Engineering, 2013, 5, 226-232
http://dx.doi.org/10.4236/eng.2013.510B047 Published Online October 2013 (http://www.scirp.org/journal/eng)
Copyright © 2013 SciRes. ENG
Cell Segmentation and Tracking in Microfluidic Platform
Lipan Ouyang1, Jiandong Wu2, Michael Zhang3, Francis Lin2, Simon Liao1
1Department of Applied Computer Science, University of Winnipeg, Winnipeg, Canada
2Department of Biosystems Engineering, University of Manitoba, Winnipeg, Canada
3Winnipeg Regional Health Authority, Winnipeg, Canada
Email: ************
Received June 2013
ABSTRACT
In this research, we have concentrated on trajectory extraction based on image segmentation and data association in
order to provide an economic and complete solution for rapid microfluidic cell migration experiments. We applied re-
gion scalable active contour model to segment the individual cells and then employed the ellipse fitting technique to
process touching cells. Subsequently, we have also introduced a topology based technique to associate the cells between
consecutive frames. This scheme achieves satisfactory segmentation and tracking results on the datasets acquired by our
microfluidic platform.
Keywords: Microfluidic Devic e; Image Segmentation; Data Association; Active Contour Model; Cell Tracking
1. Introduction
Cell migration plays an important role in many biomedi-
cal fields, such as drug test and disease diagnosis [1].
Traditionally, cell migration is observed under Boyden
chamber or Tran swell assays and other cell migration
assays. However, these conventional methods lack of
chemical gradients control and capability for quantitative
analysis and often require large amounts of reagents and
cell samples. Compared with the abovementioned me-
thods, the microfluidic devices provide a more satisfac-
tory platform for quantitative cell migration due to its
capability of configuring precise and stable chemical
concentration gradients, lower cells and reagents con-
sumption, and the potential for high-th roughput experi-
ments [2-4].
High-throughput of images makes the manual obser-
vation of cell migration a labor-requiring and time-con-
suming process, and the accuracy of manual tracking
highly depends on the experience and judgment of the
individual researchers. Therefore, an effective automatic
multiple objects tracking system is essential to conduct
the quantitative analysis.
Most cell tracking techniques are composed of two
phases, detecting and segmenting cells frame by frame,
and then associating the detected same cells over two or
more consecutive frames. A large number of segmenta-
tion methods have been introduced in the past decades,
and many of them are still receiving intensive attention
from medical image analysis community, such as water-
shed [5,6], edge detector [7], split and merge [7-9], re-
gion growth [10-12], and some clustering methods [13-
16].
In this research, we have employed the active contour
model, which was first introduced by Kass et al. [17].
Given an initial contour, this method would evolve to-
wards image features such as object boundaries, and the
evolution will continue until the energy functional
reaches the minimal. However, the original model is pa-
rametric and would fail when topology changes happen
[1]. To handle the topology changes, Caselles et al. pro-
posed the geodesic active contours with th e flexibility of
topology, which evolves the contours under a level-set
framework [18]. With the level-set framework, the cell
tracking group in Carnegie Mellon University has pro-
posed several important improvements of active contour
models to distinguish touching cells, though these me-
thods require large computational time and memory load
[19-23].
The objects association has been a focus o f research ers
in some scientific fields such as radar system and video
surveillance. Multiple Hypothesis Tracking (MHT) [24]
and Joint Probabilistic Data Association Filter (JPDAF)
[25] are two well-known examples of using Recursive
Bayesian estimation, which is an effective method in
objects association. While MHT needs the construction
of exhaustive hypothesis set to select the optimal trajec-
tory, even with the pruning techniques, this procedure
requires substantial computation time and memory space
[26]. In contrast, JPDAF is a simpler and suboptimal
approach that demands only fixed computational re-
sources per iteration [27]. Data association, in general,
L. P. OUYANG ET AL.
Copyright © 2013 SciRes. ENG
227
can be regarded as an optimal assignment problem and
could be resolved by Hungarian algorithm [28]. We refer
to [29] for a background study on data association tech-
niques.
2. Device Fabrication and Cell Preparation
We have employed the similar fabrica tion of microfluidic
devices with the same standard soft-lithography protocol
described in [30]. The pattern was designed in a comput-
er and printed into a transparency film to make a mask. A
silicon wafer was coated with a thin layer of photo resist
using a spinner. The master was finished by patterning
the design on the wafer through the mask by UV
processing. Liquid PDMS was poured on the master and
cured in an oven. The PDMS replica was then peeled off
and bonded to a glass slide by plasma treating to make
the microfluidic device. The device was then coated by
fibronection for one hour and blocked by BAS for another
hour before starting the cell experiment to help cell
bonding and migration on the substrate in the microflui-
dic channel.
The neutrophils were isolated from human whole
blood using the gradient density centrifugation method.
The cells were cultured in an incubator before loading in
the microfluidic device. A 10 nM IL-8 gradient was gen-
erated in the microfluidic channel. The device was then
put under the microscope and time-lapse image acquisi-
tion and further analysis was done by the custom-devel-
oped program.
3. Segmentation by Active Contour Model
3.1. Region-Based Active Contour Models
For an image function I(x,y) in the image domain, the CV
model proposed by Chan and Ves e [31] is:
2
12 11
()
2
22
()
( ,,)|()|
|()|| |
outside C
inside C
F C ccIxcdx
I xcdxv C
λ
λ
= −
+ −+
(1)
where C is any possible curve, inside(C) and outside(C)
are two regions inside and outside the contours, and c1
and c2 are the average image intensity of inside(C) and
outside(C), respectively. The first two terms in Equation
(1) are called as global fitting energy”, which will have
the minimum values if curve C is the real boundary of an
object.
Since the CV model is piecewise constant and do not
contain any local information, therefore, the optimal
constants c1 and c2 might be significantly different from
the real image data if the intensities inside or outside the
curve C are inhomogeneous. Considering such a situation
happens commonly when an image is captured by time-
lapse microscopy, the region-based active contour model
is a more desirable adaptation in our research. In the re-
gion-based active contour model, the global fitting ener-
gy is replaced by a Region-Scalable Fitting energy (RSF ),
which contains local intensity information . Assume Ω1 =
outside(C) and Ω2 = inside(C), the RSF for each pixel
x∈Ω
is defined as:
2
12 1
2
(,( ),( ))()
|()( )|
i
Fit
xi
i
i
Cf xfxKxy
I yfxdy
ελ
=
= −
(2)
where
λ
1 and
λ
2 are positive constants , and f1(x) and f2(x)
are the approximate image intensities in Ω1 and Ω2. The
intensities I(y) are taken into account in the fitting energy
come from the region centered at pixel x, the size of
which is under the control of the kernel function K. A
Gaussian kernel was chosen in [32].
Propagating the energy
ε
Fit
x on the entire image, it de-
rives the following:
12
12
(,(),( ))
(,(),( ))||
Fit
x
Cfxf x
Cfxfxdxv C
ε
ε
= +
(3)
The second term in Equation (3) is a penalty term to
smooth the contour C. Since this model is parametric, it
is necessary to translate the parametric active contour to
a geometric active contour, which is more desirable to
deal with topology changes [18,33]. By applying Heavi-
side and Dir ac functions, numerical approximation of the
evolution of the level set function can be written as:
2
1122
||
() ()()()
||
div
t
vdive e
εε
φφ
µφ φ
φ
δφδφλ λ
φ


∂∇
= ∇−


∂∇


+ −−
(4)
2
( )()|()( )|,1,2
ii
exKyxIxfydy i
σ
=−− =
(5)
where f1 and f2 are
(6)
For more details of the active contour model, we
would refer to [32].
3.2. Splitting Touching Cells by Ellipse Fitting
In general, the segmentation of touching cells is a chal-
lenging task [34,35]. When the traced cells enter into a
blob, the boundaries of the contacting cells are blurred,
and most segmentation algorithms would fail in finding
the edges of cells in this situation.
In our research, we first select a region larger than the
blob where touching happens, then apply the ellipse fit-
ting [36,37] to estimate the features of contacting cells.
Figure 1(a) shows an example of two touching cells. It is
L. P. OUYANG ET AL.
Copyright © 2013 SciRes. ENG
228
(a) (b) (c)
(d) (e) (f)
Figure 1. (a) Contour of two touching cells; (b) Binary im-
age of touching cells; (c) Result of ultimate erosion; (d) The
set of candidate ellipses; (e) Best fitting ellipses of all the
seeds; (f) Best fitting ellipses after overlapping deletion.
obvious that the cells could be presented by two ellipses
in this case. Therefore, splitting the cells is equivalent to
estimate the parameters of the ellipses which best fit the
real data.
To apply the ellipse fitting, first, a set of seeds for the
closed contours produced by the Region-Scalable Fitting
based Active Control model are generated by ultimate
erosion, which is a binar y operator in mathematical mor-
phology. The ultimate erosion repeat eroding an object
until the object disappears, while the residual points are
considered as seeds. Figu re s 1(b) and (c) illustrate the
beginning and result of an ultimate erosion process, re-
spectively. For convenience, we denote the pixels on the
contours as C(xc,yc), and the seeds as Si, where i = 1, 2, ...,
N and N is the number of seeds. For each of seeds Si, we
then sort C(xc,yc) into increasing order according to the
distance from C(xc,yc) to Si. At the end of so rting proc ess,
there would be N increasing order lists of C(xc,yc), de-
noted as Ci
sorted(xc,yc). First M elements are selected from
Ci
sorted(xc,yc) into a set Ci
1(xc,yc), and then incrementally
append more elements into the set Ci
k(xc,yc), where k
means at the kth stage. In each stage, an ellipse is fitted
to the pixel coordinates in set Ci
k(xc,yc) by direct least
squares fitting o f ellipse [38]. After processing all stages,
a number of candidate ellipses, as shown in Figure 1(d),
are produced and the best fitting ellipse will be selected
from them. The obtained 4 best fitting ellipses of the
seeds in Figure 1(c) are presented in Figure 1(e). To
rank the fitness of the ellipses, we have adopted the fol-
lowing measurement
(( ,))(( ,))
(|(( ,))|
|((,)) |)
ii
k cck ccobject
i
k ccobject
i
objectk cc
VCx yaEllipseC x y
bEllipse Cxy
Ellipse Cxy
ϕ
ϕ
ϕ
=⋅ ∩−
⋅ ∩+
(7)
where Ellipse(Ci
k(xc,yc)) denotes the ellipse fitted by the
point Ci
k(xc,yc),
ϕ
object represents the touching objects, and
a and b are the weights.
Two essential features are taken into account in our
criterion of fitn ess, the first term of Equation (7) rewards
the ellipse belonging to the region of object, while and
the second term penalizes the ellipse out of the region of
object. The ellips e with the high est value of this criterion
will be chosen as the best fitting from a list of candidate
ellipses. By performing the selection process to all of N
increasing order lists, we would obtain N best fitting el-
lipses from N seeds. In the ultimate erosion process,
since the number of seeds would likely be more than the
touching cells, thus it is necessary to make a decision that
which of the best fitting ellipses represents the true cell.
As a solution, we have arranged the N best fitting ellipses
in decrease order by the fitting criterion values, and
eliminated all ellipses that have an overlap over 60%
with the previously selected ellipse. The rest two ellipses
representing the touching cells are shown in Figure 1(f).
4. Data Association Using Graph Theory
An association process after successful cell segmenta-
tions is to link the corresponding cells between two con-
secutive frames. In our cell migration experiment, we
have focused on investigating the slower moving cells
which are bonded to the glass substrate. Since these un-
adhered cells are not desirable and can be discarded, we
employ a data association method based on graph theory
[39], which is less costly in computational complexity
and more suitable to address the adhered cells in our ex-
periments.
The migration speeds of cells are different in our ex-
periments. The cells moving faster are regarded as active
cells, while the ones with smaller displacement between
two consecutive frames are classified as lazy type. Zhang
et al. has presented a real -life example to explain th e idea
of this approach [39]. For example, if the neighbors 1, 2,
3, 4, and 5 of A and B in Figure 2(a) are already identi-
fied in Figure 2(b), then A, B and X, Y can be matched
correctly according to the topology information of their
identified n e ighbors.
4.1. Lazy Cells Recognition
As the example shown in Figure 2, obtaining the identi-
(a) (b)
Figure 2. Example of objects association.
L. P. OUYANG ET AL.
Copyright © 2013 SciRes. ENG
229
fied neighbors is an essential procedure to discriminate
the un-matched objects. Naturally, the objects moving
slower are more likely to be recognized, therefor e a good
association strategy is to identify these lazy type cells
first. In the situation that cells almost remain their posi-
tions and shapes, a nearest neighborhood search is an
effective method in despite of its simple basis.
Assume that N cells (Ti; i = 1, ..., N) have been tracked
up to the last frame, and M cells (Ci; i = 1, ..., M) have
been detected in the current frame. A cost function is
introduced here to present the similarity between Ti and
Ci:
22 2
2 22
1(),if
0,otherwise
ij ijijii
ij i ii
dls dj G
Cost GLd Sd
αβ γ

−×+ ×+×<

=

(8)
where Gi is the maximum Euclidean distance that a cell i
can move between two consecutive frames, Ldi and Sdi
are the maximum differences of perimeters and areas for
the possible matched cells between two consecutive
frames, r es pectively. If the distance dij is greater than Gi,
then Costij is set to zero and the correspondence will be
ignored. For each of cells in the current frame, we select
the track with the highest Cost value among the N tracks
in the last frame and then assign the cell the same label
with the track. Sin ce the assignment between a cell and a
track is a one to one relationship , a process of optimizing
is essential when more than one cell tend to be associated
with the same track. Hungarian algorithm [28] is an ef-
fective solution to obtain the optimal assignment in our
case, and is applied in this study. In our experiments,
most of cells nearly maintain th eir positions between two
frames. Therefore, lower threshold Gi can significantly
reduce the computational time since majority of cells are
unnecessary to be considered. The marked lazy cells are
presented in Figure 3.
4.2. Active Cells Associat ion by Graph Theory
After having successfully tracked lazy cells, which can
provide the essential topology information about the
neighbors of the unmatched active cells, we now will
focus on the unmatched cells pairs. The term of an un-
matched cells pair represents an unmatched cell in the
current frame and the one in previous frame.
Two phases are correlated with the linking of two un-
matched cells pairs in consecutive frames. Firstly, a
search region is assigned to each of the unmatched cells
pairs. If the neighbors in the search region of an un-
matched cells pair are the same in the consecutive frames,
the two unmatched cells pairs are claimed as associated.
In other words, the unmatched cells pair should have the
same number of neighbors that are similar in directional
positions. The directional position
(a)
(b)
Figure 3. (a) All marked cells in the previous frame; (b)
Marked lazy cells in the current frame.
is measured by calculating the difference of degree val-
ues of each correlated neighborhood pair [39]:
k1
,( ),'()
(( ),( ))
k
F RiFR j
Diff AnglekAnglek
θ
ε
+
<
(9)
where Fk and Fk+1 denote the index of frames, R(i) and
R'(j) compose an unmatched cells pair, k is the index of
the correlated neighbors in the neighborhood group, and
Angle indicates the degree value of neighbor in a space
centered on the unmatched cells pair. Figure 4 illustrates
an example of AngleFk ,R(i)(k) which is represented by
D(k).
Then, for the rest of unmatched cells, the neighbors of
the unmatched cells pair with the same label are called as
Share Source Neighborhoods (SSN). The likelihood of a
cell pair is evaluat e d by [39]:
(( ),'())
(( ),'())(( ),'())
dist SSN
QRi Rj
QRi R jQRi Rj= ×
(10)
where
(( ),'())
(( ),'())(( ),'())
[]
dist
DS
QRiR j
DistR iRjSize R iRj
exp
αβ
δδ
××
=−−
1
,( ),'()
1
((),'())
(( ))(( ))
kk
SSN
MF RikFRjk
k
QRi Rj
Angle DAngle D
exp
nbr
θ
αβ
δ
+
=

=
L. P. OUYANG ET AL.
Copyright © 2013 SciRes. ENG
230
Figure 4. The unmatched cells pair is centered in the axes.
D(k) represents the angle of each correlated neighbor.
Qdist is the measurement of internal attributes of the pair,
such as the similarity of size and location. QSSN is used to
measure the likelihood of the topology between their
neighbors. Dist and Size are the differences of distance
and size between R(i) and R'(j). αk and βk are the corre-
lated neighbors from the set of SSN. Besides, constants
δD, δS, and δθ are used to set the sensitivity of Q to each
factors. Cells pairs with largest Q values would be
matched. This matching process will b e repeated until no
pair can be matched.
5. Experimental Results
In this research, we have applied our new Cell Segmen-
tation and Tracking system to two different sets of data,
which were recor ded by our microflui dic platf o rm.
Table 1 illu strates that although temporal efficiency of
the Region-Scalable Fitting (RSF) model is lower than
those of classic algorithms, its accuracy after ellipse fit-
ting is generally higher than those of other methods in
our experiments. Considering our application is not real-
time required, we select RSF model to provide better
segmentation results. Compared with other methods,
RSF model achieves not only higher segmentation accu-
racy but also better segmented contours. The results of
our experiment, as presented in Figure 5, show that the
watershed transform results in over-segmentation inside
the cells; the graph cuts fails to detect some cells and
some obtained contours are incorrect; the edge detector
could not obtain closed contours if the edges are not sa-
lient; while the contours produced by the RSF model are
smooth and closed.
The trajectories of DataSet 1 and DataSet 2 produced
by data association based on graph theory are presented
in Figures 6 and 7. The overall tracking accuracy on
DataSet 1 and DataSet 2 are 86.7% and 91.04%, re-
spectively.
6. Conclusions
In this research, we have conducted study on trajectory
extraction based on image segmentation and data associ-
Table 1. Comparison between RSF and other classical seg-
mentation method.
DataSet 1 DataSet 2
Fail False Time Fail False Time
Edge Detection 3.0 0.8 0.5326 0.66 0.33 0.5127
Watershed 3.05 0.85 0.6672 0.93 2.4 0.6421
Graph cuts 12.9 1.5 1.7660 NaN NaN NaN
RSF model 1.75 0 10.541 0.7 0.4 10.717
a. Fail denote the average number of cells failed to be segmented; b. False
means the av erage number of regions improperly recognized; c. Time is the
average time usag e; d. NaN means the algorit hm is unable to det ect cells in
the dataset.
(a) (b)
(c) (d)
Figure 5. The comparison of results by different segmenta-
tion techniques on Dataset 1. (a) Segmented by watershed
transform on the gradient magnitude; (b) Segmented by
graph cuts; (c) Segmented by canny edge detector; (d) Seg-
mented by RSF m od el.
(a)
(b)
(c)
Figure 6. The results of applying the new Cell Segmentation
and Tracking system to DateSet 1: (a) At frame 3; (b) At
frame 14; (c) At frame 38.
L. P. OUYANG ET AL.
Copyright © 2013 SciRes. ENG
231
(a)
(b)
(c)
Figure 7. The results of applying the new Cell Segmentation
and Tracking system to DateSet 2: (a) At frame 2; (b) At
frame 22; (c) At frame 45.
ation in order to provide a solution for rapid microfluidic
cell immigration experiments. We applied region scala-
ble active contour model to segment the individual cells
and the ellipse fitting technique to process touching cells.
We have also introduced a topology based technique to
associate the cells between consecutive frames.
By applying our new Cell Segmentation and Tracking
system to two different sets of data recorded by micro-
fluidic device, we have came up with some encouraging
outcome. The overall tracking accuracy on two sets of
data is 86.7% and 91.04%, respectively.
REFERENCES
[1] C. Zimmer, E. Labruyere, V. Meas-Yedid, N. Guillen and
J. C. Olivo-Marin, Segmentation and Tracking of Mi-
grating Cells in Videomicroscopy with Parametric Active
Contours: A Tool for Cell-Based Drug Testing,” IEEE
Transactions on Medical Imaging, Vol. 21, No. 10, 2002,
pp. 1212-1221.
http://dx.doi.org/10.1109/TMI.2002.806292
[2] S. Kim, H. J. Kim and N. L. Jeon, “Biological Applica-
tions of Microfluidic Gradient Devices,” Integrative Bi-
ology, Vol. 2, 2010, pp. 584-603.
http://dx.doi.org/10.1039/c0ib00055h
[3] F. Lin, Chapter 15. A Microfluidics-Based Method for
Chemoattractant Gradients,” Methods in Enzymology, Vol.
461, 2009, pp. 333-347.
http://dx.doi.org/10.1016/S0076-6879(09)05415-9
[4] F. Li n and E. C. Butcher, T Cell Chemotaxis in a Simple
Microfluidic Device,” Lab on a Chip, Vol. 6, 2006, pp.
1462-1469. http://dx.doi.org/10.1039/b607071j
[5] S. Beucher and C. Lantuejoul, Use of Watersheds in
Contour Detection,” International Workshop on Image
Processing: Re al-Time Edge and Motion Detec-
tion/Estimation, Rennes, 1979.
[6] L. Vincent and P. Soille, Watersheds in Digital Spaces:
An Efficient Algorithm Based on Immersion Simulations,”
IEEE Transactions on Pattern Analysis and Machine In-
telligence, Vol. 13, No. 6, 1991, pp. 583-598.
http://dx.doi.org/10.1109/34.87344
[7] R. C. Gonzalez and R. E. Woods, Digital Image
Processing,” 2nd Edition, Addison-Wesley Longman
Publishing Co., Inc., Boston, 2001.
[8] P. Bonnin, J. B. Talon, J C. Hayot and B. Zavidovique,
“A New Edge Point/Region Cooperative Segmentation
Deduced from a 3d Scene Reconstruction Application,”
SPIE Applications of Digital at Image Processing XII,
Vol. 1153, 1990, pp. 579-591.
http://dx.doi.org/10.1117/12.962359
[9] P. C. Chen and T. Pavlidis, Image Segmentation as an
Estimation Problem,” Computer Graphics and Image
Processing, Vol. 12, No. 2, 1980, pp. 153-172.
http://dx.doi.org/10.1016/0146-664X(80)90009-X
[10] A. Tremeau and N. Borel, “A Region Growing and
Merging Algorithm to Color Segmentation,” Pattern
Recognition, Vol. 30, No. 7, 1997, pp. 1191-1203.
http://dx.doi.org/10.1016/S0031-3203(96)00147-1
[11] T. Sandor, D. Metcalf and Y.-J. Kim, Segmentation of
Brain ct Images Using the Concept of Region Growing,”
International Journal of Bio-Medical Computing, Vol. 29,
No. 2, 1991, pp. 133-147.
http://dx.doi.org/10.1016/0020-7101(91)90004-X
[12] R. Adams and L. Bischof, “Seeded Region Growing,”
IEEE Transactions on Pattern Analysis and Machine In-
telligence, Vol. 16, No. 6, 1994, pp. 641-647.
[13] G. B. Coleman and H. C. Andrews, “Image Segmentation
by Clustering,” Proceedings of the IEEE, Vol. 67, No. 5,
1979, pp. 773-785.
http://dx.doi.org/10.1109/PROC.1979.11327
[14] D. Comaniciu and P. Meer, Mean Shift Analysis and
Applications,” The Proceedings of the Seventh IEEE In-
ternational Conference on Computer Vision, Vol. 2, 1999,
pp. 1197-1203.
[15] D. Comaniciu and P. Meer, Mean Shift: A Robust Ap-
proach toward Feature Space Analysis,” IEEE Transac-
tions on Pattern Analysis and Machine Intelligence, Vol.
24, No. 5, 2002, pp. 603-619.
http://dx.doi.org/10.1109/34.1000236
[16] A. K. Jain, M. N. Murty and P. J. Flynn, Data Clustering:
A Review,” ACM Computing Surveys, Vol. 31, No. 3,
1999, pp. 264-323.
http://dx.doi.org/10.1145/331499.331504
[17] M. Kass, A. Witkin and D. Terzopoulos, Snakes: Active
Contour Models,” International Journal of Computer Vi-
sion, Vol. 1, No. 4, 1988, pp. 321-331.
L. P. OUYANG ET AL.
Copyright © 2013 SciRes. ENG
232
http://dx.doi.org/10.1007/BF00133570
[18] V. Caselles, R. Kimmel and G. Sapiro, Geodesic Active
Contours,” 1997.
[19] T. Kanade and K. Li, Tracking of Migrating and Proli-
ferating Cells in Phase-Contrast Microscopy Imagery for
Tissue Engineering,” In: Y. X. Liu, T. Z. Jiang and C. S.
Zhang, Eds., Computer Vision for Biomedical Image Ap-
plications, Volume 3765 of Lecture Notes in Computer
Science, Springer, Berlin, Heidelberg, 2005, pp. 24-24.
[20] S. K. Nath, K. Palaniappan and F. Bunyak, Cell Seg-
mentation Using Coupled Level Sets and Graph-Vertex
Coloring,” Medical Image Computing and Comput-
er-Assisted Intervention, Vol. 9, Pt. 1, 2006, pp. 101-108.
[21] K. Li, E. D. Miller, M. Chen, T. Kanade, L. E. Weiss and
P. G. Campbell, “Cell Population Tracking and Lineage
Construction with Spatiotemporal Context,” Medical Im-
age Analysis, Vol. 12, No. 5, 2008, pp. 546-566.
http://dx.doi.org/10.1016/j.media.2008.06.001
[22] K. Li, E. D. Miller, L. E. Weiss, P. G. Campbell and T.
Kanade, “Online Tracking of Migrating and proliferating
Cells Imaged with Phase-Contrast Microscopy,” Confe-
rence on Computer Vision and Pattern Recognition
Workshop, 2006, pp. 65-65.
[23] D. Padfield, J. Rittscher, N. Thomas and B. Roysam,
Spatio-Temporal Ce ll Cycle Pha se Analy sis Using Level
Sets and Fast Marching Methods,” Medical Image Analy-
sis, Vol. 13, No. 1, 2009, pp. 143-155.
http://dx.doi.org/10.1016/j.media.2008.06.018
[24] D. B. Reid, An Algorithm for Tracking Multiple Tar-
gets,” IEEE Transactions on Automatic Control, Vol. 24,
1979, pp. 843-854.
http://dx.doi.org/10.1109/TAC.1979.1102177
[25] T. Fortmann, Y. Bar-Shalom and M. Scheffe, “Mul-
ti-Target Tracking Using Joint Probabilistic Data Associ-
ation,” 19th IEEE Conference on Decision and Control,
1980, pp. 807-812.
[26] Y. Bar-Shalom, Multitarget-Multisensor Tracking: Ad-
vanced Applications,” Artech House, Norwood, 1990,
391 Pages.
[27] I. J. Cox, “A Review of Statistical Data Association
Techniques for Motion Correspondence,” International
Journal of Computer Vision, Vol. 10, 1993, pp. 53-66.
http://dx.doi.org/10.1007/BF01440847
[28] H. W. Kuhn, The Hungarian Method for the Assignment
Problem,” Naval Research Logistic Quarterly, Vol. 2,
1955, pp. 83-97.
http://dx.doi.org/10.1002/nav.3800020109
[29] Y. Bar-Shalom and T. E. Fortmann, Tracking and Data
Association, Volum e 179 of Mathematics in Science and
Engineering,” Academic Press Professional, Inc., San
Diego, 1987.
[30] F. Lin a nd E. C. Butcher, T Cell Chemotaxis in a Simple
Microfluidic Device,” Lab on a Chip, Vol. 6, 2006, pp.
1462-1469. http://dx.doi.org/10.1039/b607071j
[31] T. F. Chan and L. A. Vese, Active Contours without
Edges,” IEEE Transactions on Image Processing, Vol. 10,
No. 2, 2001, pp. 266-277.
http://dx.doi.org/10.1109/83.902291
[32] C. M. Li , C.-Y. Kao, J. C Gore and Z. H. Ding, Minimi-
zation of Region-Scalable Fitting Energy for Image Seg-
mentation,” IEEE Transactions on Image Processing, Vol.
17, No. 10, 2008, pp. 1940-1949.
http://dx.doi.org/10.1109/TIP.2008.2002304
[33] V. Caselles, F. Catté, T. Coll and F. Dibos, “A Geometric
Model for Active Contours in Image Processing,” Nume-
rische Mathematik, Vol. 66, No. 1, 1993, pp. 1-31.
http://dx.doi.org/10.1007/BF01385685
[34] O. Al-Kofahi, R. J. Radke, R. K. Goderie, Q. Shen, S.
Temple and B. Roysam, Automated Cell Lineage Con-
struction: A Rapid Method to Analyze Clonal Develop-
ment Established with Murine Neural Progenitor Cells,”
Cell Cycle, Vol. 5, No. 3, 2006, pp. 327-335.
http://dx.doi.org/10.4161/cc.5.3.2426
[35] W. M. Yu, H. K. Lee, S. Hariharan, W. Y. Bu and S.
Ahmed, Level Set Segmentation of Cellular Images
Based on Topological Dependence,” In Proceedings of
the 4th International Symposium on Advances in Visual
Computing, ISVC ’08, pages 540-551, Springer-Verlag,
Berlin, 2008.
[36] G. Zhang, D. S. Jaya s and N. D. G. White, Separation of
Touching Grain Kernels in an Image by Ellipse Fitting
Algorithm,” Biosystems Engineering, Vol. 92, No. 2,
2005, pp. 135-142.
http://dx.doi.org/10.1016/j.biosystemseng.2005.06.010
[37] J. Hukkanen, A. Hategan, E. Sabo and I. Tabus, Seg-
mentation of Cell Nuclei from Histological Images by El-
lipse Fitting,” Proceedings of the European Signal
Processing Conference, Aalborg, Denmark, 2010, pp.
1219-1223.
[38] A. Fitzgibbon, M. Pilu and R. B. Fisher, Direct Least
Square Fitting of Ellipses,” IEEE Transactions on Pattern
Analysis and Machine Intelligence, Vol. 21, No. 5, 1999,
pp. 476-480. http://dx.doi.org/10.1109/34.765658
[39] L. L. Zhang, H. K. Xiong, K. Zhang and X. B. Zhou,
“Graph Theory Application in Cell Nuleus Segmentation,
Tracking and Identification,” Proceedings of the 7th IEEE
International Conference on Bioinformatics and Bioen-
gineering, 2007, pp. 226-232.