A bioimage informatics approach to automatically extract complex fungal networks
Mark D. Fricker
Associate Editor: Olga Troyanskaya
Institute of Biomedical Engineering
Oxford Centre for Integrative Systems Biology
Oxford e-Research Centre
Department of Plant Sciences, University of Oxford
Motivation: Fungi form extensive interconnected mycelial networks that scavenge efficiently for scarce resources in a heterogeneous environment. The architecture of the network is highly responsive to local nutritional cues, damage or predation, and continuously adapts through growth, branching, fusion or regression. These networks also provide an example of an experimental planar network system that can be subjected to both theoretical analysis and experimental manipulation in multiple replicates. For high-throughput measurements, with hundreds of thousands of branches on each image, manual detection is not a realistic option, especially if extended time series are captured. Furthermore, branches typically show considerable variation in contrast as the individual cords span several orders of magnitude and the compressed soil substrate is not homogeneous in texture making automated segmentation challenging. Results: We have developed and evaluated a high-throughput automated image analysis and processing approach using Phase Congruency Tensors and watershed segmentation to characterize complex fungal networks. The performance of the proposed approach is evaluated using complex images of saprotrophic fungal networks with 105-106 edges. The results obtained demonstrate that this approach provides a fast and robust solution for detection and graph-based representation of complex curvilinear networks. Availability and implementation: The Matlab toolbox is freely available through the Oxford e-Research Centre website: http://www.oerc .ox.ac.uk/research/bioimage/software Contacts: The Author 2012. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions.com.
Rapid advances in imaging technologies have heralded a new era
of quantitative measurements that offer considerable potential to
improve our understanding of complex biological systems,
particularly those that need to be considered as integrated functional
units (Swedlow et al., 2003; Carpenter, 2007; Kvilekval et al.,
2010). In particular, enhanced image processing techniques
have greatly facilitated characterization of interconnected
transport and communication networks in animal systems, including
vascular systems, milk ducts, respiratory pathways and neuronal
circuitry [e.g. (Chaudhuri et al., 1989; Frangi et al., 1998;
Meijering et al., 2004; Rodriguez et al., 2008)]. In contrast,
*To whom correspondence should be addressed.
there has been remarkably little progress to characterize
macroscopic microbial network development for an entire
taxonomic group of organisms, namely the fungi. Unlike other
biological networks, which exist within an organism, the entire
growth form of fungi is as an adaptive network. Foraging
saprotrophic fungi play a central role in ecosystem biology as they are
the only organisms capable of complete degradation of wood in
temperate forests. These fungi form extensive interconnected
mycelial networks of multi-hyphal cords that forage for
scarce resources that are patchily distributed in time and space
(Fricker et al., 2007). The architecture of the network responds
to local nutritional cues, damage or predation and the local
structure is continuously remodeled through growth, branching,
fusion or regression of the hyphal cords. Despite the absence of
any centralized control system, these organisms exhibit complex
foraging and decision making behavior as a co-ordinated
individual. Unlike animal network models, microbial networks also
provide an example of an extremely tractable experimental
system that can be subjected to both theoretical analysis and
experimental manipulation in multiple replicates (Boddy et al.,
Early measures of macroscopic mycelial organisation focussed
on fractal dimension as a useful tool to capture aspects of the
network structure as a metric (Boddy and Donnelly, 2008).
However, a single summary statistic, such as the overall fractal
dimension provides little opportunity to characterize the network
structure and dynamics further or to explore the underlying
mechanism leading to network optimisation. There has been
some progress at the microscopic level to extract the physical
network structure using (semi)-automated image analysis
(Barry and Williams, 2011). However, to date, delineation of
the network architecture from the larger soil-based systems has
only been possibly manually (Fricker et al., 2007), as basic
intensity-based segmentation is not effective in this context
(M.D.Fricker, L.Boddy and D.P.Bebber, unpublished data).
As a result, the total number of macroscopic fungal networks
analysed so far is relatively low. Nevertheless, graph-theoretic
analysis of the digitised networks has provided evidence that
these indeterminate, de-centralized systems yield adaptive
networks with both high-transport capacity and robustness to
damage, but at a relatively low cost, through a Darwinian
process of selective reinforcement of key transport pathways and
recycling of redundant routes (Bebber et al., 2007). Furthermore,
fungal networks dynamically modify link strengths and local
connectivity when subject to experimental attack to readjust
the balance between transport capacity, robustness to damage
and resource allocation, resulting in increased resilience as the
environment becomes more challenging (Boddy et al., 2010).
Existing image processing approaches for semi-automated
fungal network extraction work best if the mycelium is grown
on a suitable substrate, such as cellophane (Ritz et al., 1996) or
nitrocellulose (Barry and Williams, 2011) to facilitate acquisition
of high-contrast images. The subsequent processing procedure
typically involves noise reduction, using median or band-pass
filters, intensity-based thresholding, with manual or automated
threshold selection, followed by morphological processing to
achieve an improved skeletonisation of the colony structure
e.g. Barry and Williams (2011).
However, these methods require rather specific culture
conditions and illumination regimes that cannot readily be adapted for
macroscopic networks grown on soil-based media, which is
essential to explore the natural behavioural capability of these
organisms and the range of their responses. In addition, the
branches (termed cords in these systems) are multi-hyphal
aggregates and show considerable variation in contrast as the
individual cords span several orders of magnitude in diameter from m
to mm, within a single colony. Furthermore, the background
from the compressed soil substrate is not homogeneous in texture
or reflectivity. Under these conditions, automatic
characterization of the fungal network is challenging for conventional image
processing approaches and more advanced solutions are
We have developed a high-throughput automated image
analysis approach to detect and characterize large complex fungal
networks, grown under realistic conditions. We use watershed
segmentation to extract the network rapidly, with prior
curvilinear feature enhancement to highlight the network structure in
noisy or low contrast images. The proposed enhancement
method uses a novel brightness- and contrast-invariant approach
based on the concept of local phase, called the Phase Congruency
Tensor (PCT). The resulting skeleton is then pruned on the basis
of local cost functions that incorporate both intensity and tensor
direction information. A graph representation of the network is
constructed from the pruned skeleton to give the network
topology or a weighted network that includes edge lengths. To
obtain an estimate of the edge thickness, which is important in
predicting the physiological performance of the system, the
skeleton is dilated to capture the approximate dimension at each
point, and this value is used to set a local sampling region to
estimate the reflected cord intensity for comparison with
empirically derived calibration curves. This approach ensures that even
sub-resolution branches can be analysed correctly. An addition
procedure is applied to extract the resource region which is then
used to redefine a corresponding part of the graph. Although we
apply the method here to fungal networks, it has wide
applicability to planar networks in any domain.
EXTRACTION OF NETWORK-LIKE
Recent reviews of image processing methods for network-like
structure extraction can be found in Dehkordi et al. (2011).
According to this review, most image analysis approaches to
extract network-like structures are classified into pattern
recognition, model-based, tracking, artificial intelligence and
neural networks. To set the current work in context, we outline
the basic method and the limitations of each approach below.
Many of these methods apply thresholding and object
connectivity, followed by a thinning procedure and extraction based on
graph description (Kawata et al., 1995). Alternatively, the image
intensity is represented as a hypersurface and the curvilinear
features are extracted using curvature, with the crest points of the
hyper-surface correspond to the center lines of the structure
(Prinet et al., 1996). These centerlines can then be used as
seeds in a region growing procedure that segments the full
curvilinear structure from the images (Higgins et al., 1989).
Direct segmentation of curvilinear structures can also be done
by multi-resolution segmentation approaches. After segmenting
salient structures at low resolution, less prominent network
branches can be extracted in the neighborhood of the previously
segmented regions at higher resolution (Chwialkowski et al.,
1996). Curvilinear structures can also be segmented by
mathematical morphology operators using specific structuring elements
(Zana and Klein, 1997).
Model-based approaches apply explicit curvilinear structure
models, or templates, to extract the network. In network
extraction applications, the template is usually represented in the form
of a series of nodes connected in segments and deformed to fit
the image (Summers and Bhalerao, 1995). In curvilinear or
tubular object segmentation, objects are commonly described as a set
of overlapping template ellipses (2D) or ellipsoids (3D) (Krissian
et al., 2000).
More general deformable model-based techniques find object
contours using parametric curves that deform under the
influence of internal and external forces (Klein et al., 1994).
Tracking-based approaches apply local operators on a specific
point known to be in an object of interest and track it. Tracking
approaches, starting from an initial point, detect network
centerlines or boundaries by analyzing the pixels parallel and
orthogonal to the tracking direction (Haris et al., 1997; Meijering
et al., 2004).
Artificial intelligence and neural network-based
Artificial Intelligence-based approaches use knowledge to guide
the segmentation process and to delineate network structures,
e.g. using a general curvilinear model (Smets et al., 1988). A
disadvantage of learning methods is that they depend on the
quality of the training dataset, which requires significant work
and can be susceptible to problems like over-training (Nekovei
and Sun, 1995).
ENHANCEMENT OF CURVE-LIKE STRUCTURES
When the network structure is affected by variations of intensity
contrast within the image, image enhancement operators can
highlight curvilinear features and reduce background effects.
Although other alternatives are available, here we concentrate
on methods based on tensors.
A tensor representation of an image can give information about
how much the image varies along and orthogonal to the
dominant orientations within a certain neighborhood (Westin et al.,
2001). In particular, the Hessian matrix (a secondorder
tensor) has been proposed to describe local shape orientation
for elongated structures (Sato et al., 1998). Since curvilinear
structures observed in the image can appear in different sizes,
scale space representations have been extensively used. This is
commonly achieved through the use of a family of Gaussian
filters, or their derivatives, with multiple scales achieved by
varying the value of the variance.
One of the most popular Hessian-based approaches to
enhance curvi-linear structures is known as vesselness (Frangi
et al., 1998). For a given image I(p) and scale , vesselness is
where p x; y T is the spatial location, ; 1; ; 2 are the
eigenvalues of H p (the Hessian matrix at scale ) satisfying
j ; ij j ; i1j; and c are thresholds that control the sensitivity
of the line measurement. Multi-scale vesselness, for a given set of
scales f g, can be computed as the maximum of the
vesselness values calculated at different scales, and the eigenvectors at
the same scale can be used to define local orientation (Obara
et al., 2012).
An alternative measurement of piecewise linear segments that
is also based on the Hessian matrix, called neuriteness, has been
proposed in (Meijering et al., 2004).
MATERIALS AND METHODS
The proposed approach has been tested and validated on images of
fungal networks of Phanerochaete velutina or Phallus impudicus that
were grown for 3950 days in the dark on compressed soil or sand
microcosms and photographed at intervals, as described previously, see figure
1a (Bebber et al., 2007; Boddy et al., 2010).
Phase congruency-based tensors
Herein, we introduce a novel phase concept for curvilinear feature
enhancement called the PCT. In general, local tensor-based representations
can be produced by combining the outputs from polar separable
quadrature filters, applied on several orientations (Knutsson, 1989). Although
tensor representations can be built on purely intensity-based filters (like
the Hessian), these have the downside of being sensitive to changes in
image contrast. Methods based on local phase have been proposed as a
contrast-independent alternative for feature detection. In particular,
phase congruency (Kovesi, 2000) is based on the concept that salient
features have similar values of local phase when observed at different
scales. We exploit the idea that phase congruency values are high in the
direction perpendicular to the structure, while they remain close to zero in
the direction parallel to the structure. More importantly, the values of
phase congruency are minimally affected by contrast changes. Thus, for a
given set of scales fs}, a set of orientations fo} and a given set of phase
congruency measures PCop (for each orientation o) (Kovesi, 2000), the
PCT takes the following form (Obara et al., 2012):
where no is the normalized orientation vector in the direction o,
1=m 1, with m being the dimensionality of the image and I is the
identity tensor. The local structure can then be described by eigenvectors
and eigenvalues of TPC.
4.2.1 PCT vesselness and PCT neuriteness As described in
Section 3.2, piecewise curvilinear segments can be detected by analyzing
the relations between eigenvalues and eigenvectors of the locally
calculated Hessian. In a similar way, the dominant orientation of the surface
representing a curvilinear structure is given by the dominant eigenvector
of TPC, i.e. the eigenvector corresponding to the eigenvalue of largest
magnitude. PCT-based vesselness and PCT-based neuriteness are
calculated using the original vesselness and neuriteness equations, with the
eigenvalues of TPC substituting those of the Hessian.
General approach for network extraction
4.3.1 Curvilinear feature enhancement Let us consider an image
of a curvilinear network structure I(p) of a size M N pixels, where
p x; y T represents pixel location. When the curvilinear network is
not affected by variations of intensity contrast within the image, then
the input image I(p) is directly used in the following procedures (see
fig. 1a). Otherwise, one of the curvilinear feature enhancement methods,
discussed in (Section 4.2), is applied. An enhanced image IFp as well as
the corresponding vector field IVFp are calculated. The size of image
IVFp is M N 2.
4.3.2 Watershed The watershed transformation was introduced as
a tool for segmenting gray-scale images by (Beucher and Lantuejoul,
1979), and is now used as in many segmentation procedures using
efficient algorithms (Meyer, 1994).
Lets us consider a gray-scale image I(p) (or IFp) as a topographic
surface: the gray level of a pixel becomes the elevation of a point, the
basins and valleys of the relief correspond to the dark areas, whereas the
peaks and crest lines correspond to the bright areas. The watershed line
may be intuitively introduced as the set of points where a drop of water
may flow down towards several catchment basins of the relief.
The watershed algorithm can be used for segmentation by using the
calculated catchment basins as segmented regions. In our case, however,
we are interested in watershed lines themselves, which delineate ridges in
the image and thus correspond to network branches.
4.3.3 Branches and branching points extraction The skeleton
defined by watershed lines is subsequently categorised into branches
IBp, branching points IBPp and end points IBEp using the topological
method proposed by Kong and Rosenfeld (1996). IBp; IBPp and IBEp
are images containing unique labels for the pixels that make up a specific
object. The performance of this procedure is demonstrated in figure 1b.
The majority of the skeleton corresponds visually to the clearest
structures of the network. However, the watershed transformation typically
produces an over-segmentation of the input image I(p) [or IFp] as
extremely subtle variations in image intensity can still yield basins with
corresponding watershed boundaries. These extraneous segments can
be evaluated using local cost-functions and pruned if they fail to meet
the appropriate criteria.
Algorithm 1 Pruning procedure.
Input: IFp; IVFp; IBp; IBPp; IBEp; , t
Output: IBp; IBPp; IBEp
for i 1 ! NB do
b findIBp i
c CIF; IVF; b;
if c5t then
IBp > 0 [ IBPp > 0 [ IBEp > 0
The pruning procedure used here is based on a cost function that includes
weighted contributions of both intensity information and the alignment
of the local vector field, calculated for every branch of the skeleton. The
cost of the branch defined by pixels b is computed using the following
where CI is a normalized input or enhanced image intensity-based cost
and CV is a vector field-based cost that is calculated as follows:
bi; bi1 jIVFbi dbi; bi1j
and K is a number of pixels in b. 2 0; 1 determines the relative weight
of the CI and CV cost components. |||| is the Euclidean norm. The
purpose of the vector field cost CVF is to determine branches aligned with the
direction of a vector field given by IVFp.
Finally, all branches with a cost value smaller than threshold t and
their corresponding branching and end points are removed (see fig. 1c).
The procedure is given in Algorithm 1. NB denotes number of labeled
branches in image IBp. Functions BranchPoints, BranchEnds and
Branches return images containing labeled pixels representing every
branching points, ends and branches. Function find returns non-zero
pixel positions of an image.
4.3.5 Graph extraction In order to apply network analysis tools,
the morphological structure has to be translated into an appropriate
Fig. 1. Workflow: (a) Input image as defined by the region of interest
outlined in red in Figure 2; (b) watershed-based segmentation: fungal
network skeleton (in red), branching points (in green) and endpoints
(in blue); (c) pruning (as pointed out by violet arrows); (d) graph built
form the extracted structure of the network; (e) pseudo-color coded
representation of cord thickness; (f) fungal food source detection (region of
interest outlined in green in Figure 2: the boundary is outlined in magenta
and (g) graph at the region of the source of food
network representation. We assume that the fungal network can be
represented as a graph by classifying junctions (branch-points and
anastomoses) as nodes and the hyphae or cords between nodes as links (Bebber
et al., 2007; Fricker et al., 2007). The graph representation of the network
structure is constructed by matching every branch with its two
corresponding branching points or with its branching point and endpoint, see
The input branches, branching and end points images, IBp, IBPp
and IBEp, respectively, are used to construct the graph G. For every
branch b in IBp, a set of corresponding branching points fbp} is
extracted. When the branch has two branching points then the graphs
edge G(i) is defined by fbp(1), bp(2)}, otherwise, G(i) is represented by
branching point bp(1) and the end point be. The procedure is given in
Algorithm 2 Graph extraction procedure.
for i 1 ! NB do
b findIBp i
bp findIBPp > 0 \ IBp i
if dimbp 2 then
Gi fbp1; bp2g
else if dimbp 1 then
be findIBEp > 0 \ IBp i
Gi fbp1; beg
4.3.6 Thickness A very important measure used to characterize
biological networks, is the cord thickness, as this has a significant
impact on the physiological function of the network. The thickness
value for each branch is determined by iterative filtering of the center
line image using morphological dilation and reconstruction
procedures (Serra, 1982).
The input branches and branching points and ends images,
IBp; IBPp and IBEp, respectively, are used to construct the skeleton
images ISKp. A copy of ISKp, called IWp, is then dilated using a disk
structuring element S with 1 pixel radius. The difference between IWp
and the result of dilation is stored in the image ISp that contains the
surrounding boundaries of the skeleton. Then, for a given threshold value
k, thresholding of the image IFp masked by the image ISp is performed
and the image IVp is obtained. In order to reconstruct all pixels in the
image IVp which are connected to the skeleton in the image IWp, the
morphological reconstruction of the image marker IWp under the image
mask IMp, a union of ISKp and IVp, is performed producing IRp.
The points in IRp are added onto IWp, and the procedure is repeated.
The procedure is repeated until no pixels remain to be reconstructed with
intensity IFp above k. The distance map IRDp is calculated as the
shortest distance from each of the skeleton points ISKp to the
background in the reconstructed image IWp. Finally, the thickness map
image ITKp is given by the distance map image IRDp weighted by
the mean intensity of IFp points defined by the neighborhood of each
pixel of the skeleton image ISKp.
The output of the procedure is presented in figure 1e and its workflow
is shown in Algorithm 3. In this Algorithm, function SIp denotes the
morphological dilation of an image I(p) by a structuring element S.
SIp; Jp is a function that represents the morphological
reconstruction of mask image I(p) from marker image J(p), Jp Ip. Function
dist computes the Euclidean distance transform of a binary image.
denotes the convolution operation and S(r) is a disk structuring element
with r pixel radius.
Algorithm 3 Thickness procedure.
Application to extraction of fungal networks
In all the fungal network extraction experiments, the following
parameters have been used: number of scales and orientations 6, weight
0:5, branch cost threshold t 0.2 and thickness threshold k 0.4.
In all cases, the PCT-based vesselness approach (Equation 1) is used.
An analysis of the sensitivity to different parameters for the PCT
calculation can be founded in (Obara et al., 2012).
In the particular case of the fungal networks, the graph representation
of the network has to be redefined in the region corresponding to the
fungal source of food, as the structure of the network within the food
source is not visible, but can be approximated as a single node connected
to all cords arising from the boundary.
4.4.1 Fungal food source detection In order to extract the fungal
food source, the image I(p) is segmented by a global threshold (Otsu,
1979). The segmented image is then filtered using morphological opening
and closing using a disk structuring element S, to produce the binary
image IFoodp. figure 1f shows the output of this procedure.
4.4.2 Graph for the fungal network The graph G representing the
fungal network is finally modified to account for the presence of food
resources. The graph is redefined for the vertices that intersect with the
segmented resource IFoodp. such that they all connect to a single node in
the center of the source of food as the underlying network is not visible
within the wood block (fig. 1g).
Species such as P. impudicus produce densely cross-linked
networks, with relatively well-defined thick cords. To summarise the
complete extraction process, images of this species collected at
high-resolution and high-contrast (fig. 1a) were rapidly
segmented using the watershed method (fig. 1b), with no additional
requirement for curvi-linear feature enhancement.
Oversegmentation, generally considered as a downside of the watershed
transform, allows in this case a rapid delineation of highdensity
networks. Pruning based on the average intensity of every branch
was then carried out, providing a mechanism to control the
overall level of detail of the final network (figure 1c). The graph
representation of the network was then calculated by defining the
branch or fusion points and end points throughout the network
as nodes, and then determining the edges that link them (fig. 1d).
The Euclidean length of each edge was also calculated from the
segmented skeleton, and the cord thickness estimated from a
sequence of morphological dilations of the skeleton until the
threshold criterion was reached, combined with filtered pixel
intensities to capture the difference in reflectivity for cords of
different dimensions (fig. 1e). The final step for the fungal
networks was to identify the initial food resource (fig. 1f) and then
redefine the graph in this region to connect all cords emanating
from the resource with a central node (fig. 1g). The performance
of the proposed approach applied to the entire image is presented
in figure 2.
When no enhancement was applied, the watershed and
pruning method was less reliable for low-contrast, low-resolution
images, such as those obtained for Phanerochaete velutina,
which has thinner, more diffuse cords, particularly at the
growing margin. With varying levels of threshold, the network was
initially over-segmented, but rapidly became dis-connected as the
threshold was raised, making the choice of threshold critical (fig.
3ae). In comparison, even these challenging networks were
efficiently extracted following intensity-independent PCT
enhancement (see Section 4 for details) to give a very clean network over
a broad threshold range (fig. 3fj), that greatly facilitated
subsequent pruning operations (fig. 4).
To quantify the performance of our approach, five complex
regions of interest in the fungal images were selected. Manual
tracing of network centerlines was performed exhaustively by an
expert, to give a Gold Standard (GS) reference. In total, in all
regions of interest, 2256 network branches were annotated. The
GS and extracted network were compared using the network
network distance measure "d (Gelasca et al., 2009), defined as the
average distance between each point on the GS network
centerline and the corresponding closest point on the extracted network
centerline, and vice versa. The standard deviation "d of the
network-network distance measures was also calculated. The
distance error evaluation for each ROI, where the network was
extracted using the proposed approach based on PCT vesselness,
is presented in Table 1. For all annotated regions, the average
distance error was "d 0:7393pixel . The recommended setting
used to calculate the PCT-based vesselness, can be found in
(Obara et al., 2012). Supplementary figure S4 presents
normalized histograms of distance error values "d for all analyzed
regions of interest in fungal images. Additionally, traced lines were
identified as true/false Positives depending on whether a line was
found in the gold standard at a distance smaller than two pixels.
Precision and recall were calculated for a set of comparable
approaches, and are shown in Table 2. Finally, a comparison
of the network thickness estimated using optical microscope
and our approach, for 10 randomly selected measurement
points, is presented in Supplementary figures S5 and S6.
The average runtime spent to extract the fungal networks from
the grayscale images of 1000 1000 pixels and 60 K branches
(links) is 70s (without enhancement) and 200s (with PCT
enhancement). This compares with manual segmentation of 3K
branches in about 23 days (Fricker et al., 2007). The runtime
performance of the implemented methods was tested on a PC
with Intel Core 2 Duo (T8300) system with 2GB memory,
running Linux and MATLAB R2009b.
In this article, an image analysis and processing concept for
general curvilinear network detection has been introduced. The core
method is based on extraction of the network centerline from a
watershed segmentation, followed by a pruning procedure. This
approach can be directly applied to high-contrast images, but the
combination with a curvilinear feature enhancement based on
Phase Congruency Tensors provides a contrast invariant solution
for more challenging networks.
Using the watershed transform to calculate center lines
provides several advantages over other more complex
networkanalysis routines. First, it guarantees calculation of connected
networks. Second, it requires low computation times in
comparison with other segmentation methods. By using a standard
morphological watershed transformation on raw or
PCTenhanced images, we obtain an oversegmented skeleton image
which encompasses the entire biological network, but also a
contribution of false edges associated with subtle variations in
background intensity that still yield basins in the watershed image.
These extraneous features can be removed post-segmentation by
judicious selection of cost-function weights or reduced by prior
network enhancement and noise-reduction using PCT or other
image enhancement techniques described in Section 4.
Visual inspection of the results (fig. 2 and Supplementary Figs.
S13) confirm the robustness of the proposed approach to
extract networks from complex and challenging biological
specimens. In particular, the PCT-based enhancement is effective at
dealing with highly variable intensity levels of the curvilinear
features and is capable of providing high detection responses
on low contrast edges against a noisy background (fig. 3).
These properties are essential to detect structures in low contrast
regions of noisy images that are common in a large number of
biomedical images (Meijering et al., 2004).
The results demonstrate that the proposed approach provides
a fast and robust solution to detect and extract a graph
representation of complex curvilinear networks and overcomes a
critical bottleneck in biological network analysis. This now permits
high-throughput measurements with improved resolution and
precision. The approach is generic and can be applied to a
wide range of biomedical images.
One of the major contributors to errors is optimal threshold
selection for the pruning procedure. Therefore, future work will
be focused on data-driven optimizing approaches to determine
optimal local or global threshold selections.
Once the network has been extracted, a wide range of network
parameters can be calculated (Fricker et al., 2007). As the data
are embedded in Euclidean space, a number of basic
morphological measures can also be readily derived. These values either
have a straightforward biological meaning in their own right or
they provide a comparison with network structures in other
domains. In particular, the rich network structures extracted by this
approach provide a rapid means to examine network features,
Table 1. Distance error evaluation of the proposed method applied to
five regions of interest in fungal images
No. of branches
Neuriteness PCT vesselness PCT
Recall 0.91 0.56 0.95
The assessment of the rate of false positive and false negative segments has been
performed within an error diameter of the gold standard segments equal to 2[pixels].
such as transport efficiency, resilience, cost and control
The authors thank to L. Boddy, D. ABear, J. Hynes and J.
Wood for some of the fungal images analyzed.
Funding: BBSRC, EPSRC and NERC, and an Academic
Fellowship from Research Councils UK.
Conflict of Interest: none declared.