IEEE TRANSACTIONS ON MEDICAL IMAGING, REVISED SUBMISSION, SEPT 2011 1
Supervoxel-Based Segmentation of Mitochondria in
EM Image Stacks with Learned Shape Features
Aur
´
elien Lucchi, Kevin Smith, Radhakrishna Achanta, Graham Knott, and Pascal Fua
Abstract—It is becoming increasingly clear that mitochondria
play an important role in neural function. Recent studies show
mitochondrial morphology to be crucial to cellular physiology
and synaptic function and a link between mitochondrial defects
and neuro-degenerative diseases is strongly suspected. EM mi-
croscopy, with its very high resolution in all three directions, is
one of the key tools to look more closely into these issues but
the huge amounts of data it produces make automated analysis
necessary.
State-of-the-art computer vision algorithms designed to oper-
ate on natural 2D images tend to perform poorly when applied
to EM data for a number of reasons. First, the sheer size of a
typical EM volume renders most modern segmentation schemes
intractable. Furthermore, most approaches ignore important
shape cues, relying only on local statistics that easily become
confused when confronted with noise and textures inherent in
the data. Finally, the conventional assumption that strong image
gradients always correspond to object boundaries is violated by
the clutter of distracting membranes.
In this work, we propose an automated graph partitioning
scheme that addresses these issues. It reduces the computational
complexity by operating on supervoxels instead of voxels, incor-
porates shape features capable of describing the 3D shape of the
target objects, and learns to recognize the distinctive appearance
of true boundaries.
Our experiments demonstrate that our approach is able to
segment mitochondria at a performance level close to that
of a human annotator, and outperforms a state-of-the-art 3D
segmentation technique.
Index Terms—Electron microscopy, segmentation, supervoxels,
mitochondria, shape features.
I. INTRODUCTION
I
N addition to providing energy to the cell, mitochondria
play an important role in many essential cellular func-
tions including signaling, differentiation, growth and death.
An increasing body of research suggests that regulation of
mitochondrial shape is crucial for cellular physiology [10].
Furthermore, localization and morphology of mitochondria
have been tightly linked to neural functionality. For example,
pre- and post- synaptic presence of mitochondria is known to
have an important role in synaptic function [34].
Mounting evidence also indicates that there is a close link
between mitochondrial function and many neuro-degenerative
A. Lucchi and K. Smith contributed equally to this work.
A. Lucchi, R. Achanta, K. Smith, and P. Fua are in the Computer,
Communication, and Information Sciences Department; G. Knott is with the
Interdisciplinary Center for Electron Microscopy, EPFL, Lausanne CH-1015
Switzerland. E-mail: firstname.lastname@epfl.ch.
Manuscript received December 23, 2010. Revised May 24, 2011.
Copyright (c) 2010 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to pubs-permissions@ieee.org.
diseases. Mutations in genes that control fusion and divi-
sion events have been found to cause neurodegenerative pro-
cesses [26]. For example, mutations of the gene coding for
a protein kinase called PINK1, which is known to regulate
mitochondrial division, have been linked to a type of early-
onset Parkinson’s disease [46].
Unfortunately, because mitochondria range from less than
0.5 to 10 µm in diameter [9], optical microscopy does not
provide sufficient resolution to reveal fine structures that are
critical to unlocking new insights into brain function. Recent
Electron Microscopy (EM) advances, however, have made it
possible to acquire much higher resolution images, and have
already provided new insights into mitochondrial structure and
function [39]. The data used in this work were acquired by a
focused ion beam scanning electron microscope (FIB-SEM,
Zeiss NVision40), which uses a focused beam of gallium
ions to mill the surface of a sample and an electron beam
to image the milled face [27]. The milling process removes
approximately 5nm of the surface, while the scanning beam
produces images with a pixel size of 5 × 5nm. Repeated
milling and imaging yielded nearly isotropic image stacks
containing billions of voxels, such as the ones appearing in
Figure 1.
Analyzing such an image stack by hand could require
months of tedious manual labor [40] and, without reliable
automated image-segmentation tools, much of this high quality
data would go unused. This situation arises in part from
the fact that most state-of-the-art EM segmentation algo-
rithms [25], [42] were designed for highly anisotropic EM
modalities, such as Transmission Electron Microscopy (TEM).
Such data tends to have a greatly reduced resolution in
the z-direction, and associated segmentation algorithms often
process slices individually to deal with the missing data.
Our approach processes large 3D volumes in a single step,
which is advantageous for isotropic FIB-SEM stacks. More
generic Computer Vision algorithms that perform well on
natural image benchmarking data sets such as the Pascal VOC
(Visual Object Classes) data set [13] perform poorly on EM
data, whether it is isotropic or not. There are several reasons
for this. The amount of data in a typical EM stack is a
major bottleneck, rendering these approaches intractable both
in terms of memory and computation time. Furthermore, these
approaches rarely account for important shape cues and often
rely only on local statistics which can easily become confused
when confronted with the noise and textures found in EM
data. Finally, the conventional assumption that strong image
gradients always correspond to significant boundaries does not
hold, as illustrated in Figure 1.
To overcome these limitations, we advocate a graph parti-
IEEE TRANSACTIONS ON MEDICAL IMAGING, REVISED SUBMISSION, SEPT 2011 2
CA1 Hippocampus Striatum
5 × 5 × 5 µm sample size 9 × 5 × 2.5 µm sample size
1024 × 1024 × 1000 voxels 1536 × 872 × 318 voxels
(5 × 5 × 5
nm
voxel
) (6 × 6 × 7.8
nm
voxel
)
testing
training
testing
Fig. 1. FIB-SEM data sets. The top row contains 3D image stacks acquired
using FIB-SEM microscopy. Details in the bottom row are taken from the
blue boxes overlaid on the stacks. Mitochondria, which we wish to segment,
are indicated by black arrows. The high resolution allows neuroscientists to
see important details but poses unique challenges. FIB-SEM image stack
dimensions are orders of magnitude larger than conventional images, which
limits the usefulness of many state-of-the-art segmentation algorithms, as
discussed in Sec. IV-D1. Further complicating the problem are the presence of
numerous objects with distracting shapes and textures, including vesicles and
various membranes. Finally, we can not rely on strong contrasts to indicate
object boundaries. Note that the Striatum data is split into training and testing
sections, denoted by a dashed line. A separate training stack is used for the
CA1 Hippocampus (not shown).
tioning approach that combines the following components.
• Operating on supervoxels instead of voxels. We cluster
groups of similar voxels into regularly spaced supervoxels
of nearly uniform size, which are used to compute
robust local statistics. This reduces the computational and
memory costs by several orders of magnitude without
sacrificing accuracy because supervoxels naturally respect
image boundaries.
• Including global shape cues. The supervoxels are con-
nected to their neighbors by edges and form a graph.
Most graph segmentation techniques rely only on local
statistics to partition the graph, ignoring important shape
information. We introduce features that capture non-local
shape properties and use them to evaluate how likely a
supervoxel is to be part of the target structure.
• Learning boundary appearance. EM data is notori-
ously complex, violating the standard assumption that
strong image gradients always correspond to significant
boundaries. Spatial and textural cues must be considered
when determining where true object boundaries lay. We
therefore train a classifier to recognize which pairs of su-
pervoxels are most likely to straddle a relevant boundary.
This prediction determines which edges of the supervoxel
graph should most likely be cut during segmentation.
We demonstrate our approach for the purpose of segmenting
mitochondria in two large FIB-SEM image stacks taken from
the CA1 hippocampus and the striatum regions of the brain.
We show that our approach performs close to the level of a
human annotator and is much more accurate than a state-of-
the-art 3D segmentation approach [52].
II. RELATED WORK
In this section, we begin by examining previous attempts
to segment mitochondria. We then broaden our discussion to
include the use of machine learning techniques for other tasks
in EM imagery. Finally, we discuss methods that rely on a
graph partitioning approach to segmentation.
A. Mitochondria Segmentation
As discussed in the introduction, understanding the pro-
cesses that regulate mitochondrial shape and function is
important. Perhaps due to the difficulty in acquiring the
data, relatively few researchers have attempted to quantify
important mitochondria properties in recent years. In [59],
a Gentle-Boost classifier is trained to detect mitochondria
based on textural features. In [43], texton-based mitochondria
classification of melanoma cells is performed using a variety
of classifiers including k-NN, SVM, and Adaboost. While
these techniques achieve reasonable results, they consider
only textural cues while ignoring shape information. A recent
approach, described in in [52], using state-of-the-art features
and a Random Forest learning approach for segmentation has
been successfully applied to 3D EM data in [32]. We compare
our approach to [52] in Section IV.
In [44], shape-driven watersnakes that exploit prior knowl-
edge about the shape of membranes are used to segment
mitochondria from the liver. However, this approach is adapted
to anisotropic TEM data. Recently, new features have been
introduced to segment mitochondria in neural EM imagery.
Ray features, first introduced in [51], were applied to 2D
mitochondria segmentation in [36]. Inspired by Ray features,
Radon-like features were proposed in [33], but have shown to
perform significantly worse than Ray features in [55].
B. Machine Learning in EM Imagery
Besides mitochondria segmentation, machine learning tech-
niques have found their way into other tasks in EM imagery
including membrane detection and dendrite reconstruction. We
refer the reader to [23] for an excellent survey covering some
of these applications. EM data poses unique challenges for
machine learning algorithms. In addition to the large number
of voxels involved, a variety of sub-cellular structures exist
including mitochondria, vesicles, synapses, and membranes.
As seen in Fig. 1, these structures can be easily confused when
IEEE TRANSACTIONS ON MEDICAL IMAGING, REVISED SUBMISSION, SEPT 2011 3
Fig. 2. Segmenting an image stack into supervoxels. (left) A cropped FIB-
SEM image stack containing a mitochondrion. (right) The cropped stack is
segmented using the SLIC algorithm into groups of similar voxels called
supervoxels. For visualization, supervoxels in the center of the image stack
have been removed, leaving supervoxels belonging to the mitochondrion
interior and on the caps of volume. Boundaries between supervoxels are
marked in black. Notice that voxels with similar intensities are grouped while
respecting natural boundaries.
only local image statistics are considered, especially given the
often low signal-to-noise ratio of the data. This is one of the
reasons why algorithms that perform well on natural images
are far less successful on EM data.
While a large body of research is dedicated to segmenting
axons and dendrites from EM data, only a small faction uses
a machine learning approach. In [22], a Convolutional Net-
work (CN) performs neuronal segmentation by binary image
restoration. This work is extended in [21] by incorporating
topological constraints. In [54], CNs are used to predict an
affinity graph that expresses which pixels should be grouped
together using the Rand index [49], a quantitative measure of
segmentation performance. In another recent approach [25], a
random forest classifier is used in a cost function that enforces
gap-completion constraints to segment TEM slices.
Machine learning techniques have also been applied to de-
tect membranes, a common preprocessing step in registration
and axon/dendrite reconstruction. In [24], Neural Networks
relying on feature vectors composed of intensities sampled
over stencil neighborhoods are trained to recognize membranes
in TEM image stacks. In [58], an Adaboost classifier is trained
to detect cell membranes based on eigenvalues and Hessian
features. A hierarchical random forest classification scheme is
used to detect boundaries and segment EM stacks in [5].
C. Segmentation by Graph-Partitioning
While active contours and level sets have been successfully
applied to many medical imaging problems [12], they suffer
from two important limitations: each object requires individual
initialization and each contour requires a shape prior that may
not generalize well to variations in the target objects. EM
image stacks contain hundreds of mitochondria, which vary
greatly in size and shape. Proper initialization and definition
of a shape prior for so many objects is problematic.
In recent years, graph partitioning approaches to segmen-
tation have become popular. They produce state-of-the-art
segmentations for 2D natural images [50], [14], generalize
well, and unlike level sets and active contours, their com-
plexity is not affected by the number of target objects. In
2010, the top two competitors [11], [16] in the VOC seg-
mentation challenge [13] relied on such techniques. Graph
Algorithm 1 SLIC Supervoxels
/∗ Initialization ∗/
Initialize cluster centers C
k
= [I
k
, u
k
, v
k
, z
k
]
T
by sam-
pling voxels at regular grid steps S.
Move cluster centers to the lowest gradient position in a
3 × 3 × 3 neighborhood.
Set label l(i) = −1 for each voxel i.
Set distance d(i) = ∞ for each voxel i.
repeat
/∗ Assignment ∗/
for each cluster center C
k
do
for each voxel i in a 2S × 2S × 2S neighborhood
surrounding C
k
do
Compute distance δ
ik
between C
k
and voxel i.
if δ
ik
< d(i) then
set d(i) = δ
ik
set l(i) = k
end if
end for
end for
/∗ Update ∗/
Compute new cluster centers.
Compute residual error E.
until E ≤ threshold
/∗ Post-processing ∗/
Enforce connectivity.
partitioning approaches minimize a global objective function
defined over an undirected graph whose nodes correspond
to pixels, voxels, superpixels, or supervoxels; and whose
edges connect these nodes [6], [8], [2]. The energy function
is typically composed of two terms: the unary term which
draws evidence from a given node, and the pairwise term
which enforces smoothness between neighboring nodes. Some
works introduce supplementary terms to the energy function,
including a term favoring cuts that maximize the object’s
surface gradient flux [28]. This alleviates the tendency to
pinch off long or convoluted shapes, which is important when
tracking elongated processes [42]. However, as noted in [25],
it cannot entirely compensate for weakly detected membranes
and further terms may have to be added.
A shortcoming of standard graph partitioning methods, as
we will discuss in Section III-C, is that most do not consider
the shape of the segmented objects.
III. METHOD
The first step of our approach is to over-segment the image
stack into supervoxels, small clusters of voxels with similar
intensities. All subsequent steps operate on supervoxels instead
of individual voxels, speeding up the algorithm by several
orders of magnitude. This step is described in Section III-A.
Next, a feature vector containing shape and intensity in-
formation is extracted for each supervoxel, as described in
Section III-B. The final segmentation is produced by feeding
IEEE TRANSACTIONS ON MEDICAL IMAGING, REVISED SUBMISSION, SEPT 2011 4
the extracted feature vectors to classifiers that define the unary
and pairwise potentials of a graph cut segmentation step
described in Section III-C. The learning procedure and a list
of parameters are provided in Section IV.
A. Supervoxel Over-segmentation
Many popular graph-based segmentation approaches such
as graph cuts [6] become exponentially more complex as
nodes are added to the graph. In practice, this limits the
amount of data that can be processed. EM stacks can contain
billions of voxels, making such methods intractable both in
terms of memory and computation time. Even for moderately-
sized stacks, standard minimization techniques [29], [60],
[31] become intractable. By replacing the voxel-grid with a
graph defined over supervoxels, we reduce the complexity by
several orders of magnitude while sacrificing little in terms of
segmentation accuracy.
To efficiently generate high-quality supervoxels, we extend
our earlier superpixel algorithm, simple linear iterative clus-
tering (SLIC) [48], to produce 3D supervoxels such as those
depicted in Fig. 2. The approach used in SLIC is closely
related to k-means clustering, with two important distinctions.
First, the number of distance calculations in the optimization
is dramatically reduced by limiting the search space to a
region proportional to the supervoxel size. Second, a novel
distance measure combines intensity and spatial proximity,
while simultaneously providing control over the size and
compactness of the supervoxels.
The supervoxel clustering procedure is summarized in the
table marked Algorithm 1. Initial cluster centers are chosen
by sampling the image stack at regular intervals of length S
in all three dimensions. The number of supervoxels k and the
number of voxels in the volume N determines the length,
S =
p
N/k. Next, the centers are moved to the nearest
gradient local minimum. The algorithm then assigns each
voxel to the nearest cluster center, recomputes the centers, and
iterates. After n iterations, the final cluster members define the
supervoxels.
SLIC is many times faster than standard k-means cluster-
ing thanks to a distance function measuring the spatial and
intensity similarities of voxels within a limited 2S × 2S × 2S
region
δ
ik
=
r
(I
k
− I
i
)
2
m
2
+
(u
k
− u
i
)
2
+ (v
k
− v
i
)
2
+ (z
k
− z
i
)
2
S
2
,
(1)
where I is image intensity; u
i
, v
i
, and z
i
are the spatial
coordinates of voxel i; u
k
, v
k
, and z
k
are those of cluster
center k. Normalizing the spatial proximity and intensity terms
by S and m
1
allows the distance measure to combine these
quantities which have very different ranges. Simply applying
a Euclidean distance without normalization would result in
clustering biased towards spatial proximity. Supervoxel com-
pactness is regulated by m. As seen in Figure 3, higher m
1
S and m are the average expected spatial and intensity distances within
a supervoxel, respectively. m can be adjusted to control compactness.
values produce more compact supervoxels while lower m
values produce less compact ones that more tightly fit the
image boundaries.
To ensure that the total number of distance calculations
remains constant in N, irrespective of k, the distance calcu-
lations are limited to a 2S × 2S × 2S volume around the
cluster centers. This makes the complexity O(N), whereas a
conventional k-means implementation would be of complexity
of O(kN) where N is the number of voxels.
A post-processing step enforces connectivity because the
clustering procedure does not guarantee that supervoxels will
be fully connected. Orphan voxels are assigned to the most
similar nearby supervoxels using a flood-fill algorithm. We
refer the interested reader to [4] for further details.
We found SLIC to be particularly well adapted to EM
segmentation as it delivers high quality supervoxels efficiently,
provides size and compactness control, and can operate on
large volumes. Besides SLIC, only a few algorithms are
designed to generate supervoxels. In [57], supervoxels are
obtained by stitching together overlapping patches followed
by optimizing an energy function using a graph cuts approach.
However, this approach performs worse than SLIC in terms of
segmentation quality using standard measures [4], consumes
too much memory, and it is 20 times slower with a worst
case complexity is O(N
2
). A second alternative, used in [5],
applies the watershed algorithm [57] to generate supervoxels.
However, the size and quality of the watershed supervoxels
are unreliable. Finally, other popular superpixel methods could
potentially be extended to 3D, including Quickshift [35],
Turbopixels [56], and the method of [14]. However, these
methods all produce lower quality segmentations than SLIC
in 2D [4], and are orders of magnitude slower: 13, 164 and
5 times slower, respectively. They also require much more
memory. These comparisons are documented in [4].
B. Feature Vector Extraction
After extracting supervoxels, the next step of the algorithm
is to extract feature vectors that capture local shape and texture
information. For each supervoxel i, we extract a feature vector
f
i
combining Ray descriptors and intensity histograms, written
as
f
i
= [f
Ray
i
>
, f
Hist
i
>
]
>
, (2)
where f
Ray
i
represents a Ray descriptor and f
Hist
i
represents an
intensity histogram. For simplicity, we omit the i subscript in
the remainder of the section.
1) Ray Descriptors: Rays are a class of image features
introduced in [51] that capture non-local shape information
around a given point. We extend Ray features to 3D in this
work, and propose a method for bundling a set of Ray fea-
tures into a rotationally invariant descriptor. Ray features are
attractive because they provide a description of the local shape
relative to a given location. This formulation fits naturally into
a graph partitioning framework because Rays can provide a
description of the local shape for locations corresponding to
every node in the graph. Descriptors commonly used for shape
retrieval that rely on skeletonization or contours, including
IEEE TRANSACTIONS ON MEDICAL IMAGING, REVISED SUBMISSION, SEPT 2011 5
m = 20 m = 40 m = 60 m = 80
S = 10
S=10 S=20 S=30
original image
Typical supervoxel size
S = 20
0 500 1000 1500 2000
20
40
60
80
supervoxel size
compactness, m
S = 30
Fig. 3. Supervoxel size and compactness as a function of parameters m and S of Eq. 1. (top left) A cropped EM slice containing three mitochondria.
(middle left) Typical supervoxels sizes for S = 10, S = 20 , and S = 30. (bottom left) Standard deviation of supervoxel size as a function of varying m.
(right) A matrix of supervoxel segmentations showing the effect of varying m and S. Increasing m produces more compact, regular supervoxels. Increasing
S increases supervoxel size. Note that supervoxels are three-dimensional, yet the images above show only a two-dimensional slice of each supervoxel.
(I, θ γ )
θ
r =
r
γ
,
l
l
l l
d
l
c
,
i
c
i
Fig. 4. Ray feature function r(I, c
i
, θ
l
, γ
l
). All components of the Ray
descriptor depend on this basic function. For a given location c
i
, it returns
the location of the closest boundary point r in direction l defined by angles
(θ
l
, γ
l
). d
l
is the corresponding distance from c
i
to the boundary.
distance sets [18] and Lipschitz embeddings [19], do not have
this property.
A Ray feature is computed by casting an imaginary ray in
an arbitrary direction (θ
l
, γ
l
) from a point c, and measuring
an image property at a distant point
r = r(I, c
i
, θ
l
, γ
l
) (3)
where the ray encounters an edge (depicted in Figure 4). In our
implementation, edges are found by applying a 3D extension
of the Canny edge detection algorithm [20].
For supervoxel i, we construct a Ray descriptor by con-
catenating a set of 3L Ray features emanating from the
supervoxel center c
i
, where L is a fixed set of orientations.
The L orientations are uniformly spaced over a geodesic
sphere, as depicted in Figure 5, and defined by polar angles
Θ = {θ
1
, . . . , θ
L
} and Γ = {γ
1
, . . . , γ
L
}. The Ray descriptor
for supervoxel i in an image stack I at orientation (θ
l
, γ
l
) is
written
f
Ray
(I, c
i
, θ
l
, γ
l
) = [f
ndist
, f
norm
, f
ori
]
>
, (4)
where individual Ray features are given by
f
ndist
(I, c
i
, θ
l
, γ
l
) =
kr(I, c
i
, θ
l
, γ
l
) − c
i
k
D
,
f
norm
(I, c
i
, θ
l
, γ
l
) = k∇I(r(I, c
i
, θ
l
, γ
l
))k , (5)
f
ori
(I, c
i
, θ
l
, γ
l
) =
∇I(r(I, c
i
, θ
l
, γ
l
))
k∇I(r(I, c
i
, θ
l
, γ
l
))k
·
r − c
i
kr − c
i
k
,
and ∇I is the gradient of the image stack.
In other words, each descriptor f
Ray
contains three Ray
features that measure image characteristics at the nearest edge
point r given by Eq. 3. The features in Eq. 5 are
• f
ndist
, the most basic feature, simply encodes the distance
from c
i
to the closest edge d
l
= kr(I, c
i
, θ
l
, γ
l
) − c
i
k. It
is made scale-invariant by normalizing by D, the mean
distance over all L directions,
• f
norm
, the gradient norm at r,
• f
ori
, the orientation of the gradient at r computed as the
dot product of the unit Ray vector and a unit vector in
the direction of the local gradient at r.
The final step is to align the descriptor to a canonical
orientation, making it rotation invariant. It is important that
the descriptor is the same no matter the orientation of the
mitochondria, otherwise the learning step would have difficulty
finding a good decision boundary. In Fig. 5(a), two perpendic-
ular axes n
1
and n
2
define a canonical frame of reference for
the descriptor. These axes are assigned specific locations in the
feature vector shown in Fig. 5(b), and all other elements are
ordered according to their angular offsets from n
1
and n
2
. To
achieve rotational invariance, we re-order the descriptor such
that n
1
and n
2
align with an orientation estimate.
To obtain an orientation estimate, Principle Component
Analysis (PCA) is applied to the set of Ray terminal points,
yielding two orthogonal vectors e
1
and e
2
in the directions of
maximal variance of the local shape. Because e
1
and e
2
do
![Fig. 7. Segmentation results. The top row contains results obtained for the CA1 Hippocampus data, and the bottom row contains results obtained for the Striatum data. (a)-(b) Supervoxels vs. regular cubes. We compare segmentation results obtained using SLIC supervoxels of size S = 10 to simple 10×10×10 cubes. Supervoxels, which respect boundaries in the image stack, significantly outperform the cubes while similarly reducing computational complexity. (c)-(d) Contributions of our approach. The dashed blue line labeled “Standard, fHist” represents a baseline result obtained by using a unary term that only depends on the histogram features of Eq. 6 and a contrast-based pairwise term given in Eq. 11. Replacing this pairwise term by the learned one of Eq. 12 results in the improved solid blue curve labeled “Learned, fHist.” An even larger improvement is obtained by introducing the Ray features of Eq. 2, producing the green dashed curve labeled “Standard, f .” Finally, combining the learned pairwise term and the Ray features yield the high quality result denoted by the solid green curve labeled “Learned, f”. (e)-(f) Comparing our approach to Ilastik [52]. We trained the publicly available Ilastik software on the same data we used to train our SVMs and evaluated the segmentations. The solid green curve was generated using our approach. Results obtained using Ilastik appear in as yellow dotted lines. Because Ilastik includes neither smoothing nor regularization, we plot results obtained by thresholding the unary term of Eq. 9 in our approach for a more fair comparison. The dotted curves essentially compare Ilastik’s local texture features to our shape and texture features. Note that thresholding the unary term does not perform as well as our full approach but still better than Ilastik, indicating that the features we use are better adapted to the task at hand. As noted in Section IV-C, the ROC-like plots in (a)-(f) were generated by varying the weight λ, thus changing the influence of the unary and pairwise terms in the energy function of Eq. 7 (with the exception of the dotted curves in (e) and (f), which are conventional ROCs).](/figures/fig-7-segmentation-results-the-top-row-contains-results-1fq2omvy.webp)
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