International Journal of Computational Bioscience, 2012
AN AUTOMATED METHOD
TO ESTIMATE FEMORAL SHAPE
AND MINERAL MASS
Danilo P. Pau,∗ Daniele Masala,∗∗ Xinfeng Bao,∗∗∗ Alberto Gnemmi,∗∗∗ Rachel C. Entwistle,∗∗∗∗
and Dan Dragomir-Daescu∗∗∗∗
it has the potential to dramatically reduce the processing
time that is up to 2 or 3 h to segment an osteoporotic bone,
needed in the clinic to evaluate its quality. We started from
the same high quality quantitative computed tomography
(QCT) image sets provided by the Mayo Clinic, with a resolution of 0.4 mm, and calculated bone shape and mineral
densities in areas of interest. As an option, we allowed the
users to modify the parameters used in each step of the
process. The accuracy of the estimated shape and mineral
mass could therefore be improved through the iterative use
of our algorithms. Our method consisted of three steps:
(i) a femur isolation tool (named FEMTool in this paper)
which was used to segment the bone tissue, (ii) a graphic
renderer based on a state of art implementation of the
marching cubes algorithm [5]–[9], and (iii) a bone mineral
mass computation algorithm used to evaluate the mineral
mass in areas of interest. We will refer to the complete
method as the femur shape and mineral (FSM) tool in the
remainder of the manuscript.
Abstract
Medical assessment of bone health often uses quantitative computed
tomography (QCT) scans and requires a reliable segmentation of
bone geometry from surrounding tissues for a quick determination of
bone mineral mass. Because of its shape and position in the body,
the femur is one of the most challenging bones to investigate. In
the current study, we developed a new automated way to accurately
evaluate both the shape and the mineral mass of cadaveric femur.
The results were achieved through a series of steps including the
segmentation of bone tissue from sets of QCT images, the estimation
of the bone’s outer surface, the calculation of the volume enclosed,
and finally the evaluation of bone mineral mass in a user-defined
region. We compared our algorithms outputs to results obtained
by expert manual segmentation and those obtained using other
published methods.
Key Words
Image based meshing, deformable models, femur shape QCT, mineral
mass, finite element analysis, osteoporosis
2. Methods
1. Introduction
A detailed description of all the processes in FSM is presented in the following sub-sections.
Three papers by the Mayo Clinic’s Division of Engineering
[1]–[3] describe a technique to make three-dimensional (3D)
models of the proximal femur geometry and mineral distribution using mostly manual and semi-automated methods.
Their models were used for accurate finite element estimation of stiffness and load of the bone. This paper is based
on our contribution and presentation to the Biomedical
Engineering (BioMed 2012, Feb. 15–17, 2012) conference
[4]. We used an automated process that could be performed with minimal or no human interaction. Therefore,
2.1 FEMTool for Femur Segmentation
The objective of the first step of the FSM method was to
segment a 3D model of the femur for subsequent visualization and mass computation steps. The main steps of FEMTool were derived from an existing method named brain
extraction tool (BET) [10]–[13] and re-designed to accommodate the characteristics of our femoral QCT dataset.
Prior to segmentation, a pre-processing was performed
for the femoral QCT as follows: (i) First, the minimum and
maximum intensity values of the tested femoral dataset
were found and a threshold, which would be used to roughly
separate femur region from other tissues, was calculated
based on the two intensities; (ii) second, a binary image was
computed by using the threshold value; (iii) a 3D dilation
filter, using a structuring element of size 3, was applied on
the binary image. As a result, the sparse holes inside the
Advanced System Technology, STMicroelectronics, Agrate
Brianza, Italy; e-mail: danilo.pau@st.com
∗∗ Politecnico di Torino, Italy; e-mail: dany.masala@gmail.com
∗∗∗ Politecnico
di
Milano,
Italy;
e-mail:
{xfkeats,
gnemmi.alberto}@gmail.com
∗∗∗∗ Division of Engineering, Mayo Clinic, 200 First Street
SW, Rochester, MN 55905; e-mail:
{Entwistle.Rachel,
DragomirDaescu.Dan}@mayo.edu
Recommended by Dr. Z.-H. Duan
(DOI: 10.2316/J.2012.210-1044)
∗
1
femur region were largely eliminated while a clear contour
of the femur surface was preserved.
Next, the centre of the geometry of the 3D femur
model was calculated as the centre of the femur bounding
box, together with an initial estimate of the radius and
height of an equivalent cylinder representing the femur. We
created a deformable surface mesh, which was composed
by a cylindrical body connected to two hemisphere heads
placed at the opposite sides of it. This mesh was allowed
to slowly deform, similar to the BET method, but with
some modifications to the deformation rules. These rules
were defined and applied on per iteration basis to force a
small distant deformation of each vertex, accordingly to
the deformation vector u defined as:
u = u1 + u2 + u3
requirement was met. This effort was increasing when
processing normal, osteopenic and osteoporotic bones.
2.2 Marching Cubes for Triangle Mesh
The marching cubes (MC) algorithm was first proposed
by Lorensen and Cline in 1987 [5] to reconstruct geometry
from greyscale datasets. We used the algorithm to build
a set of triangles all having the same value specified by
the user. It was therefore possible to visualize multiple
surfaces for the same dataset by using different iso-values.
This algorithm gave the user the choice to visualize an
entire femur reconstruction but also to visualize different
surfaces of the same object, each of them having a specific
greyscale value associated with material density.
We implemented a slightly different version of the MC
in order to solve the known ambiguities present in the
original definition of the algorithm. In particular, we
adopted the solution proposed by Lewiner et al. [8] based
on the computation made by Chernyaev [7] and Nielson
and Hamann [15], which led to a minimal increment in the
number of triangles of about 6%.
In addition, we adopted a solution proposed by
Glanznig et al. [9] for the modification of the iso-value
along a direction of the dataset. In this way, it was possible
to visualize a mixed surface that had different density
values with respect to the position in the model. This
feature was very useful when dealing with femur datasets
that had very high values of density in the diaphysis and
lower density values at the femoral head and neck. MC
was used to create a layered structure which was composed
of a mesh inside of another mesh. As further improvement,
we added a feature for mesh selection. The user had the
ability to view a selected layer within the mesh.
The goal of the algorithm was to build a watertight
outer contour of the bone for each QCT image slice, so
it would be possible to distinguish between external and
internal voxels involved in the MC computation. Tests
showed that when applying this procedure the number of
triangles was reduced by about 30%.
(1)
The first update component u 1 took the movement
within the local surface, along the tangential direction of
the local surface. It was used to keep the deformable
surface vertices equally spaced during the updates. u 2
moved the vertex along the local normal. The role of
this component was to increase the smoothness of the
surface. Considering the variation of curvature for the
femur surface, u 2 was defined by a nonlinear function. It
depends on the local curvature of the surface to enforce
a weak smoothing to high curvature part while a strong
smoothing to low curvature part.
u 3 also acts along the local normal and aimed at
forcing the vertex to track the femur surface. When the
deformable surface was strictly inside the femur region, the
update component 3 enforced the surface to expand. When
the vertex moved out of the femur region, it enforced the
surface to shrink. When the surface just found the boundaries of the femur, expansion or shrink was stopped. For
example, after about 300 iterations, the deformable model
was in the static state and the deformation stopped.
During vertices deformation, the average voxel
greyscale values were calculated for a region extending
3 mm outwards. The average voxel intensity was compared
to the binary dataset to determine both the direction of the
deformation, i.e., expanding or shrinking, and the value of
the movement. The deformation stopped when all vertices
reached the contour of the reconstructed femur. At this
point, a temporary mesh was created representing the
surface of the femur. For the next iteration, the mesh was
then shrunk to half of the original size and re-located to
the centre of the geometry. The modified mesh was re-used
as more detailed initial mesh of the deformable model and
the algorithm was repeated until convergence was reached
(i.e., the differences between two meshes as measured by
the Hausdorff distance (HD) [14] was below a threshold
value). Finally, the converged mesh was used to create a
3D mask and the mask was applied to the original QCT
dataset with a simple selection/rejection rule to obtain
the segmented femur. Since the deformable model was by
construction water-tight, the output of the rule was still
as such, therefore removing the need of time-consuming
manual verification on per slice basis to make sure such
2.3 Mass Computation
In order to compute it, we adopted the same strategy used
by MC because the dataset consisted of cube-like voxels.
After choosing an iso-surface that bounded the volume, the
total mass value related to that volume was the summation
of the contributions given by all the cubes crossed by the
surface and by the cubes completely inside that surface as
per (2):
M ass = Σn1 Vbc da + Σm
1 Vp dati
(2)
The first sum included n cubes completely inside the
surface and the second sum included m cubes crossed by
the surface. Vbc was the volume of the cube, da was
the density average of a cube which was estimated by
averaging the eight voxels at the corners of the cube. Vp
was the partial volume contribution of a cube intersected
by the surface. For a more accurate estimation of volume,
2
Table 1
HD Accuracy and Execution Time of Femur Segmentation
Number of Minimum Value Mean Value Maximum
Execution
Manual
Samples
(mm)
(mm)
Value
Time (s)
Segmentation
(mm)
×86 2.66 GHz
Time
4 GB RAM
Dataset 1
Osteoporotic
45803
0.000013
0.308288
4.885335
59/135
2–3 h
Dataset 2
Normal
26185
0.000041
0.429033
4.602976
75/248
15 min
Table 2
HD Comparison between Mayo Ground Truth versus Marching Cubes
Dataset 1
Iso-Values
Used
Minimum Value Mean Value Maximum Value
(mm)
(mm)
(mm)
RMS
(mm)
−t 0.1
0.000000
0.983030
6.273026
1.278504
−t 0.2
0.000001
0.670587
3.689515
0.805856
−a 0.2 0.1 0
0.000001
0.864244
4.798577
1.094258
−a 0.3 0.1 0
0.000004
0.754805
4.553466
0.937613
−a 0.4 0.1 0
0.000001
0.664291
3.721582
0.815852
−a 0.5 0.1 0
0.000001
0.675783
4.274777
0.837875
−a 0.6 0.1 0
0.000001
0.791206
5.716393
1.008160
Dataset 2
Iso-Values
Used
Minimum Value Mean Value Maximum Value
(mm)
(mm)
(mm)
RMS
(mm)
−t 0.1
0.000000
0.796746
6.382667
1.044301
−t 0.2
0.000001
0.394278
5.718165
0.638745
−a 0.2 0.1 0
0.000000
0.628749
6.230423
0.910276
−a 0.3 0.1 0
0.000000
0.531296
6.041454
0.818764
−a 0.4 0.1 0
0.000000
0.475577
5.839408
0.748784
−a 0.5 0.1 0
0.000000
0.461140
5.637133
0.699850
−a 0.6 0.1 0
0.000001
0.492587
5.408714
0.682123
the partial cube was further divided into a high number of
smaller cubes, t. Therefore, Vp = pt Vbc , where p was the
number of smaller cubes, that lay inside the surface. To
compute p, a density value was assigned to each smaller
cube and trilinear interpolation of the eight voxels at the
corners of the bigger cube was used. If this value was above
the threshold value, the smaller cube was added to the
volume of the bone. The last variable dati was the mean of
the interpolated densities above the threshold. The value
obtained represented the mineral mass of the bone region
delimited by the triangle surface created by MC with the
same iso-value threshold.
3. Results
The validation of results quality was performed at each
step. First, we compared the numerical results obtained
with our FSM method to results obtained by expert users
who employed manual segmentation methods on Mayo’s
QCT datasets (ground truth). We compared: (i) the
final iteration meshes of FEMTool step, (ii) the meshes
produced by just the MC and (iii) the meshes that resulted
from the whole FSM process. In order to compare the
meshes, the HD between any two meshes was calculated
using MeshLab v1.3.0b [16].
3
Table 3
HD Comparisons between Mayo Ground Truth and FSM
Dataset 1
Iso-Values
Used
Minimum Value Mean Value Maximum Value
(mm)
(mm)
(mm)
RMS
(mm)
−t 0.1
0.000002
0.992021
6.746704
1.361168
−t 0.2
0.000001
0.662665
3.448801
0.846973
−a 0.2 0.1 0
0.000005
0.889290
6.635574
1.215395
−a 0.3 0.1 0
0.000001
0.803438
6.602804
1.104818
−a 0.4 0.1 0
0.000000
0.755474
6.529173
1.027861
−a 0.5 0.1 0
0.000000
0.786331
6.416336
1.042601
−a 0.6 0.1 0
0.000002
0.926759
6.341863
1.187317
Dataset 2
Iso-Values
Used
Minimum Value Mean Value Maximum Value
(mm)
(mm)
(mm)
RMS
(mm)
−t 0.1
0.000000
0.756087
6.375305
1.013704
−t 0.2
0.000001
0.398594
5.718165
0.645803
−a 0.2 0.1 0
0.000001
0.611377
6.228402
0.894477
−a 0.3 0.1 0
0.000000
0.520899
6.041454
0.809416
−a 0.4 0.1 0
0.000000
0.469100
5.839408
0.744414
−a 0.5 0.1 0
0.000000
0.457635
5.637133
0.700392
−a 0.6 0.1 0
0.000001
0.490232
5.408714
0.685197
In order to test the numerical performance of the FEMTool algorithm, the contour vertex of the output image was
projected onto the reference image. We measured the error
as the HD between mesh vertices. Also, we recorded the
execution time of the FEMTool using some datasets. This
included pre-processing and initialization of a deformable
model on a 2.66 GHz ×86 computer with 4 GB of RAM.
All datasets had same voxel sizes: 0.4 × 0.4 × 0.4 mm.
Table 1 shows accuracy and computation time for two of
the datasets.
The maximum HD values were much greater than the
QCT voxel size value of 0.4 mm, while the mean distances
were comparable to the voxel size suggesting reasonable
segmentation results obtained by the FEMTool. There
were two main causes that explained these differences:
(i) the FEMTool was inaccurate when the contour of the femur had low density values of the original QCT dataset and
(ii) the outputs of the FEMTool were defined by voxels but
were compared to the referential meshes from Mayo which
were defined by re-meshed surface triangles. Although the
processing time depends on the resolution of the test femur, our femur segmentation method performs much faster
than manual segmentation which could take few hours.
For the last two validations (MC and whole FSM
method), the HD results varied according to the different
iso-values used. A smaller HD value was reached for a
certain iso-value, while the HD increased for other val-
ues. This happened because (for the characteristics of the
datasets and of MC) the volume bounded by the surface
decreased monotonically using higher iso-values. Thus, it
was possible to obtain the optimal size of the produced
mesh, as close as possible to the reference mesh, using an
intermediate iso-value. Table 2 shows the computed HD
between the ground truth and the meshes produced using
just the MC method. Datasets 1 and 2 were the same as
in Table 1. It is important to note that datasets 2 was
obtained from normal bones, while dataset 1 was obtained
for an osteoporotic bone which had lower density values.
In Tables 2 and 3, “−t” indicates a single iso-value, while
“−a” indicates a locally adaptive iso-value that varies along
the vertical direction (bottom-up). Iso-values range from
0 to 1 because the density values of the datasets were normalized during the MC calculations. Values are expressed
in mm.
Most of both mean and RMS values in the MC solution
were less than 1 mm, and they were the most important parameters to consider since directly comparable to voxel size
of the dataset being considered. Moreover, the maximum
difference of about 6.4 mm was attributed to small local
artifacts produced by the MC, located where blood vessels
enter into the femur, and it is not representative of its
global quality. These values can be considered reasonable
because the method used to build the two different meshes
were very different, and because the time durations needed
4
Table 4
Triangle Reduction Using Mesh Selection
Iso-Values
Used
Mesh
Mesh
Mesh
Dataset 1 Selection %Red Dataset 2 Selection %Red Dataset 3 Selection %Red
−t 0.1
164198
148706 10.42
250320
220920
13.31
1094220
921220
18.78
−t 0.2
243122
167949 44.76
249379
200779
24.21
2595991
1571845
65.16
−a 0.2 0.1 0
181183
148067 22.37
248691
214209
16.10
1095346
845797
29.50
−a 0.3 0.1 0
226111
150982 49.76
263979
202030
30.66
2282915
878348 159.91
−a 0.4 0.1 0
250084
210384 18.87
276016
240234
14.89
2815834
1878035
49.94
−a 0.5 0.1 0
260713
215045 21.24
307111
243092
26.34
3537815
2978481
18.78
−a 0.6 0.1 0
239064
214500 11.45
356286
312860
13.88
4105568
3400650
20.73
Table 6
Mineral Mass Convergence
Table 5
Mass Values with Different Iso-Values
Iso-Values
Dataset 1
Mass Values
Dataset 2
Mass Values
Dataset 3
Mass Values
−t 0.1
55272.415385 72176.525440 99040.706697
Smaller
Dataset 1
Cubes
Mass Values
per Side
−t 0.2
51568.280064 70331.753017 97435.210781
2
51542.819559 70305.225212 97489.704521
−a 0.2 0.1 0 54362.526165 71581.467663 98582.653369
4
51563.331653 70326.835245 97444.250922
−a 0.3 0.1 0 50228.722872 70022.751972 95784.467794
6
51568.280064 70331.753017 97435.210781
−a 0.4 0.1 0 44899.016505 67112.193533 91544.094269
8
51570.281314 70333.230100 97432.096701
−a 0.5 0.1 0 38000.993753 64473.968513 87280.599403
10
51570.852564 70334.104485 97430.647747
−a 0.6 0.1 0 31539.452710 59450.705482 82084.475701
12
51571.531224 70334.416547 97429.816306
Dataset 2
Mass Values
Dataset 3
Mass Values
value would also decrease. The values in the table were
normalized density values (mm3 ) as it has not been used a
calibration method between greyscale scalar values in the
QCT dataset and bone mineral density in g/cm3 . Table 5
shows a comparison of values obtained from Dataset 1,2
and Dataset 3. The first was an osteoporotic femur while
the second and third were normal. For the same isovalues, the mass values estimated for the normal femurs
were consistently higher than those for the osteoporotic
femur which was consistent with bone mineral loss in the
osteoporotic femur. Table 6 shows how the mass mineral
estimate converged with increased number of smaller cubes
used to divide a basic cube for an iso-value of 0.2.
One of the possible applications of a triangular mesh
was for finite element analysis (FEA), which computes and
evaluates the mechanical properties of the femur [1]. The
goal was to determine if the mesh built, using MC was
also suitable for FEA. Application of the mesh selection
algorithm was a good option for achieving this goal of
producing a good bone surface mesh. Shewchuk [17]
in his analysis underlined the importance to deal with
good-shaped triangles in order to perform correctly the
aforementioned finite element methods. In particular,
the constraints were stricter i.e., even the worst-shaped
triangle had to have a good quality. The best possible
triangle shape for FEA is equilateral.
to build these meshes were considerably lower than the
durations needed to make the manual meshes. For example we achieved a parallel implementation of MC on Intel
Mobile Core 2 Duo T7200@2.00 GHz in 15 s compared to
2–3 h of manual segmentation needed on the osteoporotic
dataset.
Table 3 presents the HD between the ground truth and
the whole FSM method.
Results obtained with the whole FSM were slightly
better than the single MC results, on dataset 2, while less
evident on dataset 1. Additionally, there was a dramatic
reduction in the number of triangles using the mesh selection option to triangulate and visualize the external surface
of the femur, as shown in Table 4 in the column %red (minimum reduction was 10.42% while maximum was 159.91%).
Dataset 3 had voxels size equal to 0.4 × 0.4 × 0.31 mm and
was obtained from normal bone.
Once algorithm validation was completed through the
building of the triangular mesh, the quality of the bone
mineral mass computation algorithm was evaluated. The
values obtained from the algorithm were compared by
varying two parameters: the iso-values and the precision
with which the computation is performed. Table 5 shows
how the computed mass varied using different iso-values.
When using higher iso-values, the volume bounded by the
built surface decreased, so it was expected that the mass
5
Table 7
Quality of the Mesh Produced by FSM
Deciles Dataset 1 Dataset 2 Dataset 3
<0.1
7.05%
6.31%
4.79%
<0.2
5.22%
4.72%
4.71%
<0.3
5.51%
8.14%
4.99%
<0.4
12.24%
8.24%
5.55%
<0.5
8.85%
7.56%
6.27%
<0.6
8.81%
8.58%
6.43%
<0.7
10.23%
10.23%
7.61%
<0.8
13.48%
13.95%
12.12%
<0.9
18.25%
21.49%
31.26%
<1
10.38%
10.79%
16.28%
Three methods [17] are primarily used to measure
the triangle shape quality: (i) maximum angle in the
triangle (smaller is better); (ii) minimum angle (larger is
better); (iii) ratio of the radius of the circle inscribed in
the triangle and the radius of the circle circumscribed by
the triangle (larger is better); this latter technique was
used in our study.
For each triangle the radii ratio was computed; these
values were normalized such that equilateral triangles have
a ratio equal to 1. Then all the values have been grouped
in 10 deciles. The first contained all the triangles having
a radio ratii less than 0.1; the second contained all the
triangles having a radii ratio less between 0.1 and 0.2 and
so on. Table 7 shows the quality of the mesh obtained
Figure 2. (a) Relative errors between two meshes; (b) gray
mesh was the ground truth; black mesh was produced by
FEMTool.
executing FSM on the three different datasets using an
iso-value equal to 0.1. Left most column reports the deciles
while each column for each dataset reports the percentage
of triangles grouped in deciles.
The majority of the triangles were concentrated in
the better quality deciles (>0.5). Nevertheless, the quantity of the worst triangles was not negligible; therefore, the
mesh produced by FSM was not suitable for use in FEA.
Future work on FSM will consider adapting the MACET
method to MC, described by Dietrich et al. [18], which
guaranteed higher shape quality.
Figure 1 shows an example of a 3D mask and the corresponding surface model obtained during the deformation
Figure 1. Temporal evolution of the 3D mask (a); corresponding surface model (b).
6
Figure 3. From left to right Marching Cube set with different thresholds, respectively 0.1; 0.4; 0.1 to 0.4 (local adaptive
behavior).
achieved by the FEMTool. Figure 2 shows one example
of the mesh produced by FEMTool and the ground truth
model after alignment. In the right image, the grey mesh
was the ground truth, while the black mesh was the one
produced by FEMTool. The differences between the two
meshes are shown on the left side. For a better visualization
of the errors, these values were converted into gray scale.
With a function of MeshLab the errors have been mapped
onto a white-gray-black color map where minimum error
corresponds from white to gray.
Some of the methods used in FSM were evaluated
by showing the meshes produced and rasterized using
OpenGL APIs. Locally adaptive procedures proved to be
very effective with the Mayo datasets. These procedures
were used to eliminate a distal end bone-cement block
from the images which was used to prepare the femora
for mechanical testing. The cement had low radiographic
density values and required the use of locally adaptive isovalues. This allowed us to correctly resolve the femoral
head, which had comparably low radiographic densities.
Figure 3 shows three meshes of the same dataset obtained
with different iso-values. The left image had an iso-value
of 0.1, the middle image had an iso-value of 0.4, while the
right image, had a locally adaptive range from 0.4 (bottom)
to 0.1 (top).
The tool has been optimized and tested on a notebook
with Intel Centrino 1.73 GHz processor, 1 GB RAM, nVidia
GeForce6600 [19] 256 MB GPU supporting OpenGL 1.5
[20]–[22]. The execution time for un-optimized serial execution on a ×86 single processor of Mesh Creation was
typically 90 s and output a number of triangles. Fifty per
cent of the time was spent on normal computations from
local gradients computed with a Sobel filter. The rendering
speed was 15–20 fps. However, if the mesh was too detailed
in the range between 1 and 4 M triangles per mesh, then
the performances were between 7 and 2 fps, respectively.
mass. The proposed method consists of a first step called
FEMTool (FEMur isolation tool) which segments the bone
tissues from the original QCT dataset, generating at its
output a water-tight model. A graphic renderer, using a
state of art implementation of the MC algorithm, integrating a number of algorithm evolutions, was used to estimate
bone shape. At the end of the process, a mass estimation
algorithm calculated the mass of a user-specified volume,
defined by a set of triangle meshes created using the same
iso-value(s) obtained during the graphic stage.
Results showed a very good quality model built with
the FEMTool, MC, and complete FSM tool compared
to the results obtained by expert manual segmentation.
A mesh selection algorithm helped reduce the number of
triangles produced and with mesh selection. The mass
computation algorithm was validated by comparing different values, estimated with different input parameters.
However, the resulted surface meshes were not suitable
for application to FEA models but will be improved in
future work.
References
[1] D. Dragomir-Daescu, J. Op Den Buijs, S. McEligot, Y. Dai,
R.C. Entwistle, C. Salas, L.J. 3rd Melton, K.E. Bennet,
S. Khosla, and S. Amin, Robust QCT/FEA models of proximal
femur stiffness and fracture load during a sideways fall on the
hip, Annals Biomedical Engineering, 39(2), 2011, 742–755,
epub 2010 Oct. 29.
[2] J. Op Den Buijs and D. Dragomir-Daescu, Validated finite
element models of the proximal femur using two-dimensional
projected geometry and bone density, Computational Methods
Programs Biomedicine, 104(2), 2011, 168–174.
[3] A. Cong, J.O. Buijs, and D. Dragomir-Daescu, In situ parameter identification of optimal density-elastic modulus relationships in subject-specific finite element models of the proximal
femur, Medical Engineering and Physics, 33(2), 2011, 164–173,
epub 2010 Oct. 27.
[4] D.P. Pau, X. Bao, D. Masala, A. Gnemmi, R.C. Entwistle,
and D. Dragomir-Daescu, An automated method to estimate
femoral shape and mineral mass, Proceeding (764) Biomedical Engineering/765: Telehealth/766: Assistive Technologies,
2012. doi: 10.2316/P.2012.764-004
[5] W. Lorensen and H. Cline, Marching cubes: A high resolution
3D surface construction algorithm, Computers and Graphics,
21(4), 1987, 163–169.
4. Conclusions
We presented in this study a new way to use femur QCT
datasets in order to evaluate their shape and total mineral
7
related system architectures for Set Top Box and mobile
application processors. He moved to STMicroelectronics
Ltd, Bristol (UK) in 2004, where he worked mainly on algorithms and architectural studies in the field of 3D graphics
for mobile processors compliant with the worldwide standard OpenGL-ES. He then moved back to Agrate, where he
continued to apply himself to 3D graphics development and
started work on 2D scalable graphics algorithms, as well
as architectural studies for Set Top Box and thin clients.
He is currently interested in computer vision, in particular
structure from motion, optical flow and visual search. On
the latter he acts as co-chair of MPEG CDVS ad-hoc group.
During his career, he has authored or co-authored many
European, American and Japanese granted patents, as well
as international publications in conferences and technical
journals. Currently he is a senior principal engineer, senior
member of technical staff in STMicroelectronics, and an
IEEE senior member.
[6] T.S. Newman and H. Yi, A survey of the marching cubes
algorithm, Computers and Graphics, 30(5), 2006, 854–879.
[7] E. Chernyaev, Marching cubes 33: construction of topologically
correct isosurfaces (Cern Libraries, Geneva: CERN Report,
1995).
[8] T. Lewiner, H. Lopes, A.W. Vieira, and G. Tavares, Efficient implementation of marching cubes cases with topological
guarantees, Journal of Graphics Tools, 8(2), 2003, 1–15.
[9] M. Glanznig, M.M. Malik, and M.E. Groller, Locally adaptive
marching cubes through iso-value variation, Proc. Int. Conf.
in Central Europe on Computer Graphics, Visualization and
Computer Vision, Plzen, Tschechien, 2009, 33–40.
[10] T. McInerney and D. Terzopoulos, Deformable models in
medical image analysis: A survey, Medical Image Analysis,
1(2), 1996, 91–108.
[11] S.M. Smith, Fast robust automated brain extraction, Human
Brain Mapping, 17(3), 2002, 143–155.
[12] S.M. Smith, BET: Brain Extraction Tool, FMRIB technical
Report TR00SMS2b, Oxford Centre for Functional Magnetic
Resonance Imaging of the Brain, Department of Clinical Neurology, Oxford University, John Radcliffe Hospital, Headington,
Oxford.
[13] K. Boesen, K. Rehm, K. Schaper, S. Stoltzner, R. Woods,
E. Lüders, and D. Rottenberg, Quantitative comparison of four
brainextraction algorithms, NeuroImage, 22(3), 2004, 1255–
1261.
[14] N. Aspert, D. Santa-Cruz, and T. Ebrahimi, Mesh: measuring G errors between surfaces using the hausdorff distance,
Proc. IEEE International Conference in Multimedia and Expo
(ICME), 1, 2002, 705–708.
[15] G. Nielson and B. Hamann, The asymptotic decider: resolving
the ambiguity in marching cubes, Proc. Visualization ’91, San
Diego, 1991, 83–91.
[16] MeshLab an open source, portable, and extensible system
for the processing and editing of unstructured 3D triangular
meshes. Software download at http://meshlab.sourceforge.net/
[17] J.R. Shewchuk, What is a good linear element? Interpolation,
conditioning, and quality measures, Proc, 11th Int Meshing
Roundtable, IMR, 2002, 115–126.
[18] C.A. Dietrich, C.E. Scheidegger, J. Schreiner, J.L.D. Comba,
L.P. Nedel, and C.T. Silva, Edge transformations for improving mesh quality of marching cubes, IEEE Transactions on
Visualization and Computer Graphics, 15(1), 2009, 150–159.
doi: 10.1109/TVCG.2008.60
[19] G. Johannson and H. Carr, Accelerating marching cubes with
graphics hardware, Proc. 2006 Conf. of the Center for Advanced
Studies on Collaborative Research, ACM, IBM Corp. Riverton,
NJ, USA, 2006.
[20] S. Richard, W.B. Lipchak, N. Haemel, G. Sellers, OpenGL
SuperBible: comprehensive tutorial and reference, 5th edn.
(Addison-Wesley, July 23, 2010). ISBN-10: 0321712617, ISBN13: 978-0321712615.
[21] R. Fosner, OpenGL Programming for Windows 95 and Windows
NT (Addison-Wesley), 1996.
[22] OpenGL Architecture Review Board, et al., OpenGL Programming guide: the official guide to learning OpenGL, version 2,
5th edn. (Addison-Wesley, 2005).
Daniele Masala received his Master’s degree in computer engineering, embedded system specialization, in 2011 from Politecnico di
Torino with 110/110 cum laude
top score. At same university, he
received his Bachelor’s degree in
2008. From April to July 2008, he
was a software developer at LogiTagTech, where he implemented
a bike-rent procedure for a bikesharing project installed in a town
close to Torino, Italy. From March 2010 to February 2011, he
did his internship at STMicroelectronics, where he created
an application to analyze and visualize 3D models from medical images (TC, MRI), using OpenGL libraries, in cooperation with the Mayo Clinic. He is currently a software engineer at GFI Informatique working on the implementation,
maintenance and upgrading of the Open Back End software
in charge of handling transactions for the flight insurance
and cruise market, worldwide.
Xinfeng Bao received his B.Sc.
degree in electronics and information engineering from Huazhong
University of Science and Technology, China, in 2008. In the same
year, he started his Master’s study
in computer engineering at Politecnico di Milano, supported by
an ICE-UNIONCAMERE scholarship. In 2010, he joined the
Graphics 4 Embedded Systems research group at STMicroelectronics in Italy as an intern researcher. During his one year of
research at STMicroelectronics, he was engaged in a joint
project with the Mayo Clinic, USA, in developing a 3D visualization and analysis tool for magnetic resonance imaging
(MRI) and quantitative computed tomography (QCT). In
early 2011, he received his M.Sc. degree from Politecnico
di Milano. Since 2011, he has been a Ph.D. student in
Biographies
Danilo P. Pau received an electronic engineering degree from
Politecnico di Milano in 1992. In
1991, he joined STMicroelectronics in Advanced System Architectures as a contractor on high
definition decoding HD-MAC
hardware design.
Since 1994,
he has been within Advanced
System Technology working on
MPEG2 video-processing algorithms, memory reduction, and
8
the video coding and architectures group at the Eindhoven
University of Technology, the Netherlands. His research interests are image and video processing, pattern recognition
and machine learning.
Sports Engineering Association and the American Association of Equine Practitioners. Currently, she is employed
as a biomedical test engineer at Heartflow, Inc.
Dan Dragomir-Daescu is an
associate professor of biomedical engineering at the College of Medicine, Mayo Clinic,
Rochester, Minnesota. His research interests are in tissue engineering, bone mechanics,
hemodynamics and cardiovascular devices. Since his appointment
as a faculty at Mayo Graduate
School’s Biomedical Engineering
track, he has advised more than
30 postdoctoral fellows, interns and Mayo Clinic graduate
students. He has served as a member on Ph.D. committees and has taught graduate level courses in biomedical
engineering and mathematics. Before joining Mayo, he
was an assistant professor at North Dakota State University, where he developed computer simulations to estimate material properties of carbon nanostructures. He
also taught graduate classes on advanced numerical methods and undergraduate classes on engineering mechanics.
He also worked at the General Electric Global Research
Center, where he led engineering teams that developed
new product performance and reliability testing methods,
as well as innovative methods and algorithms to predict
product lifetime. He received three awards for technical
excellence for his work in signal processing and reliability.
Dan currently holds six patents, with four more pending.
He has co-authored more than 60 technical papers and one
book chapter, and has presented on numerous occasions at
national and international engineering conferences. He is
member of several research and engineering organizations
and is an active reviewer of publications for engineering
journals and conference peer-reviewed proceedings. He
holds a Ph.D. in mechanical engineering from University
“Politehnica” in Timisoara (UPT), Romania, and a M.S.
degree in mechanical engineering from Arizona State University (ASU) in Tempe, Arizona, US. He also holds a M.S.
degree in Applied Mathematics from the West University
in Timisoara (WUT), Romania. He also has two B.S.
degrees, one in mechanical engineering from UPT and the
other in mathematics from WUT. During his graduate
studies he acquired expertise in materials, smart composite structures, structural dynamics, signal processing and
numerical methods including finite element analysis (FEA)
and computational fluid dynamics (CFD).
Alberto Gnemmi received his
Master’s of Science, in computer
science from University of Illinois, Chicago, USA in 2011, his
Master’s of Science in computer
engineering from Politecnico di
Milano, Italy in 2011 and a Bachelor’s degree in computer engineering from Politecnico di Milano
in 2009. He spent an internship
at STMicroelectronics, between
March 2010 and June 2010, working on 3D reconstruction of medical images in cooperation
with the Mayo Clinic. Then, he was a research assistant
at the University of Illinois in Chicago between January
2011 and May 2012, working on robotic rehabilitation of
stroke survivors at the Rehabilitation Institute of Chicago.
His interests are motor learning, motor adaptation and
human–computer interaction. He is currently a software
engineer at NAVTEQ.
Rachel C. Entwistle received her
Bachelor’s degree in engineering
science, with a mechanical concentration, from Smith College in
2005. She also spent a year abroad
studying at the University College
London while pursing her Bachelor’s degree. At Smith, she participated in two research projects,
one looking at the variation of
collagen fibril diameter in murine
Achilles tendon and the other exploring murine tail tendon functional changes associated
with a certain growth factor. In 2008, she received a Master’s of Science degree in biomedical engineering, with a
biomechanics concentration, from the University of California at Davis. Her graduate work explored bone functional
and microstructural changes associated with exercise intensity and stress fracture in equine bone. After graduate
school, she worked at the Mayo Clinic for 2.5 years as a
mechanical engineer. Her primary focus there was on a
project that aimed to evaluate bone strength in the hip.
This project used patient-specific CT scans to build computer models used for finite element models, which in turn
could provide an evaluation of bone strength in a fall-onthe-hip orientation. She has authored or been a co-author
on more than eight peer-reviewed publications, in journals
such as the Journal of Orthopaedic Research, Annals of
Biomedical Engineering, Equine Veterinary Journal and
Veterinary Surgery. She has given podium presentations
and presented posters at conferences such as the Annual
Meeting of the Orthopaedic Research Society, International
9