi cell than r as origin have no longer
meaning. So all that OD pairs can be ignored. Hence,
let R be all the OD pairs that have r for origin. Then,
if O denotes the set of all OD pairs, A can be modified
as
A(:,O r A ) = 0,
with A(:, O r A ) = {A(1,O r A );A(2,O r
A );.. .;A(r,O r A )}. The same modeling can
be applied for imposing additional origin or destina-
tion regions.
4 EXPERIMENTAL RESULTS
In this section, we propose three experiments to
demonstrate the ability and the limits of the NT-based
approach applied to a real image sequence. All these
experiments are tested by considering the sequence
shown in Fig. 1. This sequence is composed of 900
images coming from a fast 4D deconvolution mi-
croscopy (wide-field) process (Sibarita et al., 2006).
In this sequence, the background was removed during
a preprocessing step. The estimated results are re-
ported in Figs. 6 and 7. In these figures, the Voronoi
cells are represented in red, while the MIP map is
shown in the background by transparency. The differ-
ent estimated OD pairs appear as colored arrows, and
the corresponding colored numbers at the right top of
the figures are the estimated proportions of moving
vesicles for each OD pair.
A first experience was carried out with a crude
segmentation, without imposing origin or destination
regions. The results are shown in Fig. 6 (left). Ac-
cording to the expert-biologists, the vesicles are mov-
ing from the Golgi Apparatus (the central region) to
end-points located at the periphery of the cell (cor-
responding to the three other regions). But, in this
experience, the traffic is estimated going from end-
points to end-points, which is not consistent with prior
knowledge. That is why we impose, in a second ex-
periment, (Fig. 6, right image), the central regionto be
the origin Voronoi cell. The results obtained with this
additional constraint correspond to trafficking from
the Golgi Apparatus to the end-points. In that case,
the traffic tends to be quite uniform for all the end-
points.
In another experiment corresponding to another
partition of the image shown in Fig. 7 (left), the pre-
vious central Voronoi cell is divided into several cells,
Figure 6: Results obtained by applying the NT-based ap-
proach on the sequence of the Fig. 1. The arrows repre-
sent the estimated OD pairs, and the corresponding colored
numbers at the top right represent traffic proportions. Left:
no origin region is imposed; right: the central region is im-
posed to be an origin region.
and they are all constrained to be origin regions. The
estimated traffic from these origin regions to the end-
points corresponds to proportions similar to propor-
tions estimated in the previous experiment. In addi-
tion, the estimated traffic seems to be isotropic, i.e.
there is no particular directions for traffic.
Finally, an experience is conducted with the same
constrained origin region than the first experiment,
but with one more end-point at the top of the image,
and with intermediate Voronoi cells between the ori-
gin and the destinations (Fig. 7, right). Although the
destination cells are not labeled, the whole traffick-
ing is estimated from the Golgi Apparatus to the end-
points. In addition, the sum of estimated proportions
of the traffic towards the two regions at the top of the
image is quite similar to the estimated proportions of
the traffic towards the region at the top of the image
in the first experiment. However, the estimated pro-
portions of traffic towards the regions located at the
bottom of the image are different from the estimated
proportions of traffic towards the same regions in the
first experience.
5 CONCLUSIONS
In this paper, we propose several contributions: i) def-
inition of a graph by partitionning the image using a
Voronoi diagram; ii) temporal estimation of moving
vesicles; iii) application of the NT concept to real im-
age sequences. The results obtained on the real image
BIOSIGNALS 2008 - International Conference on Bio-inspired Systems and Signal Processing
160
Figure 7: Results obtained by applying the NT-based ap-
proach on the sequence of Fig. 1. The arrows represent the
estimated OD pairs, and the corresponding colored num-
bers at the top right represent traffic proportions. Left: all
the central regions are imposed to be origin regions; right:
the central region is imposed to be an origin region.
sequence suits the biologicalknowledge about the OD
regions for the Rab6 trafficking. In our experiments,
the proportions of vesicles for the OD pairs given by
the NT procedure represent new tools for biologists.
It can be applied to understand other trafficking prob-
lems where many objects are moving. Actually, the
main limit is related to image partition yet, which can
be arbitrary. Indeed, although the expert defines the
centers of Voronoi cells with biological knowledge,
the segmentation remains very crude for representing
the regions of interest. Actually, the MIP map is the
only tool available to define these regions, but is not
enough accurate. For future work, it will be necessary
to apply the NT-based approach on more relevant re-
gions. A possible way is to extract the microtubule
network and consider it as a graph for applying the
NT procedure. Moreover, it is established that the flu-
orescence decreases with time, which is neglected in
our modeling since we exploit the difference of fluo-
rescence between two time steps. However, it is well
known that the vesicles diffuse also in the cytosol.
This could be considered in future work by introduc-
ing this phenomenon in the estimation process of the
data to improve the results.
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NETWORK TOMOGRAPHY-BASED TRACKING FOR INTRACELLULAR TRAFFIC ANALYSIS IN
FLUORESCENCE MICROSCOPY IMAGING
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