A Learning Based Deformable Template Matching Method for ...

A Learning Based Deformable Template Matching Method for Automatic Rib
Centerline Extraction and Labeling in CT Images
Dijia Wu 1 , David Liu 1 , Zoltan Puskas 1 , Chao Lu 1 , Andreas Wimmer 2 , Christian Tietjen 2 , Grzegorz
Soza 2 , and S. Kevin Zhou 1
1 Siemens Corporate Research, Princeton NJ 08540, USA
2 Siemens Healthcare, Siemensstr. 1, Forchheim 91301, Germany
Abstract
The automatic extraction and labeling of the rib centerlines
is a useful yet challenging task in many clinical applications.
In this paper, we propose a new approach integrating
rib seed point detection and template matching to detect
and identify each rib in chest CT scans. The bottom-up
learning based detection exploits local image cues and topdown
deformable template matching imposes global shape
constraints. To adapt to the shape deformation of different
rib cages whereas maintain high computational efficiency,
we employ a Markov Random Field (MRF) based articulated
rigid transformation method followed by Active Contour
Model (ACM) deformation. Compared with traditional
methods that each rib is individually detected, traced and
labeled, the new approach is not only much more robust
due to prior shape constraints of the whole rib cage, but removes
tedious post-processing such as rib pairing and ordering
steps because each rib is automatically labeled during
the template matching.
For experimental validation, we create an annotated
database of 112 challenging volumes with ribs of various
sizes, shapes, and pathologies such as metastases and fractures.
The proposed approach shows orders of magnitude
higher detection and labeling accuracy than state-of-theart
solutions and runs about 40 seconds for a complete rib
cage on the average.
1. Introduction
To find rib metastases and fractures in chest CT scans,
it typically involves reading hundreds of axial CT slices to
visually track changes in rib cross-section area. However,
manual reading is rather time consuming and rib anomalies
are frequently missed in practice due to human error
[17]. Automatic extraction of rib anatomical centerlines can
1
be used to enhance the visualization of unfolded rib cage,
which will make routine bone reading tasks more efficient
and effective for the radiologists [19]. The extracted and
labeled rib centerlines can also serve as the reference to localize
organs [25], register pathologies [22] and guide correspondence
between serial thoracic CT scans for interval
change analysis [13]. In addition, the derived rib geometry
can assist with the rib cage fracture fixation surgeries [7].
(a) (b)
Figure 1. Example of different rib cross section appearances. (b)
shows more clear dark rib marrow than (a).
Despite its clinical importance, automatic detection and
labeling of ribs in CT scans has not been extensively studied
before and remains a challenging task. Most of the
prior works model the ribs as elongated tubular structures
and employ Hessian or structure tensor eigen-system analysis
for ridge voxel detection [2, 21, 23]; however, these algorithms
are usually computationally expensive and moreover,
the rib marrow is typically darker than its boundary
thus the rib center points are not exactly ridge voxels as
shown in Fig.1(b). To construct the rib centerline, tracking
based methods such as Kalman filter are usually used
to trace detected rib center points from one slice to the next
[19, 21, 9, 10]; however, some of them require manual ini-

tial seed points and more critically, these point to point
tracking methods are highly sensitive to local ambiguities
or discontinuities posed by rib pathologies like fractures as
shown in Fig.2, which are nevertheless of the most interest
to radiologists. For all of these algorithms, each rib is individually
detected and traced, hence rib labeling requires a
separate heuristic method [23, 18].
In this paper, we propose a new rib centerline extraction
approach that addresses all the above problems. First,
a learning based rib center point detection method is introduced
using computationally efficient Haar-like features
which was proposed by Papageorgiou et al. for object detection
[16]. To further speed up runtime detection, a coarseto-fine
pyramid learning structure is used. Then the obtained
probability response map is used to extract the rib
centerlines via matching of a whole rib cage template. By
extracting all rib centerlines simultaneously instead of tracing
each of them individually, the proposed template matching
not only imposes prior constraints between neighboring
ribs and therefore improves the robustness significantly, but
also provides rib labeling in the same time of the tracking.
To adapt to the deformation of the rib cage and maintain
high computational efficiency, we break the long rib into
short rib segments and carry out articulated rigid segment
matching by searching for the optimal similarity transformation
parameters in a manner similar to marginal space
learning [28]. Compared with traditional point to point rib
tracing algorithms, this new segment to segment matching
approach is much more robust against local ambiguities or
discontinuities. Finally, the piecewise rigidly matched rib
centerlines are refined and smoothed with the active contour
model [8].
(a) (b)
Figure 2. Example of different types of rib pathologies. (a) missing
rib segments as a black gap along the rib (b) rib metastases where
the rib appears much thicker than normal.
Earlier works related to articulated registration within
medical imaging were mainly applied to the problems of
skeletal structures. Baiker et al. [3] proposed a hierarchical
anatomical model of the mouse skeletal system with specified
joint positions and realistic articulation degrees of freedom.
The articulated registration is performed by traversing
the hierarchical anatomical tree in a top-down manner with
iterative closest point algorithm on micro-CT data. In [1],
du Bois d’Aische et al. employed an articulated registration
for vertebral column by searching for the best parameters of
the articulated transformation to maximize the mutual information,
constraining the vertebrae to move relative to their
neighbors. More recently, Martín-Fernández et al. proposed
a landmark based registration method for aligning hand radiographs
[5]. This method models the bone skeleton with a
wire model where wires are drawn by connecting landmarks
located in the main joints of the skeletal structure.
The remainder of the paper is organized as follows: In
Section 2, we present in detail the new learning based deformable
template matching method for rib centerline extraction
and labeling. Experimental results on 112 annotated
volumes are given in Section 3 with discussion. Section
4 offers with conclusions and outlines the future work.
2. Rib Centerline Extraction and Labeling
2.1. Rib Centerline Voxel Detection
Aforementioned, the rib can not be simply modeled as
a solid bright tubular structure due to its interior dark marrow,
hence the maximum response solely obtained by Hessian
eigen-system based filters does not always match the
rib centerline voxels reliably. In addition, ribs across different
volumes show a variety of size, shape and edge
contrast as shown in Fig.1. Therefore, we develop a robust
learning-based object specific centerline detection algorithm,
wherein the obtained probability map is used to
track and label the rib centerlines. This supervised classification
based two-level stratified learning system was successfully
used in various computer vision problems such
as semantic recognition [11], contextual analysis [26] and
edge based segmentation [12].
We manually annotated 12 pairs of rib centerlines from
40 CT volumes for training. In this work, we select 3D
Haar-like features due to their efficiency and effectiveness
in object recognition [16]. A 3D Haar-like feature considers
adjacent box regions at a specific location in a detection
window and calculate the difference between the sum of the
pixel intensities within the regions. These features can be
rapidly computed using summed area tables first introduced
in [6].
The probabilistic boosting tree (PBT) classifier is trained
with nodes composed of AdaBoost classifiers [24]. Instead
of using only one PBT, we employ a coarse-to-fine pyramid
of PBT classifiers which not only significantly speeds
up the detection by image downsampling thus reducing the
number of samples in earlier stage of the classifiers, but exploits
longer range spatial context in lower resolution which
was usually limited by Haar wavelets [14]. Finally given a
volume, the learned classifiers will generate the probability
response map P(x) that indicates the likelihood of each
voxel being the rib centerline, as shown in Fig.3. The detec-

tion runs highly efficiently and it only takes about 2 seconds
for a volume of size 200 × 200 × 200 voxels on the Intel R○
2.27GHz Xeon R○ platform with 2.75GB RAM.
Figure 3. Example of the rib centerline probability map. The left
is the original volume and the right is the generated rib probability
map with most of the other bones such as scapula and vertebrae
significantly suppressed.
2.2. Rib Cage Deformable Template Matching
The obtained probability map is not always reliable because
of the distractions from neighboring similar bone
structures such as clavicle and scapula, or local ambiguities
and discontinuities caused by rib lesions. Therefore, a
robust rib tracking and labeling method is necessary. The
traditional point to point tracing methods such as Kalman
filter [19] or region growing process [23] that forms line elements
from ridge voxels are highly sensitive to these local
rib anomalies and subject to error propagation.
To address these problems, we propose a new template
matching method for rib centerline extraction. The template
is constructed by manually annotating and labeling 12 pairs
of rib centerlines from one normal rib cage, and each rib
Ri (1 ≤ i ≤ C, C = 24) is represented by a set of evenly
sampled centerline voxels xn (1 ≤ n ≤ Ni) where Ni
is proportional to the length of rib Ri. We intend to find
the best transformation T that maximizes the sum of response
of the transformed template on the generated probability
map:
C Ni
P (T (xn)) (1)
i=1 n=1
The use of a whole rib cage template makes the new
method different from all previous rib detection methods in
that all ribs are tracked or matched simultaneously. The advantages
of this are twofold apparently: shape constraints
can be imposed on neighboring ribs during tracking or
matching to overcome the distractions from adjacent bone
structures such as clavicle or adjacent ribs; all ribs are automatically
labeled via matching.
Due to considerable deformation of the rib cage and
spacing between adjacent ribs as shown in Fig.4, simple
rigid transformation does not suffice. Traditional nonrigid
(a) (b)
Figure 4. Example of different rib cage shapes. The extracted rib
centerlines are shown in green.
transformation or registration approaches can be classified
to the intensity based methods and feature based methods.
The former methods compare intensity patterns in images or
subimages such as the well known B-spline based free form
deformations (FFD) [20] while the latter methods like the
thin plate spline based robust point matching (TPS-RPM)
[4], find correspondence between features such as points,
lines or surfaces. Both methods formulate the registration
as an energy minimization problem which comprises
a transformation smoothness term and a similarity measure
such as normalized mutual information between two images
(FFD) or Euclidean distance between two sets of corresponding
points (RPM). The objective functions are minimized
via gradient descent and expectation-maximization
(EM) like alternating optimization method respectively in
FFD and RPM. However, these optimization methods are
usually computationally expensive, furthermore, both energy
functions are non-convex thus two methods are vulnerable
to local minimum, especially in case of a large number
of outliers and significant deformation.
In this work, we present a much simpler articulated template
matching method by breaking each rib Ri into several
short rib segments Ri,k (1 ≤ k ≤ K). Each rib segment
centerline thus has much less degree of curvature and therefore
can be approximately matched via rigid transformation
by searching for the optimal similarity transform parameters
Ti,k = (ti,k, oi,k, si,k), where (ti,k, oi,k, si,k) denote
the translation, orientation and scale parameters, respectively
as shown in Eq.(2):
ˆTi,k = arg max
Ti,k∈T
Ni,k
P (Ti,k(xn)) (2)
n=1
where T is the set of similarity transformations T . Instead
of exhaustively searching the original nine-dimensional parameter
space of (tx, ty, tz, ox, oy, oz, sx, sy sz), only
low-dimensional marginal spaces are searched in a strategy
similar to the marginal space learning (MSL) [28].
To be specific, the transform estimation is split into three

steps: position estimation, position-orientation estimation
and position-orientation-scale estimation. First, the positional
marginal space is searched exhaustively and a small
portion of the best position hypothesis is preserved. Second,
the orientation marginal space is exhaustively searched
for each position candidate and a limited number of best
position-orientation candidates are kept after this step. Finally,
the scale parameters are searched in the constrained
space in a similar way. It is shown that this marginal space
searching effectively reduces the number of testing hypothesis
by six orders of magnitudes, compared with exhaustive
full space search [28].
In Eq.(2), each rib segment is searched individually and
therefore likely matched to a wrong rib due to the similarity
between adjacent ribs. To avoid this problem, we impose
the pairwise smoothness constraints on the transform parameters
of neighboring rib segments in a Markov random
field (MRF) model:
arg max
(Ti,k,Tj,k)∈T
i=1 n=1
C
Ni,k
P (Ti,k(xn)) − λ
i,j∈Nδ
L(Ti,k, Tj,k)
where λ is the regularization parameter, Nδ stands for the
set of neighboring rib pairs (i, j) and L is the similarity
function of two transform parameters defined as below:
Ni,k
L(Ti,k, Tjk) = ||Ti,k(xn) − Tj,k(xn)|| 2 /Ni,k
n=1
Nj,k
+
n=1
(3)
||Ti,k(xn) − Tj,k(xn)|| 2 /Nj,k (4)
where L measures the average Euclidean distance of two
neighboring rib segments Ri,k and Rj,k transformed by different
parameters Ti,k and Tj,k, respectively.
The proposed articulated template matching method is
illustrated in Fig.5. Each rib is split into four segments
(K = 4) and starting from the segment (k = 1) connected
to the central vertebrae, we search for the optimal
rigid transformation parameters for short segments of all
ribs Ri,k (1 ≤ i ≤ C) simultaneously by maximizing
Eq.(3). The result is used to initialize the pose of the next
rib segment (k = k + 1) and repeat the optimization until
all rib segments are matched (k = K).
The optimization of MRF energy function Eq.(3) is generally
an NP-hard problem. To simplify the problem, we
relax the neighborhood Nδ by only considering all vertical
pairs of neighboring ribs from either side (e.g., the first and
second rib on the left) and one horizontal pair of neighboring
ribs from both sides (we choose the sixth ribs on the
left and right side). The resulting H-shaped graph contains
no loops of cliques and thus can be efficiently solved via
dynamic programming. First, the transformation parameter
Ti,k is searched separately that maximizes Eq.(2) in the
manner of marginal space learning and a number of top candidates
are kept for each rib segment Ri,k (1 ≤ i ≤ C),
then the optimal combination of all rib segment transformations
ˆ Ti,k can be found by adding smoothness constraints in
Eq.(3).
In practice, we find this approximation of imposing less
neighborhood constraints already provides satisfactory results.
As will be validated in Section 3, the new segment to
segment articulated template matching approach is robust
to local rib discontinuities and anomalies such as fractures
or metastases.
2.3. Active Contour Model Refinement
Because each rib segment is transformed rigidly, the articulated
rib centerline is piecewise smooth and subject to
small deviation due to slight deformation of each rib segment
as well as limited resolution of discrete transformation
parameter search space. As a result, we employ the active
contour model or snakes [8] to further refine the matching
results:
E =
C Ni
α
2
i=1 n=1
|x′ n| 2 + β
2 |x′′ n| 2 − P (xn) (5)
where α and β control the elastic force and rigid force respectively,
and xn stands for the rib centerline points. One
of the notorious problems of applying snakes associates
with the initialization. The starting contour must, in general,
be close to the true boundary or else it will likely converge
to the wrong result [27]. But this is not a problem in
this system because the articulated matching in Section 2.2
guarantees good initialization. The minimization of function
Eq.(5) gives rise to solving corresponding Euler equations
and the iterative numerical method in [27] is used. The
result improvement with the active contour model is clearly
shown in Fig.6.
Figure 6. Rib centerline refinement using snakes.

Figure 5. Articulated rigid rib segment matching. Each rib is split into four segments and the registration is performed on a total of twelve
pairs of rib segments together starting from the segments connected to the central vertebrae.
3. Experimental Results
In the experiment, we collect 112 thoracic CT scans from
different subjects and hospitals. These volumes show a significant
variety of the size, shape and pathologies of the rib
cages, with slice distances up to 5mm. All rib centerlines
are fully annotated with a sampling distance of 0.5mm and
labeled by two radiologists based on visual assessment and
consensus review. 40 volumes are used to train the rib centerline
detector and remaining 72 volumes are used for evaluation.
With regard to the parameter setting, we select the
smoothness regularization parameter λ = 10 in Eq.(3) and
α = 50, β = 50 in snakes algorithm Eq.(5) with iterative
step size γ = 1.0. The template is first shifted by aligning
its centroid with the center of the mass of probability
map P . Then we choose the translation search space as
[−20mm, 20mm] for the first rib segments (k = 1) and
[−4mm, 4mm] for the other rib segments (k > 1) with
a sampling grid of 2mm in each direction; the orientation
search space as [−π/3, π/3] for the first rib segments and
[−π/6, π/6] for the other rib segments with a sampling grid
of π/24; and [0.9, 1.1] with a grid of 0.05 for the scale
search space. The obtained transformation parameters of
previous rib segments Ri,k are used to initialize the next rib
segments Ri,k+1, therefore the search space of the first rib
segments is set larger than the following rib segments. In
all experiments, each rib is evenly split into four segments.
We first compare our approach with another fully automated
rib centerline extraction method proposed recently
[19]. It starts from a few automatically detected seed points,
progressively traces along the rib centerlines slice to slice
using a 3D Kalman filter, and employs the Random Walker
algorithm to segment successive 2D rib cross sections and
obtain the center voxels. Because each rib is traced individually,
a separate rib pairing and ordering method is required
to label the traced ribs [18].
Table 1 lists the number of missed ribs, falsely detected
ribs (either traced to clavicle or pelvis) and mislabeled ribs
by two methods, with example extraction results shown in
No. of Ribs Tracing Matching
Missed 138 (8.0%) /40 (55.6%) 0 / 0
False 55 (3.2%) /19 (26.4%) 0 / 0
Mislabeled 692 (40.0%) /46 (63.9%) 0 / 0
Table 1. Result errors of two rib centerline extraction methods.
Each entry gives the number (percentage) of incorrect ribs and the
number (percentage) of volumes these incorrect ribs come from.
Fig.7. It is not surprising that the new articulated template
matching method is significantly more robust than the tracing
method because the latter is highly sensitive to initially
detected seed points; point to point tracing approach is more
vulnerable to local ambiguities than the segment to segment
matching; separate detection of individual rib centerline
lacks prior constraints between neighboring ribs thus
is more susceptible to labeling error; unsupervised random
walker segmentation is more sensitive to the image noise
or lower resolution compared with supervised learning with
training images collected from a variety of resolutions and
noise levels. In contrast, the new algorithm is highly robust
against the deformation of the rib cage and rib anomalies
caused by lesions. Fig.10 shows some challenging cases
where the proposed method still yields reasonably good results.
To the best of our knowledge, pathological ribs were
not discussed in previous literatures of automatic rib detection
methods.
In addition, we also compare the new MRF based articulated
rigid matching method with the nonrigid robust point
matching method (RPM) in [4]. We select the feature point
based registration method for comparison, rather than intensity
based ones, because the matching of a rib cage template
is essentially the registration of a set of points in our problem.
The target set of points is built by thresholding the
derived probability map, wherein the outliers are generated
inevitably. We use the RPM implementation developed at
Yale University [15] in this experiment. As shown in Fig.8,
the resulting rib centerlines are very likely attracted to adjacent
ribs or trapped between two neighboring ribs due to
the local minimum problem as mentioned above. The re-

Figure 7. Six example pairs of automatically extracted rib centerlines. The left is the random walker segmentation based tracing method;
the right is the proposed learning based articulated template matching method.
sults are not improved much by increasing the number of
annealing iterations. For a volume of 200 × 200 × 200 voxels
in size, it takes about 9 minutes on average for shorter
annealing process (T0 = 4, Tfinal = 2, r = 0.9 where
T0 and Tfinal is the initial and final temperature, r is the
annealing rate), and nearly 25 minutes for longer annealing
process (T0 = 20, Tfinal = 1 and r = 0.9). However,
the proposed articulated rigid matching method only takes
about 40 seconds for a volume of the same size.
For quantitative comparison, we employ the modified
Hausdorff distance between the extracted rib centerline
points and ground truth as the measurement and results are
given in Table 2. The proposed matching method outperforms
RPM by one order of magnitude. Notice that for
both methods, the top and bottom pair (especially the top)
of ribs show larger errors compared with the middle ones,
mostly because they are shorter and more curvy, with less
constraints from adjacent ribs and more distractions from
neighboring bones like the clavicles.
RPM Articulated Rigid Matching
pair 1 16.7 4.1
pair 2 12.4 1.5
pair 3-10 11.6 1.2
pair 11 11.2 1.6
pair 12 14.5 3.6
Table 2. The average modified Hausdorff distance (mm) between
the ground truth and extracted rib centerlines by two matching
methods.
inf d(a, b) inf d(b, a)
a∈A b∈B b∈B a∈A
d(A, B) = max(
,
) (6)
|A|
|B|
As mentioned in Section 1, one of the applications of
the obtained rib centerlines is to enhance the visualization
of the rib cage where the rib is digitally unfolded along the
centerline. The unfolded two dimensional image makes it
easier for the radiologists to find out the rib abnormalities

(a) (b)
Figure 8. RPM registration results. (a) T0 = 4, Tfinal = 2 and
r = 0.9; (b) T0 = 20, Tfinal = 1 and r = 0.9. The red points
represent the registered rib cage template and the green points are
obtained by probability map thresholding.
such as fractures or varying severity of rib metastases. Two
examples of rib unfolding images are shown in Fig.9 with
multiple rib fractures.
(a) (b)
Figure 9. Two examples of rib unfolding images. (a) left rib cage;
(b) right rib cage. In both cases, multiple rib fractures occur.
4. Conclusion and Discussion
In this paper, we presented a learning based deformable
template matching method to extract and label rib centerlines.
Compared to previous rib detection and segmentation
approaches, this method is highly robust because of multiple
reasons. First, a supervised learning based detector
is trained to locate the rib centerlines. It is more reliable
with regard to the image noise or lower resolution given a
reasonably large training dataset. Then, a template matching
method is used to track all rib centerlines simultaneously
with constraints between neighboring ribs imposed in
a MRF model. This helps prevent individual rib tracked
to adjacent ones and also makes the labeling much easier.
Finally, we introduced an articulated rigid transformation
method where the ribs are matched segment to segment. It
is much more robust against local rib anomalies than traditional
point to point rib tracing methods.
Although this paper focuses on the problem of rib centerline
extraction, the proposed articulate template matching
method constrained by Markov random field in the transformation
parameter space can be applied to other articulated
structures such as the vertebrae. Ongoing work will include
the extension of this algorithm to partial rib cage which not
all twelve pairs of ribs are present in the volume, which requires
a more flexible template. In addition, the precision
of two rib endpoints can also be improved with some learning
based algorithms. Currently, the search of the transform
candidates takes most of the time in the whole system, and
a coarse to fine pyramid may be used to speed up this component.
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