Robust filtering based segmentation and analysis of dura mater vasculature using epifluorescence microscopy.

Abstract

We show that an adaptive robust filtering based image segmentation model can be used for microvasculature network detection and quantitative characterization in epifluorescence-based high resolution images. Inhomogeneous fluorescence contrast due to the variable binding properties of the lectin marker and leakage hampers accurate vessel segmentation. We use a robust adaptive filtering approach to remove noise and reduce inhomogeneities without destroying small scale vascular structures. An adaptive variance based thresholding method combined with morphological filtering yields an effective detection and segmentation of the vascular network suitable for medial axis estimation. Quantitative parameters of the microvascular network geometry, including curvature, tortuosity, branch segments and branch angles are computed using post segmentation-based medial axis tracing. Experiments using epifluorescence-based high resolution images of porcine and murine microvasculature demonstrates the effectiveness of the proposed approach for quantifying morphological properties of vascular networks.

Full text

Robust Filtering Based Segmentation and Analysis of Dura Mater
Vasculature using Epifluorescence Microscopy
V. B. Surya Prasath1, F. Bunyak1, O. Haddad1, O. V. Glinskii2,4,5, V. V. Glinsky3,4,5
V. H. Huxley2,4, K. Palaniappan1
Abstract— We show that an adaptive robust filtering based
image segmentation model can be used for microvascula-
ture network detection and quantitative characterization in
epifluorescence-based high resolution images. Inhomogeneous
fluorescence contrast due to the variable binding properties
of the lectin marker and leakage hampers accurate vessel
segmentation. We use a robust adaptive filtering approach to
remove noise and reduce inhomogeneities without destroying
small scale vascular structures. An adaptive variance based
thresholding method combined with morphological filtering
yields an effective detection and segmentation of the vascu-
lar network suitable for medial axis estimation. Quantitative
parameters of the microvascular network geometry, including
curvature, tortuosity, branch segments and branch angles are
computed using post segmentation-based medial axis tracing.
Experiments using epifluorescence-based high resolution im-
ages of porcine and murine microvasculature demonstrates
the effectiveness of the proposed approach for quantifying
morphological properties of vascular networks.
I. INTRODUCTION
Vessel extraction, tracing and measurement are important
image processing stages for clinically characterizing the be-
havior of tissue function in normal and diseased states. Var-
ious techniques exist in the literature for extracting vessels
in neurological, cardiovascular, and ocular imaging. Among
them, multi-scale Hessian, structure tensor or eigen analysis
and segmentation based approaches are very popular [1].
For example, Zhou et al [2] use a ridge scan-conversion
deformable model and a bifurcation detection approach [3]
for boundary extraction in CT lung images, Lam and Yan [4]
use a divergence vector field scheme for retinal vessel
extraction. In fluorescence microscopy imaging, 3D vessel
extraction using a GPU implementation is proposed in [5]. A
shape-based geodesic active contour scheme is studied in [6]
using a Hessian-based initialization level set approach.
Fluorescent imaging techniques are becoming critical tech-
niques for visualizing and analyzing dynamic biological
processes, which benefits from the development of new
fluorophore-based labeling methods and the development of
sophisticated algorithms for the analysis of light microscope
imagery. In epifluorescence imaging labeled SBA lectin
or WGA lectin is used to stain microvascular structures
followed by high resolution fluorescence microscopy. The
application of interest here is to automatically extract the
Authors are with the University of Missouri-Columbia, Columbia, MO
65211 USA, 1Department of Computer Science, 2Department of Medical
Pharmacology and Physiology, 3Department of Pathology and Anatomical
Sciences, 4National Center for Gender Physiology, and 5Research Service,
Harry S. Truman Memorial Veterans Hospital, Columbia, MO 65201 USA.
structural components of the microvascular system with
certain accuracy from images acquired by fluorescence mi-
croscopy [7]. Due to uneven contrast, leakage, and high
variance in foreground (vessel) intensity, traditional global
thresholding schemes [8] can fail to accurately detect salient
microvasculature structures. The majority of active contour
models [9], [10], [11], [12], [13] typically rely on edge-
or region-based indicators, and such schemes may not cap-
ture all of the vascular network structures present in a
given epifluorescence image. Thus, current approaches to
vessel segmentation lead to poor results when applied to
epifluorescence imagery of the microvasculature. Hence, a
robust denoising process can be beneficially incorporated
into the segmentation process in order to extract accurate
morphological information.
In order to preserve important structures in the seg-
mentation of the vascular network images such as narrow
and low-contrast branches, we utilize an adaptive filtering
scheme derived from edge preserving filtering [14], [11] and
robust statistics theory [15] along with a local-variance based
thresholding step. Such edge-preserving smoothing is related
to the well-known anisotropic diffusion filters [16], [17] and
bilateral filters [18], see [19]. We derive an improved numer-
ical scheme in the context of robust estimation with emphasis
on edge preservation aimed at avoiding local minima prob-
lems, which often arise in the context of nonlinear smooth-
ing [20], [21]. The proposed approach provides favorable
smoothing results, and its application to microvasculature
network structure extraction illustrates the applicability of
the method in the field of nanoscale imaging. We present a
semiautomated computer-assisted quantitative assessment of
microvascular structure from dura mater images which offers
a measurable approach to assess microcirculation changes.
These studies can be used to understand the physiological
and molecular mechanisms leading to gender dependent
pathological conditions.
The major contributions of our work include novel com-
binations of (a) a robust local filtering model with edge
preserving properties, and (b) vascular network morphology
detection from the smoothed image for further analysis. The
rest of the paper is organized as follows. Section II presents
the proposed smoothing based microvasculature network
detection including the pre- and post- processing steps.
Section III describes the vessel network graph extraction
and defines the quantitative measures. Section IV provides
experimental segmentation results and quantitative analysis
of extracted microvasculature networks.

(a) (b) (c) (d)
Fig. 1. Illustration of the smoothing and microvasculature extraction steps
on an epifluorescence image taken from a Yucatan miniature swine. (a)
Input image (b) Estimated background using top-hat transformation (4) (c)
Background subtracted and filtered image uby running scheme (3) for
T= 5 iterations (d) Adaptive thresholding with Niblack’s scheme after post
processing with morphological opening and closing to remove outliers.
II. ROBUST SMOOTHING BASED VASCULATURE
DETECTION
Let Ω⊂R2be the image domain, typically a rectangle
and the input image I: Ω →Rwith I(x)represents the
value at a pixel x∈Ω. In a robust statistics framework
finding a best fit of a smooth image ufrom a given noisy
input image Ican be posed as a minimization problem [14],
min
u

X
x∈ΩX
y∈Nx
ω(x−y)ρ(I(x)−u(x), σ)


(1)
with a robust estimator function ρ. Here Nxrepresents the
neighborhood of a pixel x,ωis a spatial weighting function
(e.g. Gaussian kernel) and σis the scale (variance) parameter.
Among a wide variety of choices for the robust norm, ρ, in
this paper we use Tukey’s biweight robust function due its
strong edge preserving property. To solve the minimization
problem (1) we use the dilation convex approximation [14]
of the Tukey function,
ργ(ξ, σ) = (γ2σ2
6(1 −[1 −(ξ/γσ)2]3)|ξ| ≤ γσ,
1/3otherwise. (2)
Here γ > 0is the dilation parameter. We use an iterative
reweighted method to solve (1) [14],
ut+1
y=Px∈Nyω(x−y)c(I(x)−ut(y))I(x)
Px∈Nyω(x−y)c(I(x)−ut(y)) (3)
where c(ξ) = ρ0
γ(ξ)/ξ and titeration number. Then, our
micro-vessel extraction routine consists of the following four
sequential steps.
1) Pre-processing: Using the morphological top-hat op-
erator to estimate the inhomogeneous background
present in epifluorescence images,
tophat(I) = I−((ISE)⊕SE)(4)
where (ISE)(˜x) = min{I(x+˜x) + SE(x)}and
(I⊕SE)(˜x) = max{I(x+˜x) + SE(x)}define the
opening with structuring element SE with ˜x ∈ Nx, a
neighborhood of x, see Figure 1(b) where the estimated
background from a given image is shown.
2) Robust image filtering: Running the proposed robust
smoothing algorithm in (1) on the enhanced image,
see Figure 1(c).
3) Adaptive thresholding algorithm: Niblack’s threshold-
ing algorithm [22] which is based on the local mean
and variance values.
4) Post-processing: Using morphological opening and
closing to remove small outlier regions to obtain the
segmentation mask Mvessel, see Figure 1(d).
We observe in Figure 1(c) that noise and inhomogeneous
subregions are effectively removed in the resulting image
after the adaptive smoothing step. Moreover, the major parts
of vasculature are accurately preserved in the detection step,
see Figure 1(d), such as some narrow and low-contrast
branches; see also Figure 2(b) for more examples. Next, we
describe the network graph extraction module and quantita-
tive parameters computed using the graph.
III. VESSEL NETWORK GRAPH EXTRACTION
AND QUANTITATIVE MEASUREMENTS
This module constructs a vessel network graph by com-
puting the skeleton/medial axis (using thinning procedures
as in [23]) from segmentation results obtained using pre-
processing and the segmentation module described in the
previous section. Further quantitative analysis is performed
on the resulting labeled vessel branches.
Step 1: Skeleton (medial axis) Svessel is extracted from
vessel mask Mvessel.
Step 2: Branching/bifurcation points Bvessel in Svessel are
identified.
Step 3: Skeleton Svessel is disconnected at branch points.
Connected component labeling is applied to the set of
branch points Bvessel and disconnected vessel skeleton
Svessel resulting in uniquely labeled branching points B=
{b1, b2, ..., bm}and skeleton segments S={s1, s2, ...sn}.
Step 4: A vessel network graph G= (S,B, E)is constructed
using branch points Band skeleton segments Sas vertices
in G. Each connected branch point biand segment sjare
topologically linked using an edge Eij .
Step 5: Short skeleton segments associated with spurs are
removed and corresponding branch points are updated.
Step 6: For each branch point bi, the set of incident skeleton
segments Si={si,1, si,2, ..}are identified.
Step 7: Labeled skeleton segments Si={si,1, si,2, ..}are
traced and corresponding parametric curves are obtained,
S(s)=(x(s), y(s)).
The major skeleton segments are used to obtain the follow-
ing quantitative measures characterizing the microvascular
network.
1) Vessel Curvature
κ=˙x¨y−˙y¨x
( ˙x2+ ˙y2)3/2(5)
=(xp−xp−1)(yp+1 −2yp+yp−1)
(p(xp−xp−1)2+ (yp−yp−1)2)3
−(yp−yp−1)(xp+1 −2xp+xp−1)
(p(xp−xp−1)2+ (yp−yp−1)2)3
where the dot refers to derivatives with respect to
parameter s. The second expression gives the central

(a) (b) (c) (d) (e)
Fig. 2. Segmentation, medial axis and quantitative parameter estimation results for images taken from three different mice exhibiting varying characteristics;
row 1 (Mouse 1 - 012606ERbWT14), row 2 (Mouse 2 - 012706ERbKO15b), row 3 (Mouse 3 - 100605ERbKO14). (a) Original epifluorescence images
stained using a green fluorescence marker. (b) Final segmentation mask obtained using the scheme outlined in Section II. (c) Medial axis (red channel)
computed using the segmentation mask and superimposed on the original image (green channel) with segments labeled. (d) Quantitative curvature image
computed using medial axes and extracted network graphs. (e) Automatically detected branch points and associated branch angles (in degrees).
differences formula for the derivatives involved. Fig-
ure 2(d) shows the unsigned curvature map |κ|, for
each of the images highlighting the geometry of the
vascular network for three distinct cases.
2) Vessel tortuosity
τ=Arc length
Chord =Rl
0rdx
ds 2+dy
ds 2ds
p(x0−xl)2+ (y0−yl)2(6)
where arc length is the arc length computed from
parametric vessel segment curve S(s)and chord is
calculated using the Euclidean distance between the
end points of S. Normal vessels are generally smooth
and remain straight for low tortuosity values, whereas
increased tortuosity results from vascular changes asso-
ciated with hypertension. Figure 3 show the normalized
histograms of tortuosity values for all the branches.
These correspond to the branches marked in three
different images given in Figure 2(c).
3) Branching angles We compute the angle (in degrees)
between two daughter vessels using tangent lines at
branching points. Branching angle is often related
to blood flow efficiency. Low angles are associated
with hypertension whereas increased angles have been
related to decreased blood flow. In Figure 2(e) we show
the computed branch angles at the main bifurcation
points superimposed on the input images.
IV. EXPERIMENTAL RESULTS
The main motivation is to investigate the influence of sex
hormones on angiogenesis as well as vasculature remodeling
in murine and porcine brain dura mater. The endothelial
cells were stained using AlexaFluor 488 fluorescently labeled
SBA lectin for pig and WGA lectin for mouse laminae
respectively, to yield a high contrast image of the vascular
walls (foreground) and low intensity avascular background.
The experiments are performed on epifluorescence-based
high resolution images of dura mater microvasculature ac-
quired using a video microscopy system (Laborlux 8mi-
croscope from Leitz Wetzlar, Germany) equipped with 75
watt xenon lamp and QICAM high performance digital
CCD camera (Quantitative Imaging Corporation, Burnaby,
Canada) at 0.56 micron per pixel resolution and image
dimensions 1360 ×1036 pixels.
The robust smoothing based segmentation scheme and
the quantitative vascular network parameter estimation al-
gorithms were implemented in Matlab. To implement the
relaxed minimization scheme (1), we further use an adaptive
logarithmic decrease for the scaling parameter γof dilated
Tukey biweight function (2), γt=γ(0) +ln(t+ 1)(1 −
γ(0))/ln(T+ 1), for t= 0,1, . . . , T with maximum iteration
set to T= 5. The neighborhood Nxin the iterative
scheme (3) is fixed at the size of 9×9which is found to
give better results for our dataset. The scale in (2) is fixed
using the mean absolute deviation criteria,
σ= 1.4826 ×median(|∇I| − median(|∇I|)).(7)

(a) Mouse 1 - 012606ERbWT14 (b) Mouse 2 - 012706ERbKO15b (c) Mouse 3 - 100605ERbKO14
Fig. 3. Normalized histograms showing the distribution of local point-wise
curvature (row 1), branch segment based tortuosity (row 2), and branching
angles (row 3) for three images shown in Figure 2.
Figure 2 shows some sample segmentation results along
with medial axis analysis using our laminae extraction rou-
tine described in Section II. As can be seen the segmentation
results capture the microvasculature networks and provide
a well-defined mask for finding the medial axis, see Fig-
ure 2(b). The medial axis is extracted from the segmentation
binary mask using morphological thinning and is cleaned for
small spurs. Figure 3 shows the normalized histograms of
the distribution of local point-wise curvature (row 1), branch
segments based tortuosity (row 2), and branching angles (row
3) respectively for the three images shown in Figure 2(a).
V. CONCLUSIONS
We study a scheme for microvasculature detection in
epifluorescence images using a robust smoothing model
along with adaptive thresholding to obtain a foreground-
background segmentation. The robust noise resistant edge
preserving smoothing filter proposed in [14] is adapted for
the segmentation stage of obtaining vascular network graphs
in the presence of background fluorescence response (noise)
and inhomogeneous fluorescence labeling. Experimental re-
sults on murine dura mater epifluorescence images show
promising segmentation results. We extract the medial axis
network graph of the microvasculature segmentation in order
to estimate quantitative parameters such as curvature, tortuos-
ity and branch points. The proposed automatic segmentation
and vascular network quantification software tool will be
used for studying ovary excised versus normal intact cases
in animal models to understand the systemic influence of
hormone therapy on angiogenesis and vascular remodeling.
Further studies are being planned to determine the relation-
ships between microvascular morphological changes, disease
states, and effects of therapeutic interventions.
ACK NOWL EDG EME NT
This work was partially supported by NIH 5R01
HL078816 and R33 EB00573. Dennis Lubahn kindly pro-
vided test animals for the experiments.
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