The State of the Art in Biological
Image Analysis
I. INTRODUCTION

FIGURE 1 Chain of image acquisition and treatment. 
The general chain of image acquisition and treatment
can be sketched as shown in Fig. 1. Before undertaking
analysis of a collected set of images, one should
identify the most suitable procedure to be followed. In
particular, two different approaches can be outlined:
 An image processing procedure (whose output is an
image) requiring the use and development of tools
for image enhancement.
 An image analysis procedure in which further
quantitative statistics of both morphological and
fluorescence intensity parameters are determined,
leading to numerical data output.
II. IMAGE PROCESSING
The first steps to be performed are noise reduction,
shading correction, contrast, and edge enhancement.
Depending on the noise sources and the hardware
devices involved, images can be processed via software
or hardware. Different standard image processing
routines can be run and eventually adapted according
to the kind of captured and stored data input
(RGB, grey scale, or binary color space, multilayered or
singlelayered, compressed or uncompressed).
For software data treatment, special algorithms
(filters) are used or developed, either directly acting on
the original numerical matrix (representative of the
image) or within the frequency domain obtained by a
particular mapping of the spatial data set through the
Fourier transform (Diaspro
et al., 2002). Although automated software with a wide range of standard and
optimised filters is available, the use of these tools as
black boxes can cause new unexpected artefacts to be
added to images. This can be particularly risky when
dealing with biological samples whose degree of complexity
may often prevent the user from relying on his
common sense. The final goal of these procedures is
that of improving the signal to noise ratio (SNR),
leading to better image visualisation without any loss
of intrinsic amount of information.
III. IMAGE ANALYSIS
Quantitative image analysis deals with both collecting
information from fluorescence intensity signals
and obtaining morphologicalgeometrical parameters
from the sample. Different biological treatments and
data acquisition procedures (using specific offline
processing) are typically required, according to the
topic under study. It is worth listing some of the most
commonly used procedures:
colocalization, morphological
analysis [geometrical parameter estimation on threedimensional
(3D) and twodimensional (2D) samples],
image classification (fractal analysis and feature extraction),
and frequency domain analysis (Diaspro
et al., 1990;
Castleman, 1996).
IV. COLOCALIZATION
The observations of
in vivo cellular details and
events often involve the use of single or multifluorescence
labelling with a high degree of specificity with
the respect of the structures under investigation. The necessity of simultaneously imaging different functional
parts of samples (such as microtubules, nuclei
or mitochondria) demands the use of multiple distinct
fluorescence dyes in order to reveal the parts of interest
by keeping them visually distinct from one another.
In this situation, image acquisition is typically carried
on separately at the different excitation wavelengths
and the later offiine analysis may deal, among other
things, with one more problem: that of extracting
information about the eventual overlap (colocalization)
between the different fluorescence signals
expressed by the various part of the sample, which
thus occupy the same physical location. This is a
crucial task, especially in biological and medical
studies where one is interested in studying the molecules
distribution with the respect of particular functional
structures such as receptors.

FIGURE 2 Twophoton imaging (750nm wavelength) of an artery endothelial bovine pulmonary cell.
Mitochondria (labelled with MitoTracker) are visible in the red channel, actin filaments (labelled with
BODIPY) in the green one, and nuclei (labelled with DAPI) in both. The emission intensity of the nucleus is
much higher than the others due to the strong concentration of DNAbounded DAPI inside the cell with
respect to the other dyes. Colocalized pixels are yellow ones in the RGB image (Diaspro, 2001). 

FIGURE 3 Scatter plot: purple dots represent highly
colocalized redgreen intensity pixels. 
Provided that the probes' emission spectra are sufficiently
separated and correct filter sets are used
during the data acquisition, colocalization means that
the emitted fluorescence signals (colors) are pictured
within the same pixels. In the case of twoprobe
labelling (Fig. 2), data analysis can be performed by
generating a scatter plot in which xy coordinates represent,
respectively, red and green intensity values,
and the intensity of each point (according to a suitable
color code) represents the number of pixels with that
intensity value (Fig. 3).
In addition to this visualisation, a proper quantification
of the degree of colocalization can be obtained
by comparing each of the acquired images by means
of suitable coefficients (Fig. 4), which may account
either for the similarity of shapes between the two
images (without considering intensities) or for the difference of intensity between colocalized pixels,
depending on the kind of information one is interested
in.

FIGURE 4 Snapshot of a typical image analysis user interface for colocalization analysis. Courtesy of
Marco Raimondo and Paola Ramoino, LAMBS, http://www.lambs.it. 
A. Morphological Analysis and Classification
Morphological investigations of images are strictly
connected to the idea of topological space due to the
mathematical environment wherein tools for quantitative
analysis are developed. As a first step, this requires
a unequivocal relationship between each image array
and a set of real space coordinates to be established. For
singlelayered images, this goal can be accomplished
by dividing the field of view (i.e., the real dimension of
the region within the image) by the number of pixels,
thus getting the effective size of the elementary dot in
the image. This is all one typically needs for geometrical
calculations in the plane. Multilayered images
naturally involve a third dimension so that one more
relationship needs to be established between the
optical sections and their real world distance from one
another. The simplest approach for solving this task
consists of assigning the optical sectioning distance
(eventually scaled to account for further data acquisition artefacts) to two contiguous slices. Once these correspondences
are established between the images and
the topological space, further and more complex computer
based processing can be performed, including
3D sample reconstruction (Fig. 5), morphometrical
estimations, object counting, and localization (Bianco
and Diaspro, 1989; Diaspro
et al., 1990).

FIGURE 5 Snapshot of a 3D sample data acquisition (left) and 3D sample reconstruction (right). 
The need of morphometrical measurements is often
the main prerequisite in most biological and medical
comparative studies where the shape and dimension
of structural components of the samples (such as
tissues, cells, and organlets) are strictly related to their
functions. In these cases, an effective 3D visualization
may be nice looking while failing to provide accurate
results in terms of accurate characterization of the
structural properties of interest. It is far better to use
suitable stereological methods, implemented using
highly efficient software, involving single slices. These
procedures can be either semiinteractive or completely
automated. The main difference between these
two approaches is that the latter ones are faster but
require reliable automatic thresholding and segmentation
routines for the recognition of the objects of interest
within the images.
Several different stereological methods have been
tested and improved over the years: the optical dissector
principle (Gundersen, 1986; Sterio, 1984) or the
unbiased sampling brick rule (Howard
et al., 1985) for
particles counting; the nucleator (Gundersen, 1988)
and the planar rotator (Jensen and Gundersen, 1993)
applied to a stack of optical sections for estimating the
mean particle volume; the optical rotator (Kieu and
Jensen, 1993; Tandrup
et al., 1997), spatial grid method
(Sandau, 1987), and "Fakir method" (Kubinova and
Janacek, 1998) for surface area estimation; and the vertical
slices method (Gokhale, 1990) and global spatial
sampling (Larsen
et al., 1998) for length estimation.
Moreover, volume and surface area or curve length
estimation can be obtained with known precision and
are considered to be free from any systematic error
(bias) relating to the sample strategy. Furthermore,
they can be undertaken without any previous assumptions
about the shape or the structure of the objects
under investigation, thus allowing the user to get a
realistic average value of the parameters of interest as
a result of an average obtained from repeated measurement
processes. One more important parameter for
many computer vision tasks, such as image classification,
is texture segmentation, consisting of splitting
an image into regions of similar texture. This task
is usually performed in two stages: texture feature
extraction (to characterize each texture) and further
texture segmentation (to determine homogeneous
regions), allowing a proper segmentation of the image.
The limiting factors for all these investigations are
the resolution of the imaging system, determined by
its point spread function (PSF), and the intrinsic reproducibility
of the observed phenomenon itself, which if
poor might demand an improvement in the accuracy
of the data acquisition protocol (Bianco and Diaspro,
1989; Castleman, 1996).
The approaches discussed so far mainly rest on
some common properties of the familiar topological
space, but there exist in nature objects whose properties
are not fully analysable by any possible set of
standard topological parameters. When considering
the morphology of samples, for instance, it is very
common to take into account those geometrical parameters
suggested by a suitable modelling of structures,
involving elementary shapes such as lines, circles,
spheres, or simple polygon. This allows one both to
obtain a preliminary quantitative analysis of the geometrical
properties of the samples and to cluster them
according to the values of some characteristic parameters.
Unfortunately, this method cannot always be
applied successfully, as most of the complex biological
structures cannot be modelled easily by simple shapes.
One popular example is that of the branching structure
of many biological structures, such as the arteries,
veins, nerves, the parotid gland ducts, or the bronchial
tree in the human body. The presence of a certain selfsimilarity
and the lack of a welldefined scale suggest
that a complete characterization cannot be based
simply on a conventional surface/volume estimation,
as such a numerical value does not convey any further
information about the degree of complexity of the
shape to which it is related. These empirical evidences
lead to the idea that some other independent parameter
might exist, something like a spacefilling factor:
this is the fractal dimension (
fd), existing somewhere
between the usual topological dimensions, whose
value ranges between 1 and 2, respectively, depending
on whether the object fills almost no space (such as in
the case of a line) or fills all the available space (such
as in the case of a square or a circle). A combination of
fractal dimension and standard texture features has
been shown to provide better discrimination than
standard texture features alone. An example of this application is that related to the study of the breaking
strength of bones. Despite the fact that there is a strong
dependence of breaking strength on mineral density,
more refined models are required to explain variations
in the strength of bones having identical densities.
Consideration of the way in which mineral density is
arranged within the bones, thus influencing their structural
resistance, has led to the use of the fractal index
as a parameter, which is both calculated easily from
images and particularly efficient for their classification.
Other studies employing fractal analysis have involved
the characterization of mammographic patterns
(Caldwell
et al., 1990), colorectal polyps (Cross
et al.,
1994), trabecular bones (Cross
et al., 1993a; Majumdar
et al., 1993; Benhamou
et al., 1994), retinal vessels
(Mainster, 1990), renal arteries (Cross
et al., 1993b),
Papanicolaoustained cervical samples (MacAulay
et al., 1990), and epithelial lesions (Landini
et al., 1990).
It is worth pointing out here that a variety of procedures
have been proposed for estimating the fd of
images, such as the boxcounting method (BC) or the
fractional Brownian motion method (FBM); the best
algorithm for the job will vary according to the kind of
images under study. It can be shown that the BC
method is ineffective if applied to lowresolution
images, whereas the FBM one reveals its limits when
applied to noisy images or to systems with strong local
scaling factors.
Moreover, because every
fd calculation needs a
threshold level to be set in order to discriminate different
regions within the same image, this implies the
existence of a fractal spectrum in which the value of fd
depends on the threshold level. The best choice for this
threshold can be made either from prior knowledge
about the inner structure of the sample or through
some parameters (such as the linear correlation coefficient
for the BC method), intrinsic to the particular fd
algorithm used, which may somehow account for the
fractal dimension.
B. Frequency Domain
Some image analysis techniques employed in a
wide range of applications, such as image filtering,
reconstruction and compression, turn time domain
inputs into frequency domain outputs. A representation
of a given multidimensional signal in the
frequency domain is often useful for identifying
periodical components within signals.
The Fourier transform provides a unique and
invertible mapping of original data to frequency
domain data represented as complex numbers, termed
structure factors, in which the frequency characteristics
are displayed in terms of their magnitudes and phases. Both the magnitude and the phase functions of
the structure factors are necessary for the complete
reconstruction of an image from its Fourier transform.
The magnitudeonly image is unrecognizable and
has severe dynamic range problems. The phaseonly
image is barely recognizable, i.e., severely degraded in
quality. The advantage of using the Fourier transform
lies in its invariant properties. It is easy to demonstrate,
for instance, that rotating the object merely
causes a phase change to occur and that the same
phase change is caused to all the structure factors. The
magnitude is independent of the phase and so is unaffected
by rotation. (This is an example of the very
important property of shift invariance.) Second, consider
a change of size of the object. This does not
change any of the phases and changes the magnitudes
of all the structure factors by the same factor. If the
magnitude of the spectrum is normalised, then it is
invariant to object size as well. Finally, consider the
effect of noise and quantisation errors on the boundary.
This will cause local variation of high frequency
components and will not change the low frequencies.
Hence, if the high frequency components of the spectrum
are ignored, the rest of the spectrum is unaffected
by noise. Thus, for object recognition, the Fourier
descriptor offers many advantages and is very useful
not only in comprehensively understanding digital
image analysis, but also in digital image processing. It
could be a useful tool to deal with texture analysis,
which is an important field in remote sensing, and it
is fast to compute.
V. CONCLUSIONS
This article outlined the fundamental concepts of
image processing and image analysis, addressing the
main methods and giving a full list of references for
deeper insights on topics of interest.
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