Leblond, Frédéric

Lesage, Frédéric

Peshko, Olesya

Shan, Shidong

English

Mathematics in Industry Information Service Eprints Archive

Extracting Autofluorescence from Diffuse Optical Images
Frédéric Lesage
Coordinator, École Polytechnique de Montréal
Frédéric Leblond
Industrial representative, ART Inc.
Olesya Peshko
Report writer, McMaster University
Shidong Shan
Student, University of British Columbia
1. Introduction
The problem studied by the team was proposed by the company ART Advanced Research Tech-
nologies Inc., which “designs, develops, and markets optical imaging products for the medical and
pharmaceutical industries” (see the web site http://www.art.ca/en/art/profile.php). Also,
“ART has developed several products that relate to medical imaging, diagnostics, medical research
and drug discovery”. Among these products one finds Optix, “an in vivo optical molecular imaging
device designed to monitor physiological changes in small animals during preclinical drug studies”.
Optix is used worldwide by industry and academic leaders. The students in the team, Olesya
Peshko and Shidong Shan, were supposed to investigate the algorithms used in this product and
their work led to the improvement of one aspect of the optical data processing carried out by
Optix. In the rest of this section we discuss biomedical imaging in general. Section 2 describes the
approaches investigated by the team and the results obtained.
The advent of new biomedical imaging techniques has brought significant progresses in how we
image humans and animals. In particular, the emergence in the mainstream of new modalities, such
as diffuse optical imaging (see [13], [8], [12], [4], [5]), has enabled researchers to image hemodynamics
in vivo in a non-invasive fashion. The relatively low absorption and low scattering in the 600-1000
nm spectral range allow detection of photons travelling through several centimetres of biological
tissue. Coupled with accurate models of light propagation, the NIR (Near Infra-Red) techniques
enable imaging of deep tissue with boundary measurements using non-ionizing, low dose radiation.
Applications of clinical significance have emerged for this modality; among those, breast cancer
detection and neuronal activation measurement for cognitive studies are applications currently being
actively pursued. In particular, optical imaging is currently arousing interest in the neurosciences.
Absorption of near infra-red light by blood (oxy- and deoxy-haemoglobin), see [13], [8], and [12],
can be used to measure functional information during brain activation. For example, using different
wavelengths, it is possible to map changes in hemodynamics and oxygenation levels to changes in
light intensity during some neuronal task (see [4] and [5]). The advantages of this modality are
that one can distinguish between oxygenated and deoxygenated blood, and that NIR techniques are
more convenient and lightweight. Its main weaknesses concern spatial resolution and quantification.
6 F. Lesage et al.
Figure 1. Small animal imaging with fluorescent probes targeting cancer
In parallel, associated with the emergence of endogenous diffuse optical imaging in humans, a
new approach is emerging that enables to follow molecular products injected in animals, in vivo,
through fluorescence. This new imaging technique (see [6], [9], [14], and [3]), referred to as molecular
imaging, holds great promises: whereas one would detect diseases through anatomical changes
and anomalies, we can now use new methods to provide a minimally invasive characterization
and measurement of biological processes at the cellular and molecular levels of living organisms.
Applications abound: early detection of diseases, real-time assessment of therapy effectiveness,
and specific and selective delivery of drugs to targeted tissues. The recent emergence of genomic
information clears the way for more individualized and specific drugs. Angiogenesis, hypoxia and
pH, hyper-metabolism, micro-calcifications, and protein expression are all potential targets for these
new techniques. Optical biomedical imaging has, over the last few years, enabled researchers to
take significant steps towards this new paradigm. Fluorescent optical imaging, however, is subject
to inherent difficulties. Tissues also generate fluorescence, and one needs to determine whether the
measurements originate from the molecular compound that was injected or from autofluorescence.
Whether it is necessary to localize structures originating from targeted inclusions in the images
or to filter out autofluorescence to improve image quality, the problem consists of segmenting out
components of the image whose properties allows us to characterize them as either inclusions or
autofluorescence. Figure 1 displays a small animal with fluorescent probes targeting cancer, and
Figure 2 a model exhibiting a target and interference generated by simulated autofluorescence.
A defining characteristic is that inclusions have a relatively high-contrast, well-defined, almost
round shape, while autofluorescent objects are characterized by irregular, lower-contrast shapes. In
this workshop, several filtering techniques have been implemented to identify the structures, such
as wavelet transform, principal component analysis, and normalized cross-correlation and shape
fitting.
Extracting Autofluorescence from Diffuse Optical Images 7
Figure 2. Numerical model exhibiting a target and interference generated by simulated autofluorescence
2. Problem Approaches
2.1. Wavelet Transform
Method
The general denoising procedure using a wavelet transform involves three steps: decompose,
threshold, and reconstruct (see [7] and [10]). Firstly, a wavelet transform and a decomposition level
N are chosen, and the wavelet decomposition of the signal at the level N is computed. Secondly,
for each level from 1 to N , a threshold is selected and soft or hard thresholding is applied to the
detail coefficients. Finally, a wavelet reconstruction is computed using the original approximation
coefficients of the level N and the modified detail coefficients of levels from 1 to N . When this
technique is applied to an image of fluorescence, the reconstructed image can be considered as the
main inclusion from targeted probes after extracting the autofluorescence from tissues.
Results
In this project, the wavelet transform approach was carried out by using the Matlab wavelet
toolbox [1]. Specifically, we have utilized the 2D discrete stationary wavelet transform (swt2) with
“db1” wavelets to carry out the wavelet decomposition. The reconstructed images were produced
by the inverse stationary wavelet transform (iswt2) after soft thresholding.
Figure 3 illustrates a 3-level wavelet decomposition on the synthetic image obtained in Case 1
with Detector 1. Figure 4 shows a comparison of one original image and the reconstructed main
component of the image using the inverse wavelet transform. Note that the structure of the main
inclusion can be identified more easily in the reconstructed image than in the original image.
8 F. Lesage et al.
Figure 3. 3-level wavelet decomposition for the synthetic image �case 1 detector 1)
Figure 4. Original and reconstructed image of the main component
Discussion
The well-known wavelet package Wavelab is available at
http://www­stat.standford.edu/∼wavelab/
(see [2]). Because of the time limitation, we could use the Matlab wavelet toolbox only. It would
be interesting to explore the use of Wavelab for extracting autofluorescence from the diffuse optical
images. Wavelet thresholding is an efficient technique to filter additive noise and restore original
signals. The quality of the reconstructed signal depends on the choice of threshold and the method
of thresholding. The specific thresholding strategies should be selected according to the basic
Extracting Autofluorescence from Diffuse Optical Images 9
autofluorescence model. Moreover, different thresholding techniques need to be tested in order to
determine which method produces the best results for the diffuse optical images of fluorescence.
2.2. Principal Component Analysis
Method
Another way of segmenting the inclusions and other objects in the image is by using a Principal
Component Analysis (PCA). Here, it is carried out by performing a Singular Value Decomposition
(SVD) and choosing only the components corresponding to the largest singular values (to reveal
the most important structures in the image). The image is represented by a matrix A of size m×n.
The SVD of A is a matrix factorization of the form A = USV t. Let s1 ≥ . . . ≥ si ≥ . . . ≥ sr ≥ 0 be
the singular values of A, where r = min (m�n). S is diagonal with singular values in non-decreasing
order and U and V have orthonormal columns; each column of U (resp. V ) is a left-singular (resp.
right-singular) vector of A. It is well known that the first p (1 ≤ p ≤ r) singular values capture
the most important features of A. Thus we define the ith component Ai as USiV
t, where Si is a
matrix obtained from S by zeroing all the diagonal elements except for si.
Results
In our experiments, we have empirically chosen the first three components, because they contain
almost all the meaningful information. For some images, considering as few as two components
is enough. Figure 5 displays the results of the PCA for a synthetic image. In the original image
(see Figure 5 top left), one can see an inclusion with some background fluorescence in the upper
left corner. Figures 5 top right, 5 bottom left, and 5 bottom right represent the A1, A2, and A3
components, respectively. In this case, the inclusion is almost completely contained in A1, while
the background fluorescence is in A2. Component A3 contains some negligible details. For this
image, the background fluorescence can be removed easily.
Figure 6 top left demonstrates an image of the mouse with an inclusion (black arrow). You can
observe a lot of fluorescence from the organs in addition to the target inclusion. Figures 6 top right,
6 bottom left, and 6 bottom right represent the A1, A2, and A3 components, respectively. In this
case, the number of fluorescent objects in the image is relatively large and separating them out is
not as straightforward as in the previous example.
Discussion
If any preliminary knowledge about the objects in the image is available, the information from
the three components can be combined in a certain way, i.e. αA1 + βA2 + γA3, where A1, A2,
and A3 are the image components, and α, β, and γ the coefficients that reflect the weight of
each component. While the success of the PCA segmentation depends on image sophistication, the
target inclusion is almost always present in the A1 component because it has a relatively well-defined
shape and shows high-contrast fluorescence. Separating out the components, however, cannot be
considered an acceptable solution in many cases, since it often degrades the overall quality of the
image. Below we develop a more robust approach, which is capable of separating out objects from
the image. Moreover, it does not depend upon the number of the objects and can even handle
partially overlapping objects.
2.3. Cross­Correlation and Shape Fitting
Method
In this approach, we try to separate out the elliptical shapes in the image. This is justified by
the following assumptions: 1) target inclusions are almost always round, and 2) autofluorescent
10 F. Lesage et al.
Figure 5. Components of the PCA for the simulated image
Figure 6. PCA analysis of a real image
Extracting Autofluorescence from Diffuse Optical Images 11
objects, though generally of irregular shapes, are low-contrast, and in many cases can be treated as
consisting of one or several partially overlapping elliptical shapes. The general idea of the algorithm
is to separate out objects from the image one by one, and estimate their shapes to determine what
kind of object is extracted at each iteration; the nature of the object will help one decide whether it
should be removed from the image or not. As there can be many fluorescent objects, a smaller region
of the image is chosen at each iteration. We use a Gaussian model fp to define an elliptical shape:
fp(x� y) = v0+ v1e
−s�x�y), where s(x� y) is defined as a1(x− bx)
2+2a2(x− bx)(y− by)+ a3(y− by)
2,
x and y are the coordinates of the pixels in the image, (bx� by) is the centre of the bump, and a1,
a2, and a3 define the elliptical shape. Note that a1a3 − a
2
2 > 0. We choose several highly probable
bump sizes and compute the location of the bumps in the image by maximizing normalized cross-
correlation of the model and the image data. Then we choose the parameters of the bump that
conform to the largest number of template sizes or to the one containing the brightest pixels. These
estimated parameters serve as a first guess for refining the optimization procedure.
In order to remove the bump from the image, we fit the image data Φx�y to the model fp(x� y)
by solving an optimization problem with the model parameters bx, by, a1, a2, a3, v0, and v1:
min �fp(x� y)− Φx�y�
2.
A similar idea, for a different model, is explored in [11], where it is described in more detail.
Results
Figure 7 top left demonstrates a light intensity function from a synthetic image that contains
one well defined bump and a background fluorescence caused by another (close) bump. Figure 7
top center shows the fitted model and Figure 7 top right the result of the removal of the detected
bump. The remaining bump can be separated from the image in the same fashion. Figure 7 bottom
shows the results of a similar procedure carried out on an in vivo image of a mouse. At the first
iteration a target inclusion was detected (see Figure 7, bottom left and center). Figure 7 bottom
right displays the bumps that can be detected at the subsequent iterations of the algorithm.
Discussion
Generally speaking, this algorithm requires a fine tuning of the parameters, based on what is
known about imaging data; this is so because the success of the optimization procedure depends
on the quality of the first guess. For example, it is useful to have a notion of the possible bump
sizes in order to obtain a good fit. The choice of the stopping criteria is another important issue.
For instance, the number of iterations may be fixed beforehand in the case where the number of
extracted objects is known or can be guessed reasonably well. On the other hand, the algorithm
may be stopped if it can be inferred from the image or bump parameters that there are no inclusions
or autofluorescent objects left in the image.
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2. http://www­stat.stanford.edu/~wavelab.
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Figure 7. Results of the cross-correlation technique
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Can the cerebral metabolic rate of oxygen be estimated with near-infrared spectroscopy?,

Matlab wavelet toolbox documentation.

Novel receptor-targeted fluorescent contrast agents for in-vivo tumor imaging,

Volumetric diffuse optical tomography of brain activity,

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Nonlinear Dimension Reduction for Microarray Data

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