3D CONFOCAL MICROSCOPY DATA ANALYSIS USING

LEVEL-SET SEGMENTATION WITH ALPHA DIVERGENCE

SIMILARITY MEASURE

Leila Meziou

, Aymeric Histace

, Fr´ed´eric Precioso

, Bogdan J. Matuszewski

and Franck Carreiras

ETIS UMR 8051 CNRS /ENSEA/ Cergy-Pontoise University, 95000 Cergy, France

I3S - UMR 6070 - CNRS/Nice Sophia Antipolis University, France

ADSIP Research Centre, University of Central Lancashire, Preston, U.K.

ERRMECe, Cergy-Pontoise University, 95000 Cergy, France

Keywords:

Image Segmentation, Active Contours, Alpha-divergence, Level-set, Confocal Microscopy.

Abstract:

Segmentation of cellular structures is of primary interest in cell imaging for a 3D reconstruction of cell shape.

Such an analysis provides crucial information about cell morphology and is instrumental in understanding

of biological processes leading to development of a particular pathology. The work presented in this paper

reports on a novel method for segmentation of cellular structures (nuclei and cell boundaries) from 3D single

channel actin tagged ﬂuorescence confocal microscopy images. The proposed segmentation method uses

histogram-based image similarity measure in a level-set active-contour framework. The novelty of the method

is in application of the alpha-divergence distance measure which can be seen as a generalization of classic

Kullback-Leibler and χ

measures. The resulting alpha-divergence level-set formulation leads to a single front

evolution formula for both nuclei and cell boundaries segmentation, with no requirements for any enhancement

or preprocessing of acquired cell images (a monolayer of human cells (PNT2) culture).

1 INTRODUCTION

Segmentation of cellular structures is an essential tool

in cell imaging as it enables measurements which can

be used to track cell divisions or help to reconstruct

corresponding cell lineage tree providing data for cal-

culation of different parameters like cell proliferation

rate for instance. More speciﬁcally, the work pre-

sented in this paper has been carried out in a con-

text of analyzing changes of cell cytoskeleton prop-

erties in a response to ionizing radiation insult. The

ﬁnal goal of this research effort is to better under-

stand cell bio-mechanical responses during cancer ra-

diation therapy. Indeed, actin tagged ﬂuorescence

confocal microscopy imaging enables to character-

ize important properties of cytoskeleton, in particu-

lar actin ﬁlaments which are involved in many cellu-

lar processes like cell adhesion, locomotion, inter-cell

transport and general cell structural integrity, to name

a few. Nevertheless, due to a highly complex actin

appearance, a high level of noise and a strong non-

homogeneity of intensity and gradient information,

the segmentation of cell structures in such imaging

data, is a very challenging task. In this context, we

propose a (quasi-)automatic segmentation approach,

reducing to a minimum manual interventions – which

represent practical bottleneck when considering many

monolayer acquisition – in order to extract nuclei and

cell boundaries that provide spatial reference frame

for analyzing cytoskeleton changes.

To date, only few methods propose to address seg-

mentation of cell structures in ﬂuorescence confocal

microscopy images (FCMI). In former approach pro-

posed in (Ortiz De Solorzano et al., 1999), authors fo-

cused on nuclei segmentations. In (Yan et al., 2008)

authors proposed cell segmentation in 2D-ﬂuorescent

images with two channels (actin and nucleus tag-

ging) using a multiphase level-set combining Chan-

Vese (Chan and Vese, 2001) and geodesic active

contour models, together with repulsive force intro-

duced to prevent segmented cells from overlapping.

In (Mosaliganti et al., 2009; Zanella et al., 2010),

automated 3D cell segmentation from 3D confocal

acquisition of early Zebraﬁsh embriogenesis is pro-

posed, two different ﬂuorescent markers (red for nu-

clei and green for membrane) are used to easily dis-

405

Meziou L., Histace A., Precioso F., J. Matuszewski B. and Carreiras F..

3D CONFOCAL MICROSCOPY DATA ANALYSIS USING LEVEL-SET SEGMENTATION WITH ALPHA DIVERGENCE SIMILARITY MEASURE.

DOI: 10.5220/0003820004050409

In Proceedings of the International Conference on Computer Vision Theory and Applications (VISAPP-2012), pages 405-409

ISBN: 978-989-8565-03-7

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

criminate nuclei from cell membranes. In (Zanella

et al., 2010), authors introduced an adapted version

of the subjective surface technique (Sarti et al., 2002)

for surface reconstruction from missing boundary in-

formation whereas (Mosaliganti et al., 2009) use a

multiphase level-set based on propability correlation

functions.

Although our method is somewhat similar to (Yan

et al., 2008; Mosaliganti et al., 2009) focusing on

level-set framework, the objective is different since

our microscopic 2D images are extracted from a 3D

single channel confocal acquisition with only one ﬂu-

orescent marker used for actin tagging making it a

more challenging problem. Nuclei and cell bound-

aries segmentations are considered as two separate

tasks but both use the same Partial Differential Equa-

tion (PDE) describing evolution of the active contour.

Finally, as it will be shown, no enhancement or pre-

processing will be required to segment acquired im-

ages.

The data used in this paper were obtained from

human prostate cells (PNT2). Once conﬂuent cells

were ﬁxed, actin were labelled with phalloidin-FITC

according to the manufacturers instructions (Invitro-

gen, UK). All imaging was carried out using a Zeiss

LSM510 confocal microscope. Fig. 1 shows some

images extracted at different slice levels from the

3D microconfocalacquisition of the monolayer PNT2

cell culture. The stack volume is deﬁned on the

512×512×98grid of pixels each 0.21µm × 0.21 µm

× 0.11 µ in size.

The remaining of this paper is organized as fol-

lows: in Section 2, the alpha-divergence measure

and our histogram-based active contour segmentation

approach are explained together with the derivation

of the corresponding governing PDE in the level-set

framework; Section 3 focuses on experiments fol-

lowed by conclusions drawn in Section 4.

2 THEORETICAL FRAMEWORK

Originally proposed in (Kass et al., 1988), the basic

idea of the active contour is to iteratively evolve an

initial curve towards the boundaries of target objects

driven by the combination of internal forces, deter-

mined by the geometry of the evolving curve, and ex-

ternal forces, induced from the image. Image segmen-

tation methods using active contour are often derived

from a variational principle in which a functional de-

ﬁned on contours encodes our knowledge about de-

sirable solution. The functional minimization leads to

a partial differential equation (PDE), constructed as

the Gateaux derivative gradient ﬂow which steers the

evolution of the active contour.

In the particular framework of a region-based ac-

tive contour segmentation (Aubert et al., 2003) ,

several functional deﬁnitions have been proposed to

take into account the Probability Density Functions

(PDFs) of both the inner and outer regions of the

evolving curve. The corresponding variational crite-

rion is based on the minimization of a distance be-

tween PDFs calculated for the inner and outer regions

as deﬁned by the evolving contour and predeﬁned

reference PDFs of targeted and background objects.

Common distances used to compare PDFs are, for in-

stance, the χ

distance (Aubert et al., 2003) or the

Kullback-Leibler divergence (Lecellier et al., 2010).

In this paper, we propose an original histogram-based

active contour approach integrating alpha-divergence

as distance to minimize between two PDFs which can

be estimated parametrically or not. Let ˆq denotes an

estimated PDF and p a reference one for a particular

region Ω extracted from the image. As ˆq represent the

current PDF, it is non-parametrically estimated using

Parzen window method. This choice is motivated by

the fact that ˆq has to be differentiable for the next cal-

culation step of the minimization scheme. Distance

between ˆq and p using the alpha-divergences is now

deﬁned as follows (Beirami et al., 2008):

( ˆqkp, Ω) =

ℜ

( ˆq(λ, Ω), p(λ))dλ , (1)

with ϕ

the cost function related to alpha-divergence

measure deﬁned by:

( ˆq(λ, Ω), p(λ)) =

α(1− α)



α ˆq(λ, Ω)+ (1− α)p(λ)

− [ ˆq(λ, Ω)]

[p(λ)]

1−α



, (2)

where α ∈ ℜ.

A complete study about the mathematical properties

of alpha-divergence can be found in (Beirami et al.,

2008). Nevertheless, considering Eq. (2), for spe-

ciﬁc values of α, some aforementioned standard dis-

tances can be connected to alpha-divergences, for in-

stance: D

(Ω) =

(Ω), D

(Ω) = 2D

Hellinger

(Ω),

(Ω) =



lim

α→0

(Ω) + lim

α→1

(Ω)



In the general framework of the histogram-based

active contours the alpha-divergence functional can

now be deﬁned as follows for grayscale images (n =

1):

(Γ, Ω

, Ω

out

) = ξ

ℜ

( ˆq(λ, Ω

), p

(λ))dλ

+ ξ

out

ℜ

( ˆq(λ, Ω

out

), p

out

(λ))dλ

+ β

ds (3)

VISAPP 2012 - International Conference on Computer Vision Theory and Applications

406

where Ω

and Ω

out

are respectively the foreground

(targeted object) and the background areas, Γ the

evolving boundary between Ω

and Ω

out

and ξ

, ξ

out

and β three positive weighting parameters. Consid-

ering now the standard level-set embedding function

U of J

, the Lagrangian minimization scheme of J

leads to the following associated PDE for active con-

tour evolution:

∂U

∂t

= δU



β∇·



∇U

|∇U|



−

|Ω

−C

)

out

|Ω

out

−C

out

)



, (4)

with

= ∂

( ˆq(λ, Ω

), p

(λ)) ∗ g

(I(x)), (5)

ℜ

∂

( ˆq(λ, Ω

), p

(λ)) ˆq(λ, Ω

)dλ,

where i = {in, out} and ∂

denotes the ﬁrst deriva-

tive order of ϕ

function with respect to ˆq, g

is the

Gaussian kernel (with standard-deviation σ) used in

the Parzen window estimation of ˆq, I is the intensity

function of the segmented image at a pixel x. The

implementation of Eq. (4) is achieved with a semi-

implicit version of the Additive Operator Splitting

scheme.

3 EXPERIMENTAL RESULTS

In order to achieve the automatic segmentation of

both nuclei and cell boundaries, inner and outer refer-

ence PDFs, corresponding to the targeted structures,

are computed applying a standard three class (for

cell boundaries, cytoplasm and nucleus) Expectation-

Maximization (EM) algorithm on the equator slice

of the PNT2 acquisition. This rough classiﬁca-

tion is good enough to deﬁne the reference PDFs

using Parzen window technique: the strategy is

then one class (“nucleus”, resp. “cell boundaries”)

against the two others (“cell boundaries+cytoplasm”,

resp.“nucleus+cytoplasm”). The segmentation pro-

cess is initialized on the equator slice (Fig. 1 mid col-

umn) through the monolayer. For both nuclei and cell

boundaries segmentations, the zero level-set initial-

ization of the function U

is given as a set of small

circles uniformly distributed across the whole slice.

Finally, the segmentation process is spread all along

the different slice level of the monolayer.

Fig. 1 summarizes results obtained for different

slices from the acquired 3D image stack and for dif-

ferent values of the parameter α. All tests are done

with the same optimal parameters ξ

(here ξ

= ξ

out

)

and β for both nuclei and cell boundaries (empirically

tuned on the equator slice image) in order to focus on

analysis the inﬂuence of the α parameter only.

Considering nuclei segmentation, as shown in

Fig. 1 in green, thanks to the level-set formulation

and to the integration of alpha-divergence measures,

all nuclei are detected during a single run of the algo-

rithm, even those with incomplete shape (at the bor-

der of image). This is a major advantage when com-

paring with the Chan-Vese approach which needs to

be carefully adapted (in its regularized form) to per-

form the same task as shown in some of our previ-

ous work (Meziou et al., 2011) on that topic. It is

also important to notice that the more accurate results

are obtained with non-standard values of α as shown

in Figs. 1. (b). where α = 0.75. The real difﬁculty

is to obtain a robust segmentation result of each nu-

cleus to avoid small structures segmentation within

cytoplasm reﬂecting the complexity of the cytoplasm-

nucleus boundary. For the higher values, false detec-

tions could appear and non signiﬁcant small structures

are segmented as shown in Figs. 1. (e).

For each slice segmentation, an expert can man-

ually suppress false detected nuclei that can occur

when a hole representing an empty space between

cells is present in the cell culture for instance: Sta-

tistically speaking, the PDF of a hole is very close to

the PDF of a nucleus and can be difﬁcult to differen-

tiate automatically.

In the case of cell boundaries, shown in red in

Fig. 1, segmentation is more demanding since even

for experts it is not always easy to visually identiﬁed

them: the non-homogeneity of the actin ﬂuorescent

marker can strongly inﬂuence the pixel levels corre-

sponding to cell boundaries which could explain dif-

ﬁculties to get continuous contours. Results obtained

are similar to those obtained with Chan and Vese seg-

mentation which performed well for this particular

task and can be considered as a reference for that kind

of single channel acquisition. However, major advan-

tage of the proposed approach for cell boundaries seg-

mentation is the use of the same evolution criterion

(alpha-divergence measure) for both cell boundaries

and nucleus segmentations. Inﬂuence of the α param-

eter, as for nuclei segmentation, is interesting since

it can be noticed again that the most interesting re-

sults are obtained for a value of α that does not cor-

respond to standard histogram distance measures. In

terms of cell boundaries segmentation, the proposed

results have to be considered as prospective ones but

very encouraging. From an expert point of view, the

best results are obtained for a high value of α (for ex-

ample α = 1.5 shown in Figs. 1.(d)).

3D CONFOCAL MICROSCOPY DATA ANALYSIS USING LEVEL-SET SEGMENTATION WITH ALPHA

DIVERGENCE SIMILARITY MEASURE

407

(a) α = 0.5.

(b) α = 0.75.

(d) α = 1.5.

(e) α = 2.

Figure 1: Segmentation of cell nuclei (in green) and cell

boundaries (in red) with different values of α (row) and for

different slice index in the acquired 3D image stack (col-

umn, from left to right slices from bottom, middle, and top

of the stack).

4 CONCLUSIONS

In this paper a novel histogram based level-set ac-

tive contours method is proposed for segmentation

of nuclei and cell boundaries in 2D images from a

3D single channel confocal microscopic acquisition

of a PNT2 cells monolayer. Introduction of alpha-

divergence measure within the variational framework

leads to a single evolution PDE for segmentation of

both nuclei and cell boundaries. The segmentation re-

sults obtained for the nuclei and cell boundaries, show

that the method enables to control in an efﬁcient way

a range of distances that can be used in very different

segmentation scenarios. Moreover, compared to pre-

vious works, the proposed method does not require

any enhancement or preprocessing since the perfor-

mance of alpha-divergence measure can be adapted

to the level of the corrupting noise and if expert man-

ual interactions are permitted, they can be reduced to

a minimum. Additionally, as already mentioned, the

cell structure segmentation could be achieved in the

particular case where only actin is tagged in opposi-

tion to other recent studies reported in the literature.

It is envisaged that the future work will include: (i)

improvement of cell boundaries segmentation using a

local adaptation of α parameter based on noise char-

acteristics of each classes , and (ii) development of a

joint nuclei and cell boundaries 3D segmentation.

ACKNOWLEDGEMENTS

This work was supported by the UK Engineering and

Physical Sciences Research Council [TeRaFS project,

grant number EP/H024913/1].

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DIVERGENCE SIMILARITY MEASURE

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