Generation of digital phantoms of cell nuclei and simulation of image formation in 3D image...

Generation of Digital Phantoms of Cell Nuclei and

Simulation of Image Formation in 3D Image Cytometry

David Svoboda, Michal Kozubek, Stanislav Stejskal

� AbstractImage cytometry still faces the problem of the quality of cell image analysis results.Degradations caused by cell preparation, optics, and electronics considerably affectmost 2D and 3D cell image data acquired using optical microscopy. That is why imageprocessing algorithms applied to these data typically offer imprecise and unreliableresults. As the ground truth for given image data is not available in most experiments,the outputs of different image analysis methods can be neither verified nor comparedto each other. Some papers solve this problem partially with estimates of ground truthby experts in the field (biologists or physicians). However, in many cases, such a groundtruth estimate is very subjective and strongly varies between different experts. To over-come these difficulties, we have created a toolbox that can generate 3D digital phan-toms of specific cellular components along with their corresponding images degradedby specific optics and electronics. The user can then apply image analysis methods tosuch simulated image data. The analysis results (such as segmentation or measurementresults) can be compared with ground truth derived from input object digital phantoms(or measurements on them). In this way, image analysis methods can be comparedwith each other and their quality (based on the difference from ground truth) can becomputed. We have also evaluated the plausibility of the synthetic images, measured bytheir similarity to real image data. We have tested several similarity criteria such as vis-ual comparison, intensity histograms, central moments, frequency analysis, entropy,and 3D Haralick features. The results indicate a high degree of similarity between realand simulated image data. ' 2009 International Society for Advancement of Cytometry

� Key termsdigital phantom; synthetic image; procedural texture; point spread function; fluores-cence optical microscope; 3D image cytometry

CURRENT biomedical research relies strongly on computer-based evaluation, as the

vast majority of commonly used acquisition techniques produce large numbers of

numerical or visual data. Each individual technique (optical microscopy, PET, MRI,

CT, ultrasound, etc. (1)) has its advantages that make it suitable for use in selected

fields of research. However, each technique also has its own drawbacks (blur, noise,

various aberrations) (2–4). In this sense, one should keep in mind that biomedical

data supplied by scientific or diagnostic instruments always suffer from some imper-

fection and therefore cannot be directly used for further analysis, evaluation or mea-

surement. To guarantee more accurate results, some preprocessing is required.

Let us focus on the area of image reconstruction. Here, the search for ground

truth approximation is called an image restoration (5–7), and it constitutes the best

possible method for image recovery. It is done in time-reverse order; that is, the

image defect caused by the phenomenon that appeared in the whole acquisition pro-

cess as the first one must be eliminated as the last one. The same holds for the sec-

ond, the third and the following defects. As soon as the captured image is restored, it

can be further submitted to measurement or segmentation algorithms. If all the

defects and the noise were removed during image restoration, we should get the

Centre for Biomedical Image Analysis,Botanicka 68a, Faculty of Informatics,Masaryk University, 602 00 Brno, CzechRepublic

Received 16 May 2008; Revision Received10 October 2008; Accepted 3 February2009

Additional Supporting Information may befound in the online version of this article.

Contract grant sponsor: Ministry ofEducation of the Czech Republic;Contract grant numbers: LC535, 2B06052.

*Correspondence to: D. Svoboda, Centrefor Biomedical Image Analysis,Botanicka 68a, Faculty of Informatics,Masaryk University, 602 00 Brno, CzechRepublic

Email: [email protected]

Published online 16 March 2009 inWiley InterScience (www.interscience.wiley.com)

DOI: 10.1002/cyto.a.20714

© 2009 International Society forAdvancement of Cytometry

Original Article

Cytometry Part A � 75A: 494�509, 2009

original unaffected ground truth image data as well as derived

ground truth analysis results. In practice, this is not possible.

The task is too complex, so the imperfection is diminished

rather than totally pruned away. Moreover, due to the non-

existence of ground truth image data, it is difficult to judge

whether the restoration has been done correctly and hence

whether the final evaluation is valid.

Let us avoid searching for inverse sequences and instead

try to follow the chronological order, that is, the acquisition

process. First, let us create a digital phantom of an object that

we want to observe. Then let us submit this object to all the

phenomena that appeared during the real acquisition. The

final synthetic image will be very similar to the image acquired

under real conditions. In this way, we design a simulator: a

tool for digital phantom generation and simulation of its

acquisition. A user can then use the simulator to evaluate the

correctness of various image restoration (or image analysis)

algorithms by comparing their results with ground truth

image data (or ground truth analysis results) derived from the

digital phantom (see Fig. 1).

It is noteworthy that the quality of each simulator

depends strongly on the demands of its designer. The simula-

tor can be simple or very sophisticated. At present, the simula-

tors appear in nearly every field of biomedical research.

Although many authors designed their simulators as compact

toolboxes, the simulation process can always be split into three

principal parts: (I) digital phantom object generation, (II)

simulation of signal transmission, and (III) simulation of sig-

nal detection and image formation.

(I) Phantom Generation

Macroscopic objects like the kidneys, heart, brain, mus-

cles, or blood vessels are examples of objects that are relatively

easy to model, as their shape and behavior are well under-

stood. The problem is to choose the model that fits the

observed data to the greatest extent possible. Generation of

the static models has already been studied extensively when

creating the reference phantom image for the brain (8–12).

Jensen et al. proposed simple models of the kidneys and the

fetus (13). When handling these types of image data, no move-

ment is expected. Completely different object types represent

the heart or blood vessels, where activity is studied and kinetic

models (14–17) are needed.

In contrast with the macroscopic world, when handling

microscopic objects like cells, the main issue is that their com-

ponents and DNA structure cannot be simply observed with

the naked eye. The observer needs a special technique in order

to acquire at least some visual draft of the studied objects. As

there are many unwanted phenomena causing image imper-

fection in this case, the final image is strongly affected by these

degradations, and some amount of image restoration is

required. Unfortunately, the process of restoration is not

exactly reciprocal to acquisition; one must admit that the

restored image is an estimate rather than the original image

data. That is why no one knows the exact shape of microscopic

structures; hence, there is no ground truth describing the exact

shape of these objects. For many microscopic objects, either

they are expected to have a very simple structure, or their

shape is deliberately simplified.

Regarding the simplest point-like objects such as FISH

(18,19) spots, Grigoryan et al. proposed a simulation toolbox

for generating large sets of spots (20). Each spot was repre-

sented by a sphere randomly placed in 3D space. Two indivi-

dual spheres were allowed to overlap, but only under specific

conditions. Manders et al. also addressed the issue of virtual

spot generation (21). They verified a novel region-growing

segmentation algorithm over a large set of Gaussian-like 3D

objects arranged in a grid.

When creating cell-like or nucleus-like objects, the algo-

rithm uses the most popular shapes, such as circles and ellipses

in 2D and spheres and ellipsoids in 3D space. To check the

quality of the new cell nuclei segmentation algorithm, Lockett

et al. (22) generated a set of artificial spatial objects in the

shape of curved spheres, ellipsoids, discs, bananas, satellite

discs, and dumbbells. Lehmussola et al. (23) designed a more

complex simulator called SIMCEP that could produce large

cell populations. However, the toolbox was designed for 2D

images only, and its extension to higher dimensions was not

straightforward. Later, Svoboda et al. (24) extended this model

to manipulate fully 3D image data, but with a limited number

of generated objects.

Up to now, the majority of authors have focused on the

design of spots or nuclei. Recently, Zhao et al. (25) designed

an algorithm for generating an entire 2D digital cell phantom.

Here, they modeled the whole cell, including the nucleus, pro-

teins, and cell membrane, using machine learning from real

data. This is a different approach than that of other studies

that use basic shapes and their deformations. The advantage

of the machine learning approach is that it might extract a

more precise shape model from real data, but the disadvantage

is that the model cannot be described in precise mathematical

terms.

Although the previously mentioned papers and articles

were interested in individual object modeling, Graner et al.

(26) focused on generating large cell populations. They

adopted the statistical large-Q Potts model to simulate the

reorganization of uniformly distributed cell-like objects to

guarantee the natural shape and distribution of the cells.

(II) Signal Transmission

The second stage covers the period during which a signal

is transmitted through the environment. One of the most typi-

cal environment characteristics is the impulse response of the

system, often called the point spread function (PSF) (2),

which is common in optical microscopy as well as in PET and

ultrasound imaging. This is the pivotal phenomenon drasti-

cally affecting the quality of the final results, and it is usually

simulated (27) by convolving the incoming signal with the

given PSF. However, the vast majority of the authors reduced

this simulation to the simple Gaussian kernel (20,21,28,29), as

it is commonly understood to be a good approximation of any

PSF. This phenomenon is not the only one affecting the trans-

ORIGINAL ARTICLE

Cytometry Part A � 75A: 494�509, 2009 495

mitted signal. In optical microscopy, for example, an incorrect

position of the light source, uneven illumination (24), chro-

matic (30) and monochromatic aberrations (31), or some

reflection or refraction on lens surfaces may create some arti-

facts as well. One should keep in mind that signal reflection

and refraction happen in other modalities as well. Ultrasound

imaging is an example of a technique using these phenomena.

(III) Signal Detection and Image Formation

The final stage corresponds to the detection of the signal

with the device sensors and its conversion to the digital repre-

sentation, which naturally has some problems. The use of

sensors introduces Poisson noise (22,23,27,28), which is an

artifact typically seen even with the naked eye. Aside from

Poisson noise, the A/D converter and amplification electronics

introduce a certain level of additive white Gaussian noise

(22,29). If the equipment is not properly cooled, the level of

dark current noise increases. The CCD detectors, for example,

are well known for their fixed-pattern noise and blooming

effect. Finally, one should keep in mind that the arrangement

of the signal sensors determines the final image sampling.

Examples of Simulators

Depending on the acquisition device, simulators can eas-

ily be split into several groups: optical microscopy, CT, PET,

MRI, and ultrasound imaging (see Table 1).

Figure 1. Quality control (QC) in biomedical image data processing and the advantage of using simulators rather than expert know-

how for this purpose. From the image processing point of view, ground truth derived from expert knowledge is imprecise and labori-

ous to obtain, whereas phantom-based ground truth is exact and easy to generate in large quantities. On the other hand, from the

biological point of view, expert-based approximate ground truth might be more precise because it corresponds to real objects, not

synthetic digital phantoms. In this article, however, we concentrate on image processing QC, not QC related to modeling a biological

system.

ORIGINAL ARTICLE

496 Generation of Digital Phantoms of Cell Nuclei and Simulation of Image Formation in 3D Image Cytometry

In the area of ultrasound imaging, Jensen et al. (13,39)

designed a very complex and flexible engine called Field II,

based on manipulation with a 3D linear acoustic field. An

alternative approach is Ultrasim (38), which could generate at

most 2D data. Unlike other authors, Wojcik et al. (41)

designed a nonlinear model of acoustic wave propagation in

tissues. In the field of elastography, D’hooge (37) focused par-

ticularly on simulating and tracking heart movement.

In the MRI area, Cocosco et al. designed a web interface

called BrainWeb (36), which also included a very useful brain

phantom database (11). Waks designed a complex cardiac

motion simulator (14), focusing on tagged MRI data.

Ma (28) found MRI phantom data very useful when

designing a PET simulator of brain images. In CT imag-

ing, Rosenberg designed a general purpose CT simulation

toolbox (34).

In optical microscopy, great progress in simulating image

data has been made mainly during the past 3 years, during

which several papers (20,23,24,33) have given straightforward

recipes or even offered useful software toolboxes. However, the

development of simulators in this area is still beginning;

hence, great progress might be expected.

In this article, we present a novel fully 3D technique

simulating the whole process of image acquisition from optical

microscopes. The whole process is split into three main inde-

pendent consecutive sub-processes: digital phantom genera-

tion, simulation of signal transmission, and simulation of

signal detection and image formation, outlining the structure

of section 3. Section 4 presents the results. In the figures, we

present the quality of our method as well. In the conclusion,

we discuss the goals that we have achieved.

REFERENCE DATA

Before starting to develop any simulation toolbox, one

should have expert knowledge or at least access to a suffi-

ciently large database of real reference data. Such a source of

information is very important: digital phantom generation is

pointless without knowledge of the nature and the structure of

the images of real objects. In particular, this knowledge is

helpful when tuning the final simulator behavior.

Equipment

In this article, the optical microscope Zeiss Axiovert

200M with Yokogawa CSU-10 confocal unit and Andor

iXon 887 back illuminated EM CCD camera connected to

standard PC were used to acquire real image data. Con-

cerning the microscope settings, the alpha Plan-Fluar objective

(1003/1.45 NA) was used.

For the time being, the simulator (developed in GNU

C/C11) can imitate an optical system comprising four differ-

ent CCD cameras (see Table 2) and four optical microscopes

(see Table 3) with two types of confocal units and various

objectives. In general, there is no restriction put on the whole

optical system; that is, the component list can be extended

Table 1. An overview of the recent toolboxes and papers dealing with the generation of phantoms of biomedical objects and

their acquisition

SIMULATED

TOOLBOX NAME AUTHOR(S) STAGES DIMS REFERENCE YEAROBJECT TECHNIQUE

Spots Fluorescence microscopy – Manders et al. I,III 3D (21) 1996

Spots Fluorescence microscopy – Grigoryan et al. I,II,III 3D (20) 2002

Nuclei Fluorescence microscopy – Lockett et al I,III 3D (22) 1998

Nuclei Fluorescence microscopy – Solorzano et al. I,II,III 3D (29) 1999

Nuclei Fluorescence microscopy – Svoboda et al. I,II,III 3D (24) 2007

Cells Fluorescence microscopy SIMCEP Lehmussola et al I,II,III 2D (23,32) 2005

Cells Fluorescence microscopy – Dufour et al. I,II,III 3D1time (33) 2003

Cells Fluorescence microscopy – Zhao et al I 2D (25) 2007

* Fluorescence microscopy SVI Huygens Voort et al. II,III 3D (27) 1995

Cells CompuCell3D Graner and Glazier I 3D1time (26) 1992

* CT CTSIM Rosenberg II,III 2D (34) 2002

Brain PET PETSIM Ma et al. II,III 3D (28) 1993

Brain MRI – Collins et al. I 3D (12) 1998

Brain MRI – Tofts et al. I 3D (8) 1997

Heart motion MRI – Waks et al. I,II,III 3D (14) 1996

Brain MRI – Rexilius et al. I 3D (9,10) 2003

Brain MRI Brain Web Kwan et al. I,II,III 3D (35,36) 1996

Tissue motion Ultrasound – Schalaikjer et al. I 3D (16,17) 1998

Heart motion Ultrasound – Rabben et al. I 3D (15) 1993

Heart motion Ultrasound – D’hooge et al. I,II,III 2D (37) 2003

* Ultrasound Ultrasim Holm II,III 2D (38) 2001

* Ultrasound Field II Jensen et al. I,II,III 3D (13,39,40) 1996

* Ultrasound – Wojcik et al. II,III 3D (41) 1997

ORIGINAL ARTICLE


arbitrarily. The only requirement is that each component has

to be described properly.

We evaluated the results with two servers. The first one

had two Intel Core 2 Quad 2.0 GHz processors, 8GB RAM

and the SUSE Linux operating system. The latter one had an

Intel Core 2 Quad 2.4 GHz processor, 4 GB RAM, and the

Microsoft Windows Server 2003 operating system. We pro-

grammed the system in Matlab (Mathworks) with the DIP-

image toolbox (Delft University of Technology, Netherlands).

Biological Material

Microspheres. TetraSpeckTM microspheres (Molecular Probes,

Eugene, OR) of 0.1 lm (T-7279), 0.2 lm (T-7280), and

0.5 lm (T-7281) diameter were used in this study. Each

microsphere is stained with four different fluorescent dyes

simultaneously: blue (365/430 nm), green (505/515 nm),

orange (560/580 nm), and dark red (660/680 nm). In this

study, we observed only the green channel. For illustration, see

Figure 2, in which the given 3D image data are visualized.

HL-60. One cell line representing tissue cultures was used:

human promyelocytic leukemia cells HL-60 (European Collec-

tion of Cell Cultures) maintained between 1 and 5 3 105 cells/

ml (see Fig. 3). These cells grow in RPMI-1640 medium con-

taining 10% fetal bovine serum, penicillin (100 U/ml), and

streptomycin (100 mg/ml) at 378C in a 5% CO2 atmosphere.

Dense suspension of cells in PBS (50–100 ll) was dropped

onto poly-L-lysine coated microscopic slides. After attachment

to the slide (about 15 min), cells were fixed with 3.7% parafor-

maldehyde in 250 mM HEPEM (RT;12 min) and washed in

13 PBS (3 3 5 min). After washing, chromatin in the cell

nuclei was stained with DAPI.

Granulocytes. Granulocytes are a category of terminally dif-

ferentiated white blood cells characterized by the presence of

granules in their cytoplasm. Granulocytes are also called poly-

morphonuclear leukocytes (PML) because of the varying

shapes of the nucleus. Human leukocytes that contain granu-

locytes (see Fig. 4) were isolated from heparinized peripheral

donor blood from healthy patients using density gradient sedi-

mentation composed from Telebrix (Guerbert, France) and a

3.8% solution of dextran (Sigma) in a 2:8 ratio. Granulocytes

were isolated from the upper layer with leukocytes using His-

topaque-1077 double gradient density centrifugation (Sigma).

Residual erythrocytes were removed by an erythrocyte lysis

buffer. Concerning fixation and staining of the granulocytes,

the same method was used as in the case of HL-60 cells.

METHOD

Following the introduction, the whole toolbox is split into

three independent parts: digital phantom generation, signal

transmission, and signal detection and image formation. Each

one represents a specific stage appearing during the final image

synthesis. The text of this section will follow this structure.

Digital Phantom Generation

Initially, the toolbox selects the type of the object to be

simulated. Currently, the toolbox can simulate three types of

objects.

HL-60. In the experiments using the HL-60 cell line, investi-

gators are usually interested in studying the cell nucleus that

occupies most of the cell volume. Therefore, the following text

will focus on modeling nucleus shape and texture.

When simulating the appearance of the HL-60 standard

cell line, we can presume the shape of the initial object to be

spherical, as this object type is topologically equivalent to a

sphere. However, the basic objects like spheres or ellipsoids are

too simple and regular. Because the aim is to simulate real

Table 2. List of simulated cameras

VENDOR CAMERA NAME

Andor iXon 887 BI

Photometrics CoolSNAP HQ

Photometrics Quantix KAF-1400

Princeton Instruments MicroMax 1300-YHS

Table 3. List of simulated microscopes

VENDOR MICROSCOPE NAME OPTIONAL EXTENSION

Zeiss Axiovert 200M CSU-10 confocal unit

Zeiss Axiovert 100S CARV confocal unit

Leica DMRXA CSU-10 confocal unit

Leica DMIRE2 –

Figure 2. A sample image containing microspheres of 0.5 lmdiameter with peak excitation/emission wavelengths of 560/

580 nm. This 3D figure consists of three individual images: the

top-left image contains a selected xy-slice, the top-right imagecorresponds to a selected yz-slice, and the bottom one depicts a

selected xz-slice. Three mutually orthogonal slice planes are

shown with ticks.

ORIGINAL ARTICLE


objects, a certain amount of irregularity is required. For this

purpose, we used the PDE-based method to distort the object

shape. The idea is based on viewing the object boundary as a

deformable surface. The deformation is realized with fast level

set methods (42) using artificial noise (43) as a speed function

(44). An example of such a deformation process result can be

seen in Figures 5a and 5b.

Besides the shape, the texture of the nucleus image profile

reveals important information about the cell activity. In each

stage of the cell cycle, chromatin has different properties, and

hence when stained, it looks different. For these purposes, the

study and the measurement of heterogeneity of chromatin is

an important task (45). Essentially, there are two ways to gen-

erate synthetic texture: algorithms for texture synthesis (46–

48) and methods for procedural texture modeling (43). Here,

we decided to use the latter one. The texture function is

defined as a sum of several Perlin’s noise functions (43):

Texture x; y; zð Þ ¼XN�1

i¼0

noise ðx; y; zÞ � bi� �ai

ð1Þ

where b controls flickering of the texture, a is responsible for

smoothness, and N controls whether the result is still coarse

(for N\ 5) or fine enough (see Fig. 5c). However, certain nu-

cleus parts may not contain chromatin and hence may remain

unstained. These locations are either left blank (without any

texture) or defined as very dark. The latter case corresponds to

an unwanted staining effect. The nucleoli (see Fig. 3) might be

an example of such an object type that typically appears as a

dark (not stained) place in the image of a nucleus. It was dis-

covered empirically that there is only one nucleolus per

healthy nucleus in human cells. As for cancerous cells, there

might be more than one nucleolus. The shape of such a

nucleolus is mostly spherical or slightly deformed. Because of

this property, its generation follows the same idea as the gen-

eration of the whole HL-60 nucleus.

Granulocyte. Granulocyte is a type of cell containing a

nucleus with highly condensed chromatin. Such a nucleus

typically has three to five lobes connected by very narrow,

barely perceivable channels. The shape of each lobe resembles

a slightly deformed sphere. Concerning the inner structure,

each lobe contains a cavity, as the chromatin is mostly concen-

trated in the nucleus periphery. Similarly to the HL-60 cell

line, we are mainly studying the nucleus context, and hence

Figure 3. An example of four real HL-60 cell nuclei stained with DAPI. White arrows show the location of one selected nucleolus. Each 3D

figure consists of three individual images: the top-left image contains a selected xy-slice, the top-right image corresponds to a selectedyz-slice, and the bottom one depicts a selected xz-slice. Three mutually orthogonal slice planes are shown with ticks.

ORIGINAL ARTICLE


the digital phantom designed in the following text is expected

to represent only the nucleus.

First of all, note that the lobes are distributed within a

very small area and are sometimes even tightly pressed to

each other. When generating the granulocyte structure, a cen-

ter of mass is either given by the user or generated randomly

within the image space. Subsequently, the position of each

lobe follows the Gaussian distribution with a mean in the

given center and a very low standard deviation. Because of

the similarity of the basic lobe profile with the HL-60 cell nu-

cleus, the same approach as in the previous paragraph was

used to generate each lobe. Finally, the lobes were connected

with spatial cubic splines simulating the channels between the

individual lobes. The simulation of chromatin concentration

near the nucleus periphery was managed with a distance

transform weighted by the procedural texture (see Fig. 6c).

Microsphere. Microspheres are spherical objects of known

diameter without any texture or distortion. Hence, a simple

sphere with a given diameter can represent each digital bead

phantom. The microspheres are typically used when calibrat-

ing the optical system. Here, they can be used to verify the cor-

rectness of the selected PSF and hence the plausibility of the

final synthetic image.

Notation. To summarize the previous paragraphs, the genera-

tion of any digital phantom can be described simply as:

Iphantoms ¼ Ibackground þX

p2P MakePhantom pð Þ ð2Þ

where Ibackground is an initial empty image with the nonspecific

staining effect, and P is a multiset of all the available phantom

types. When staining the objects using fluorescent dyes, some

parts of the specimen or cover glass may unwillingly be

stained. This phenomenon manifests itself as a barely percepti-

ble veil covering the whole glass. Finally, MakePhantom(.) is

any function responsible for creation of a selected digital

phantom. As three types of objects are currently ready for

simulation, the variable p can be substituted for HL-60, granu-

locyte, or microsphere.

Signal Transmission

Light conditions. In traditional light microscopy, both laser

and mercury lamps are used for visualization purposes, but

neither type can spread light within the specimen uniformly.

Figure 4. An example of four real granulocyte nuclei stained with DAPI. Each 3D figure consists of three individual images: the top-left

image contains a selected xy-slice, the top-right image corresponds to a selected yz-slice, and the bottom one depicts a selected xz-slice.Three mutually orthogonal slice planes are shown with ticks.

ORIGINAL ARTICLE


Therefore, the distribution of the light intensity is assumed to

be quadratic (49) over each xy-slice:

Ilight x; yð Þ ¼ a0 þ a1x þ a2y þ a3xy þ a4x2 þ a5y

2 ð3Þ

where vector a 5 (a0, a1, a2, a3, a4, a5) defines the shape of a

quadratic surface typically widely opened. In some cases, there

may even be two quadratic profiles in the image. This happens

if the mercury lamp arc and its mirrored image are located far

from each other. Very often, the quadratic surface peak is not

centered with respect to the image center. This is usually the

case if the camera or lamp is shifted relative to optical axis of

the microscope.

This phenomenon makes objects that are placed farther

from the optical axis look darker than the others. Cropping

such an object from this large image usually leads to neglect-

ing this effect because within this small sub-image the effect is

hardly recognized with the naked eye. Submitting such an

image to the discrete Fourier transform (DFT), one can reveal

the uneven illumination again, though this is not seen with

the naked eye. The explanation is based on DFT properties.

Because the Fourier domain is strictly periodic, one should

keep in mind that the right side of an image is virtually joined

with the left side and the upper side with the lower one. If

there is at least a small amount of light gradient across the

image, due, for example, to uneven illumination, the left side

does not join the right side smoothly. This phenomenon man-

ifests itself as a centered cross in the Fourier domain. The

stronger the light gradient, the stronger the cross appears (see

Fig. 7).

When eliminating this phenomenon, a quadratic surface

is typically fitted to the original image. The result is then

obtained as the pixel-wise ratio of the original image and the

given surface. Because in the case of simulation we solve the

inverse problem, we can apply the estimated quadratic surface

to the given image simply by multiplying.

Figure 5. HL-60 nucleus digital phantom generation: (a) the original ellipsoid representing the rough primitive mask of a generated cell nu-

cleus and (b) the same object after the 3D PDE-based deformation. (c) Object equipped with texture defining the internal structure. (d) The

image after passing through the optical system. Each 3D figure consists of three individual images: the top-left image contains a selected

xy-slice, the top-right image corresponds to a selected yz-slice, and the bottom one depicts a selected xz-slice. Three mutually orthogonalslice planes are shown with ticks.

ORIGINAL ARTICLE


Impulse response

Each optical system can be described by a point spread

function (PSF) that is the impulse response of this system

determining the amount and the characteristics of image blur.

The PSF can either be measured empirically (real PSF) or esti-

mated (theoretical PSF (50)). The theoretical PSF is usually

based on prior knowledge of the optical system properties

(confocal or wide-field microscope, objective, wavelength,

etc.). Here, we used a real PSF. The PSF was subsequently used

as a convolution kernel applied to the given image (see Fig. 5d

or 6d).

Notation

The consecutive processes of this stage can be described

formally as follows:

Iblurred ¼ Iphantoms � Ilight� � � PSF ð4Þ

where Iphantoms is the image containing pure digital phantoms,

and Ilight is the image representing the light decay effect. The

operator ‘‘.’’ corresponds to pixel-wise multiplication, and the

operator ‘‘*’’ corresponds to convolution.

Signal Detection and Image Formation

Signal detector resolution. One should keep in mind that

there are several factors affecting the image resolution. The

signal detector contributes with its pixel size, which, together

with total magnification of the optical system, defines spatial

sampling frequency. In our application, we establish the cor-

rect image resolution based on this information.

Dark current signal. There is a signal generated internally in

the detector even if no photon is coming, for example, in the

darkroom. This phenomenon is called dark current signal and

is linearly proportional to the exposure time. The detector

vendor specifies dark current generated per pixel per unit time

(in electrons/pixel/s). For example, the best CCD cameras gen-

erate less than 0.1 electrons/pixels/s. If this constant is multi-

plied by the exposure (acquisition) time, the total dark current

Figure 6. Granulocyte digital phantom generation: (a) the initial group of ellipsoids representing the rough primitive estimate of lobes; (b) each

lobe slightly deformed; (c) the lobes equipped with cavities and nonhomogeneous structure of chromatin; (d) image after passing through the

optical system. Each 3D figure consists of three individual images: the top-left image contains a selected xy-slice, the top-right image correspondsto a selected yz-slice, and the bottom one depicts a selected xz-slice. Three mutually orthogonal slice planes are shown with ticks.

ORIGINAL ARTICLE


signal is obtained. This type of signal is strongly dependent on

the detector temperature: the lower the temperature, the lower

the number of unwillingly generated electrons.

Fixed pattern noise. Every CCD chip produces a small num-

ber of hot pixels, which appear as very bright pixels in the final

image matrix, and dead pixels, which appear as very dark pix-

els. The first case can be simulated by filling corresponding

pixel positions with an overwhelming number of electrons. The

dead pixels are simulated as pixel positions with no electrons.

Quantification uncertainty. The most important noise in

low-light imaging (which is typical for fluorescence micros-

copy) is shot noise, which is usually modeled with a Poisson

distribution. This phenomenon stems from physical laws that

say that the relative measurement error increases as signal in-

tensity decreases. This noise, also known as Poisson noise, is

neither additive nor multiplicative. Its value depends directly

on the input signal in each position. Mean noise level equals

the square root of the quantified signal (number of electrons).

The higher the value of the input signal, the lower is the rela-

tive amount of noise present.

Readout noise. The signal amplification process produces a

certain amount of readout noise, which is modeled as additive

white Gaussian noise. The amount of this noise is also speci-

fied by the detector vendor (in electrons per pixel). The best

CCD cameras generate less than 10e2/pixel. Subsequently, the

A/D converter is used; that is, the electrons representing the

signal are quantized into analog-digital units (ADU). Each

such ADU defines a particular intensity level in the final digi-

tal image.

Notation. To summarize the processes of this stage, we can

write:

Ifinal ¼ ADC gp r Iblurredð Þ þ Idð Þ þ ggh i

ð5Þ

where r(.) stands for signal sampling, gp(.) defines the Poissonnoise, gg defines the additive Gaussian noise, Id defines the

dark current signal including hot/dead pixels, and ‘‘ADC[.]’’

stands for the quantization process of conversion from elec-

tron units to ADUs. Theoretically, Iblurred should be a continu-

ous signal, and r(.) should be a real sampling function defined

by the detector properties. However, we cannot handle a con-

tinuous signal. To simulate this, we can up-sample the initial

image Ibackground to a higher resolution. Afterwards, the r(.)

function is simply a down-sampling filter. This approach

allows generating images with sub-pixel precision.

RESULTS AND DISCUSSION

Currently, the simulator can generate three different types

of objects. The simplest one is the microsphere, which is usu-

ally used to measure optical system properties. The latter two

objects are HL-60 cell nuclei (see Fig. 8) and granulocyte

nuclei (see Fig. 9). As these two types of objects are quite com-

plex, one needs a lot of experience to set all the required simu-

lator parameters correctly in order to get the expected shape

and the internal structure. Close collaboration with biologists

helped us tune the parameters of individual methods in the

process of digital phantom generation. In this way, we

obtained the most suitable values. They are part of the source

code, which is freely available under the GNU GPL.

The plausibility of the results can be assessed in many

ways. The most common method for biomedical image data

comparison is visual inspection by an expert. On one hand,

this approach is important for a coarse estimate when decid-

ing whether the given image is visually similar to the class of

real images. On the other hand, it is tedious and cumbersome,

and the human eye may be simply deceived. This is especially

true with spatial (3D) image data.

Another way of comparison is more straightforward,

more exact and faster. The idea is based on image descriptors.

Such a descriptor can, for example, characterize the objects

contained within the image, measure some local texture prop-

erties, or evaluate some simple statistics over the whole image.

In the past, various measures (also called descriptors or fea-

tures) have been introduced, and some of them have been in

principle accepted as a standard. The measures have been

designed either for generic image data (51,52) (especially the

texture measures) or for segmented image data (51,53). The

latter include, for example, the number of objects within an

image, the circularity or size of the objects, or the distance

between the objects. Until recently, the vast majority of

descriptors have been designed and consequently evaluated

only over 2D image data. Lately, due to progress in the devel-

opment of computer hardware, most of the features have been

extended to 3D (54,55).

In this work, we focused on evaluating a selected set of

global texture features that includes 2nd to 6th central

moment (51) and 3D Haralick features (55). We compared the

features computed from real image data with those computed

from simulated image data directly, whereas a recent study

(25) compared the real and simulated data indirectly based on

classification results inferred from the features.

We also studied image intensity histograms and entropy.

Aside from these measurements, we also validated some of the

Figure 7. Uneven illumination of the specimen that occurs during

image acquisition causes the Fourier transform counterpart to

contain a cross centered in the position of zero frequency: (a) the

original image; (b) its Fourier power spectrum.

ORIGINAL ARTICLE


optical system properties with a Fourier analysis (we already

discussed this issue in Section 3.2).

Measurements

Central moments. The nth central moment is a statistical

measure evaluated over a given discrete random variable.

ln ¼XL�1

i¼0

zi �mð Þnp zið Þ ð6Þ

where

m ¼XL�1

i¼0

zipðziÞ

Here, the variable is marked as zi and denotes the particular

intensity level present in the image. Hence, the sum covers the

range of all the image intensity levels (L). Each moment (ln)has its own specific meaning. The second moment is known as

the variance of the given data. The third moment expresses

the skewness of the measured data, and the fourth moment

describes the relative flatness.

Entropy. Entropy [see Eq. (7)] comes from information theory

and defines the amount of uncertainty (the amount of informa-

tion) hidden in the measured data. The uniform area has zero

entropy, whereas scattered data carry more information and

hence can be characterized with a higher entropy level.

H ¼ �XL�1

i¼0

pðziÞ log pðziÞ ð7Þ

Haralick features. The Haralick features (52,55) are one of

the most popular texture feature sets. They are a collection of

statistics calculated from a so-called co-occurrence matrix.

Haralick features include angular second moment, contrast,

correlation, variance, inverse second difference moment, etc.

Each of these statistics relates to a certain image feature. For

example, the statistic ‘‘contrast’’ measures the amount of local

variation in an image.

Intensity histograms. The intensity histogram (56) is a graph

specifying how many pixels within a given image have the

same intensity. Typically, the zero (leftmost) position indicates

the number of pixels with the lowest intensity, and the right-

Figure 8. An example of four synthetic images of HL-60 cell line. These images should be compared with those in Fig. 3. Each 3D figure

consists of three individual images: the top-left image contains a selected xy-slice, the top-right image corresponds to a selected yz-slice,and the bottom one depicts a selected xz-slice. Three mutually orthogonal slice planes are shown with ticks.

ORIGINAL ARTICLE


most histogram position indicates the number of pixels with

the highest intensity. It is clear that similar images should have

nearly the same histogram. Moreover, rotating or shifting the

objects within the image does not affect the histograms.

Hence, slightly shifted or rotated objects still produce the

same histograms.

Evaluation

It is common to evaluate a large number of features over

each image to get a so-called feature vector. These feature vec-

tors are typically computed for each individual image and sub-

mitted to a suitable decision tool. Such a tool can either be a

classifier (e.g., a neural network, support vector machine, clus-

tering methods) or a statistical method (e.g., distribution plot,

goodness-of-fit test). In this work, we used the latter approach.

To show that the synthetic images produced by the simu-

lation toolbox are almost the same as the real images acquired

from the optical microscope, we evaluated all the introduced

measurements over 500 synthetic images and real images

(individually for each object). Tables 4 and 5 show the results.

To illustrate that both the real and the synthetic data sets come

from populations with a common distribution, we use quan-

tile–quantile plots (57) (see Figs. 10 and 11). Regarding quan-

tile–quantile plots, if the two sets come from a population

with the same distribution, then the points should fall

approximately along the 45-degree reference line. The greater

the deviation from this reference line, the greater the evidence

for the conclusion that the two data sets came from popula-

tions with different distributions.

Figure 9. An example of four synthetic images of granulocytes. These images should be compared with those in Fig. 4. Each 3D figure con-

sists of three individual images: the top-left image contains a selected xy-slice, the top-right image corresponds to a selected yz-slice, andthe bottom one depicts a selected xz-slice. Three mutually orthogonal slice planes are shown with ticks.

Table 4. Evaluation of central moments and entropy over the real

and simulated image data representing HL-60 cell line

MEASURE REAL IMAGE SIMULATED IMAGE

2nd c.m. 0.1304 � 7.6 3 1024 0.1569 � 5.1 3 1024

3rd c.m. 0.0069 � 1.7 3 1025 0.0083 � 1.9 3 1025

4th c.m. 0.0012 � 0.8 3 1026 0.0013 � 1.0 3 1026

5th c.m. 0.0004 � 1.3 3 1027 0.0004 � 1.7 3 1027

6th c.m. 0.0001 � 1.9 3 1028 0.0001 � 2.4 3 1028

Entropy 5.384 � 0.22 5.682 � 0.12

Each measure is expressed as a mean value over the whole

dataset including standard deviation.

ORIGINAL ARTICLE


The individual quantile–quantile plots in Figure 10 show

that the feature vectors for both real and synthetic HL-60 data

follow very similar distributions. In the case of granulocyte

nuclei (see Fig. 11), the same is valid except for the last quan-

tile–quantile plot, which is characterized by a slight deviation

from the reference 45-degree line.

Concerning 3D Haralick texture features, we evaluated 19

features in total. In (55), where the evaluation was done

locally, some texture features were found to be highly corre-

lated. Therefore, only 15 features were considered, and later in

(58), the number of independent features was further reduced

to eight. In our study, we simplified the method presented in

(55) to get global texture features. In that way, we found 9 fea-

tures to be uncorrelated. These features include: sum average,

texture entropy, texture contrast, texture correlation, texture

homogeneity, maximum probability, sum entropy, difference

entropy, and information measure of correlation. There is a

close correspondence between our selection and the previously

(58) mentioned subset of eight Haralick features (six of them

are common to both studies).

Similarly to the evaluation of central moments over the

image data, we generated nine quantile–quantile plots for each

image dataset. For HL-60 dataset, eight of nine plots exhibited

similarity between individual features for both real and syn-

thetic images. Regarding the granulocyte dataset, five of nine

plots also showed that the feature vectors for both real and

synthetic data follow very similar distributions. The rest of the

quantile–quantile plots did not follow the expected 45-degree

line, which was also the case for the last plot in Figure 11. In

future work, we will search for the differences between the real

and the synthetic data that caused the imperfection of some

quantile–quantile plots.

Figures 12 and 13 show the intensity histograms illustrat-

ing the similarities between the two image datasets. Notice that

the corresponding histogram pairs exhibit a similar shape.

Figure 10. Comparison of descriptors computed from real and synthetic HL-60 images. Quantile—quantile plots illustrate whether the

measured datasets come from populations with similar distributions. Generally, if the two sets come from a population with the same dis-

tribution, the points should fall approximately along the reference line.

Table 5. Evaluation of central moments and entropy over the real

and simulated image data representing granulocytes

MEASURE REAL IMAGE SIMULATED IMAGE

2nd c.m. 0.4978 � 1.2 3 1023 0.4667 � 1.0 3 1023

3rd c.m. 0.0140 � 1.7 3 1025 0.0126 � 3.0 3 1025

4th c.m. 0.0031 � 1.6 3 1026 0.0024 � 1.7 3 1026

5th c.m. 0.0012 � 3.0 3 1027 0.0010 � 4.0 3 1027

6th c.m. 0.0004 � 1.0 3 1027 0.0003 � 1.0 3 1027

Entropy 6.134 � 0.07 6.295 � 0.13

Each measure is expressed as a mean value over the whole

dataset including standard deviation.

ORIGINAL ARTICLE


Figure 11. Comparison of descriptors computed from real and synthetic granulocyte images. Quantile—quantile plots illustrate whether

the measured datasets come from populations with similar distributions. Generally, if the two sets come from a population with the same

distribution, the points should fall approximately along the reference line.

Figure 12. Mean of log intensity histograms for (left) real HL-60 images, (right) synthetic HL-60 images.

Figure 13. Mean of log intensity histograms for (left) real granulocyte images, (right) synthetic granulocyte images.

CONCLUSION

In this article, we presented a very complex and efficient

tool for generating phantom biomedical images. Furthermore,

it simulates the whole process of image acquisition from an

optical microscope, from the very beginning when preparing

the specimen, to the very end when converting the analog sig-

nal into its digital form and storing it to a hard drive. This

toolbox generates 3D objects but does not have any limita-

tions; hence, it can be extended to any higher dimension (time

sequences or spectral imaging) and generate other types of

cells. The whole simulation toolbox can be split into three in-

dependent parts: digital phantom generation, signal transmis-

sion, and signal detection and image formation.

For the time being, the toolbox generates three types of

objects (HL-60 nuclei, granulocyte nuclei, and microspheres).

In the future, we intend to generate more types of objects: cells

(nucleus, cell shape, and selected sub-cellular components)

and cell clusters that typically appear in tissue scans.

The simulator proposed in this article is freely available

under the GNU GPL at: http://cbia.fi.muni.cz/simulator/.

ACKNOWLEDGMENTS

Thanks are also due to Martin Maska for his implementa-

tion of PDE-based methods, Honza Skalicky for the micro-

scope management, and the HCILAB from the Faculty of

Informatics at Masaryk University for computational support.

We also greatly appreciated the help of Ludvık Tesar from the

Institute of Information Theory and Automation (Czech

Academy of Sciences, Prague) with the 3D Haralick feature

implementation. A talk based on this paper has been given at

the ISAC XXIVCongress in Budapest (May 2008). The simula-

tion toolbox is freely available under GNU GPL at http://cbia.

fi.muni.cz/simulator/.

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