Image Anal Stereol 2018;37:55-62 doi:10.5566/ias.1708
Original Research Paper
A SHAPE-CONTEXT MODEL FOR MATCHING PLACENTAL CHORIONIC
SURFACE VASCULAR NETWORKS
ELIN FARNELLB,1, SHAWN FARNELL2, JEN-MEI CHANG3, MADISON HOFFMAN4, ROBIN
BELTON5, KATHRYN KEATY6, SANFORD LEDERMAN6 AND CAROLYN SALAFIA7
1Department of Mathematics, Colorado State University, 1874 Campus Delivery, Fort Collins, CO 80523;
2Plasma Controls, 1320 C/D Engineering Research Center, Fort Collins, CO 80523; 3Department of
Mathematics and Statistics, California State University, Long Beach, 1250 Bellflower Blvd, Long Beach, CA,
90840-1001; 4Department of Mathematics and Statistics, Kenyon College, 201 N College Rd, Gambier, OH
43022; 5Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717; 6New York
Methodist Hospital, 506 Sixth Street Brooklyn, New York 11215; 7Placental Analytics, LLC, 187 Overlook
Circle, New Rochelle, NY 10804
e-mail: elinfarnell@gmail.com, shawncfarnell@gmail.com, jen-mei.chang@csulb.edu,
madisonchoffman@gmail.com, robin.belton@montana.edu, katkeaty@gmail.com, sal9047@nyp.org,
carolyn.salafia@gmail.com
(Received February 10, 2017; revised October 4, 2017; accepted November 20, 2017)
ABSTRACT
Placental chorionic surface vascular networks (PCSVNs) are essential high-capacitance, low-resistance
distribution and drainage networks, and are hence important to placental function and to fetal and newborn
health. It was hypothesized that variations in the PCSVN structure may reflect both the overall effects of
genetic and environmentally regulated variations in branching morphogenesis within the conceptus and the
fetus’s vital organs. A critical step in PCSVN analysis is the extraction of blood vessel structure, which has
only been done manually through a laborious process, making studies in large cohorts and applications in
clinical settings nearly impossible. The large variation in the shape, color, and texture of the placenta presents
significant challenges to both machine and human to accurately extract PCSVNs. To increase the visibility
of the vessels, colored paint can be injected into the vascular networks of placentas, allowing PCSVNs to be
manually traced with a high level of accuracy.
This paper provides a proof-of-concept study to explain the geometric differences between manual tracings
of paint-injected and un-manipulated PCSVNs under the framework of a shape-context model. Under
this framework, paint-injected and un-manipulated tracings of PCSVNs can be matched with nearly 100%
accuracy. The implication of our results is that the manual tracing protocol yields faithful PCSVN
representations modulo a set of affine transformations, making manual tracing a reliable method for studying
PCSVNs. Our work provides assurance to a new pre-processing approach for studying vascular networks by
ways of dye-injection in medical imaging problems.
Keywords: altered geometry, paint-injection, placenta, shape matching, tracing.
INTRODUCTION
Altered patterns of angiogenesis with resultant
variation in mature vascular network structures have
been correlated with functional alterations in many
species and many viscera including lung (Makanya
et al., 2007; Hu et al., 2011), kidney (Carev et
al., 2008), pancreas (Saldeen et al., 2006) and the
angiogenesis that results in neurogenesis (Vasudevan
and Bhide, 2008; Vasudevan et al., 2008). Related
gene families control branching morphogenesis in
these “permanent” viscera (Davies, 2002) and in
the placenta, a “temporary” fetal organ that is
separated from the baby at birth. The placenta is an
ideal organ to study fetal angiogenesis because its
branching villous growth is driven by angiogenesis.
Abnormal placental angiogenesis underlies a number
of pregnancy complications, from preeclampsia to
fetal growth restriction and pre-term birth (Herr et al.,
2009; Leach et al., 2009; Barut et al., 2010). Recent
research has also demonstrated connections between
placental features to the health and development of
newborn babies (Yampolsky et al., 2009; Chang et
al., 2012; Kaneti et al., 2013; Salafia et al., 2010;
2013b). For example, placental chorionic surface
shapes and vascular networks features (e.g., mean
vessel thickness, mean vessel tortuosity, and number of
branch points) have been linked to immediate neonatal
outcomes such as birth weight after adjustment for
gestational length (Yampolsky et al., 2009; Chang
et al., 2012) and risk for Autism Spectrum Disorder
(ASD; Salafia et al., 2012; 2013a; Shah et al., 2016;
Chang et al., 2016). In particular, PCSVNs associated
with placentas of high-risk ASD pregnancies generally
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FARNELL E ET AL: Placental chorionic surface vascular networks
had fewer branch points, thicker and less tortuous
vessels, better extension to the surface boundary, and
smaller branch angles than their population-based
counterparts (Chang et al., 2017).
Currently, it is difficult to conduct placenta
studies in large cohorts due to the difficulty in
reliably extracting PCSVN features from images
of the placenta. The challenges are rooted in the
nature of these digital photographs and the way
the placentas were prepared for image acquisition.
The low contrast between the vascular network and
its damp background makes it extremely difficult
to isolate the vascular features for further analysis.
Therefore, to increase the visibility of the PCSVNs
and consequently the feasibility to accurately extract
PCSVNs, medical practitioners have highlighted the
PCSVNs by injecting veins and arteries with colored
paint, see, e.g., Fig. 1b. After paint-injection, small
vessels (e.g., vessels that are less than 2 pixels in
width) become visible under the human eye. It allows
the human tracer to identify vascular structures with a
much higher confidence, as illustrated in Fig. 1d.
The paint-injection process increases the visibility
of otherwise invisible vessels, which allows medical
professionals to study PCSVNs in greater detail.
Furthermore, the paint-injection process improves
(a) (b)
(c) (d)
Fig. 1. Examples of placenta images before and after
paint-injection along with corresponding tracings of
arterial network (venous tracings are similar). (a) Un-
manipulated placenta. (b) The same placenta as in (a)
after paint-injection. (c) Tracing of arterial vascular
structure drawn from image in (a). (d) Tracing of
arterial vascular structure drawn from image in (b).
Note that visibility of vessels is significantly increased
via the paint-injection process.
(a) (b)
(c) (d)
Fig. 2. Examples of placenta images before and
after paint-injection along with the PCSVN extraction
results. (a) An image patch of an un-manipulated
placenta. (b) An image patch of a paint-injected
placenta. (c) PCSVN extraction result of (a) after
applying a multiscale method based on shearlets and
Laplacian Eigenmaps. (d) PCSVN extraction result
of (b) after applying a multiscale method based on
shearlets and Laplacian Eigenmaps.
the potential success of automated feature extraction
algorithms such as those documented in Frangi et
al. (1998); Almoussa et al. (2011); Chang et al.
(2012). For example, Fig. 2 shows the PCSVN
extraction results of applying a directional multiscale
mathematical framework based on the combination of
shearlets and Laplacian Eigenmaps (Yacoubou Djima
et al., 2017) to images of un-manipulated (Fig. 2a)
and paint-injected PCSVNs (Fig. 2b). There is a
noticeable improvement in the extraction result after
paint-injection, as seen in Fig. 2c,d.
The benefit of the paint-injection process in
studying the connections between human placental
vascular networks and many adult diseases can be
visualized in Fig. 3. Ultimately, we wish to decide
whether an intervention is needed simply by taking a
digital photograph of the placental chorionic surface
vascular networks (Fig. 3a–f). In order to accomplish
this, we need to precisely identify which features from
the PCSVNs (Fig. 3e) are capable of differentiating
placentas that are associated with a fetal outcome or
adult disease from those in the general population.
Extracting a detailed description of the vascular
networks serves as a crucial step in this ultimate
research goal.
The purpose of our work is to provide a robust
validation framework to the manual tracing protocol.
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Image Anal Stereol 2018;37:55-62
Fig. 3. Medical application and implication of our work.
During the paint-injection process, many important
placental characteristics such as tortuosity and the
number of vessel endpoints are altered. In (Shah
et al., 2015), tracings of PCSVNs before and after
paint-injection were shown to be comparable, with
unsatisfactory matching scores. Their work concluded
that the vascular networks of un-manipulated and
paint-injected placentas are similar with roughly 71%
confidence; however, the sources that caused the
remaining 29% to mismatch were not identified.
Therefore, it was unclear whether the tracing protocol
used in obtaining the traced networks were accurate
modulo the geometric changes that are invariant under
their comparison model.
MATERIALS AND METHODS
DATA SET
Our data is obtained from 19 singleton full-
term birth placentas and is the same as that used
in Shah et al. (2015). The placentas in the data
set were cleaned, paint-injected, and photographed in
New York-Presbyterian Brooklyn Methodist Hospital
(see, e.g., Fig. 4a). The PCSVN of each placenta,
before and after the paint-injection, was then traced
manually by a trained expert using the software GIMP
and following the protocol described in Shah et al.
(2015). In short, the tracer distinguishes the placental
chorionic surface arterial network from the subjacent
venous network and uses different colors and pencil
sizes to mark different vessel thicknesses and locations
of the chorionic plate boundary and umbilical cord
insertion. It takes roughly 4 to 8 hours to trace a single
PCSVN. See Fig. 4b for an example of a traced image.
Our data set is as follows. From each of the
19 placentas, we obtain two pairs of tracings: the
arterial network before and after paint-injection, and
the venous network before and after paint-injection.
An example of one pair in the data set can be
seen in Fig. 1 (c) and (d). We seek to design an
algorithm that reflects the geometry of the tracings
and that successfully matches the 38 tracing pairs,
consequently demonstrating that meaningful placental
features are preserved in the paint-injection process.
(a) (b)
Fig. 4. (a) Paint-injection process. (b) A manually
traced image. Notice that the location of the umbilical
cord insertion is marked with a yellow dot and the
scale is given by the two blue dots on 12 and 13 of
the ruler.
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FARNELL E ET AL: Placental chorionic surface vascular networks
PRE-PROCESSING
Color tracings were uniformly scaled and
converted to 1380× 1440 pixel binary images. One
centimeter was marked with two blue dots on a ruler
within the original photograph of the placenta to
give scale. Roughly 35 pixels in the digital image
corresponded to 1 cm on the placenta. Tracings were
aligned so that the umbilical cord insertion lies at the
center of the image. A one-pixel-wide skeletonization
of the PCSVN tracing was created in Matlab to prepare
for the computation of geometric signatures called
shape contexts (Belongie et al., 2002; Zhang and
Malik, 2003; Wang et al., 2007). Visual inspection
of tracings shows that paint-injection can introduce
variability in vessel thickness; by using a one-pixel
skeleton, we remove vessel thickness from the model
while preserving PCSVN structure.
SHAPE CONTEXT
We aim to design a model that helps explain both
geometric differences introduced through the process
of paint-injection and features that are preserved in
that process. This model may then provide a validation
framework to the manual tracing protocol and help to
establish assurance to a new pre-processing approach
for studying vascular networks by way of paint-
injection. A shape-context model is thus particularly
appropriate for this setting. We modify an approach
introduced in Belongie et al. (2002) and encourage the
interested reader to see this source for a comprehensive
background of related methods.
Our algorithm matches un-manipulated and paint-
injected tracings based on comparison of points in
tracings near chosen reference points. Specifically, we
choose N reference points pi within a circle of radius
360 pixels (one-fourth of the width of an image) about
the umbilical insertion, where p1 corresponds to the
umbilical insertion and each pi, i 6= 1, is randomly
selected.
For each reference point, we let the positive x-axis
be the ray starting at the reference point and pointing
to the right. Points are represented by polar coordinates
(r,θ), where r is measured in pixels from the reference
point and θ is measured in degrees counterclockwise
from the positive x-axis.
An m×n shape-context matrix H is defined at each
reference point, whose entries Ha,b are the number of
points in the tracing that satisfy
(a−1) ·
(rmax
m
)
< r < (a) ·
(rmax
m
)
and
(b−1) ·
(
360
n
)
< θ < (b) ·
(
360
n
)
,
normalized by the number of points that fall in the
circle centered at pi with radius given by the parameter
rmax. That is, the entries in the shape context matrix
represent the relative frequency of vessel pixels within
each angular and radial region partitioned by the
choice of m and n in the polar grid. See Fig. 5 for a
shape context example.
(a)0.029 0.105 0.184 0.190 0.135 0.0630 0 0.154 0.133 0.007 0
0 0 0 0 0 0

(b)
(c)
Fig. 5. A shape context example. A single bin and
its corresponding entry is highlighted throughout the
subfigures. (a) A one-pixel skeleton tracing shown with
a coarse polar mesh (m = 3,n = 6). (b) The shape
context matrix H. Each entry is the relative frequency
of pixels from the tracing in the corresponding bin
of the mesh. (c) A visualization of H. Lighter colors
correspond to higher values.
ROTATION
Since some movement of local placental features
can occur during paint-injection, we allow for matches
near a reference point pi between shape contexts
of paint-injected tracings rotated about the umbilical
insertion with shape contexts from tracings of un-
manipulated placentas. Results are reported based on
T uniformly-spaced rotations with T = 90.
SCALING
To model the altered geometry introduced in paint-
injection, we introduce a scaling parameter at each
reference point. Consider a shape context Hi with
parameters m, n, and rmax for pi = (ri,θi) in a
tracing U , where (ri,θi) are coordinates relative to the
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Image Anal Stereol 2018;37:55-62
(a) (b) (c)
(d) (e) (f)
(g) (h)
(i) (j)
Fig. 6. An illustration of the matching algorithm using shape contexts. (a) Un-manipulated tracing with umbilical
insertion p1 in blue, a second reference point p2 in red, and corresponding polar meshes. Smallest diameter
vessels are removed. Note that the polar meshes are 36×36; the full meshes are not shown for visual purposes.
We use rmax = 432. (b) Shape context for umbilical insertion in (a). The histogram matrix accumulates the relative
frequency of vessel pixels within each angular (x-axis) and radial (y-axis) bin; lighter shades represent higher
values. (c) Shape context for p2 in (a). (d) Paint-injected tracing that corresponds to un-manipulated tracing in
(a), with p1 in blue, p2 in red, and corresponding polar meshes. (e) and (f) Shape contexts for (d) based at p1
and p2, respectively, with s1 = s2 = 1. Note that without rotation and scaling, these do not provide a good match.
(g) Rotated paint-injected tracing with scaled polar mesh that provides the best match to shape context in (b).
(h) Shape context for p1 in (g). Parameters are s1 = 1.15 and angle of rotation 124◦. (i) Rotated paint-injected
tracing with scaled polar mesh (and scaled location) for p2 that provides the best match to shape context in
(c). (j) Shape context for p2 in (i). Parameters are s2 = 1.1 and angle of rotation 128◦. Chi-square values are
approximately (e) 1.87, (f) 1.76, (h) 0.78, and (j) 0.82.
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FARNELL E ET AL: Placental chorionic surface vascular networks
umbilical insertion. We create a scaled shape context
Ĥi,si with parameters m, n, and sirmax at p
′
i = (siri,θi)
in the tracing I. Theoretically, si is a continuous
variable that models the geometric scaling introduced
during the injection process. In our algorithm, we
allow si to take on values in the following discrete
set: {0.95,1,1.05,1.10,1.15,1.20} . Visual inspection
of the data set suggests that stretching is more common
than shrinking at a local level; hence most allowed
values of si are greater than or equal to one.
SHAPE-CONTEXT MATCHING
A distance function is needed to compare two
shape contexts, H and Ĥ. Here, we follow the
convention in Belongie et al. (2002), known as the chi-
square test statistic:
d(H, Ĥ) =
m
∑
a=1
n
∑
b=1
(Ha,b− Ĥa,b)2
Ha,b + Ĥa,b
,
where the sum is taken over entries for which the
denominator is non-zero.
A tracing of an un-manipulated placenta U with
shape contexts H1, . . . ,HN is matched to the tracing
of a paint-injected placenta I if I yields the set of
shape contexts Ĥ1,s1 , . . . , ĤN,sN , where each rotation
and scaling parameter is chosen to be optimal, that
minimizes the quantity ∑Ni=1 d(Hi, Ĥi,si). Note that it
is possible for the rotation and scaling parameters to
differ across the set of shape contexts in the above
objective function.
Major contributions of our work are the
inclusion of several spatial reference points and the
consideration of local geometric changes in PCSVNs
through rotation and scaling parameters. Fig. 6
provides a visualization of shape-context matching.
RESULTS AND DISCUSSION
Small vessels become more visible in paint-
injected tracings; therefore, a natural comparison is
one where the smallest-diameter vessels are removed.
Our best results are achieved with five reference points,
small vessels (those with width less than 0.6 mm)
removed, and local scaling. In this case, our algorithm
correctly matches an average of 37.6 out of 38 pairs
of tracings over 10 random trials. Note that the only
aspect of the algorithm that changes over the 10
random trials is the reference points.
In comparison, 27 out of 38 matches were reported
in Shah et al. (2015) when small vessels are removed.
The results in Table 1 suggest that our model is robust
to parameter variations and capable of producing
matches with a consistently high success rate. These
results demonstrate a strong link between the un-
manipulated and paint-injected tracings and provide
an explanation for the source of differences between
the two types of images. For example, improved
accuracy with increased numbers of reference points
implies that the paint-injection process induces non-
uniform changes across the placenta and that sufficient
shape information is preserved to match tracings when
local information is taken into account. Additionally,
improved accuracy from the inclusion of local scaling
confirms that the paint-injection process stretches or
shrinks the placenta at a local level, also in a non-
uniform way.
Since paint-injection leads to improved extraction
of PCSVNs from images of placenta, it is desirable
to study the PCSVNs of paint-injected placenta.
The work presented here explains the nature of the
geometric differences between manual tracings of
paint-injected and un-manipulated PCSVNs under the
framework of a modified shape-context model and
Table 1. Average number of matches out of 38 possible matches over 10 random trials. N is the number of
reference points and rmax is the maximum radius (in pixels) of a circle centered around a reference point for
which points in the skeleton are included in the shape context. In the “No scaling” portion of the table, no scaling
is allowed when comparing tracings (i.e., each si = 1). In the “Scaling allowed” portion, each si is allowed to
vary incrementally between 0.95 and 1.20.
Smallest vessels included Smallest vessels removed
No scaling Scaling allowed No scaling Scaling allowed
rmax 432 576 720 432 576 720 432 576 720 432 576 720
N
1 29.0 26.0 26.0 30.0 31.0 32.0 31.0 29.0 31.0 33.0 32.0 37.0
2 27.8 26.7 27.0 33.3 32.8 32.2 31.3 30.8 30.5 35.7 35.9 36.7
3 28.3 27.4 27.5 33.6 33.3 32.8 32.5 31.8 31.4 36.3 36.6 36.7
4 28.9 27.5 27.1 33.7 33.7 33.1 32.7 31.4 31.2 36.3 36.3 36.7
5 28.7 27.6 27.6 33.8 33.8 34.3 33.0 31.5 31.4 37.6 37.0 36.9
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Image Anal Stereol 2018;37:55-62
confirms the validity of the tracing protocol described
in Shah et al. (2015). Our work provides assurance to
a new pre-processing approach for studying vascular
networks by ways of dye-injection in medical imaging
problems.
ACKNOWLEDGEMENTS
The authors wish to thank Terri Girardi, who
developed the tracing protocol and vetted tracings, and
Ruchit Shah for correspondence regarding Shah et al.
(2015). We also wish to thank the reviewers, whose
comments helped to refine and strengthen the article.
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