NETWORK TOMOGRAPHY-BASED TRACKING FOR

INTRACELLULAR TRAFFIC ANALYSIS IN FLUORESCENCE

MICROSCOPY IMAGING

Thierry P´ecot

1,2

, Charles Kervrann

1,2

and Patrick Bouthemy

IRISA/INRIA, Campus universitaire de Beaulieu, F-35042 Rennes, France

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

 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

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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

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

e,t

be the level of ﬂuorescence to be determined on

edge e at time t:

1,t+1

− Z

1,t

= Y

1,t+1

−Y

2,t+1

4,t+1

−Y

3,t+1

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

distance. Finally, we propose to solve the follow-

ing optimization problem:

Y = min

k ∆Z− MY k

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

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

and rows with zero values Y

n−l

. The minimization

can be then modiﬁed as follows:

(

Y) = min

l,Y

k ∆Z− M

+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

the (r − l) × t matrix

corresponding to Y restricted to rows with signiﬁcant

measurements (non zero), M

the neighbourhood ma-

trix that matches Y

, 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

= min

≥0

k ∆Z− M

2. compute e =k ∆Z− M

+ρl,

3. remove the row l

′

that contains the higher

number of 0 values,

4. update the matrices Y

′

and M

′

with (l − 1) com-

ponents,

5. compute

′

= min

′

≥0

k ∆Z− M

′

6. compute e

′

=k ∆Z− M

′

+ρ(l − 1),

7. accept

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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157

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

= (Y

1,t

,...,Y

r,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

). In this trafﬁc ﬂow

problem, we then assume the following model:

= AX

, (2)

where X

= (X

1,t

,...,X

c,t

)

, and A denotes a

r× c routing matrix which binary elements A

= 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

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

... ...











∑

k=1

i,k

, i = 1,.. .,r,

cov(Y

′

) =

∑

k=1

i,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

≥ 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

∑

i=1

= 1 as an additional constraint. The pre-

vious system can be written more compactly as:









Λ, (3)

where Λ = (λ

,...,λ

)

contains the temporal mean

of the trafﬁc ﬂow, S = {cov(Y

′

)} 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

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

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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

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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FLUORESCENCE MICROSCOPY IMAGING

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