Добавил:
Sekretar
kiopkiopkiop18@yandex.ru
t.me/Prokururor I Вовсе не секретарь, но почту проверяю
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_3592_Библиотеки_им_академика_М_И_Перельмана
.pdf
Vascular and Intravascular Imaging Trends, Analysis, and Challenges, Volume 1
https://t.me/medicina_free
main advantage of this model is that the MRF energy function can be optimized by
linear programming. Zikic et al [50] propose an MRF model using only second order
terms for more efficient optimization. The approximation at a certain point in the
parameter space is the normalized sum of evaluations of the original energy at
projections of that point to two-dimensional subspaces. Also, a strategy for refinement of the search space is employed over iterations so as to increase registration
accuracy and keep the number of labels small for efficiency.
An alternative approach for searching the global optimum for non-convex cost
functions is template-based optimization. In this approach, all possible spatial
transformations of a certain degree of freedom within a range are sampled and their
DRRs are compared to the 2D image by a robust similarity measure [35]. Local
extrema are surely avoided by exhaustive searches in a limited computation time,
however, discretized parameter values have to be interpolated by either a function or
a local optimizer.
10.5.2 Stratified methods
Optimization strategies that stratify the transformation parameters into separate
subsets and then perform a sequential estimation of the subsets of parameters may
be employed. This is particularly useful for estimation of 3D rigid-body transformation in order to increase the sensitivity of any similarity measure to the out-ofplane translation of the 3D image. Namely, the sensitivity is generally highest when
all other rigid-body parameters are close to their optimal values. Because the
dimension of the search space is reduced in the individual sequential steps, the
registration process is usually faster than with iterative optimization and an
exhaustive search can be used in low-dimensional parameters space to overcome
large initial alignment errors.
Using the stratified parameter estimation, several researchers first determined the
in-plane translation parameters by exhaustive grid search [51, 52] or frequency
domain methods [53]. Kerrien et al [51] found the in-plane translations by
optimizing normalized cross correlation (NCC) over a fixed grid, followed by
optimization of all rigid-body parameters. In a two-stage method, Kita et al [53] first
determined the in-plane translations by optimizing NCC in the frequency domain.
By optimizing NCC over fixed grids in a three-stage approach, Hentschke and
Tönnies [52] first determined the in-plane translations, then the out-of-plane translation and in-plane rotation and, finally, the two remaining rotations. Kubias et al
[54] determined the in-plane prior to the out-of-plane parameters in a multiresolution and multi-stage optimization strategy using low- and high-resolution
images in consecutively applied global and local optimizers, respectively. To recover
the rotations and scale, Van der Bom et al [55] used projection-slice theorem,
followed by phase correlation to recover the in-plane translations, however, the
method resulted in high alignment errors around 20 mm. Aksoy et al [35] matched
rotation templates (a set of DRRs of segmented 3D images in a discrete set of
rotations) to a segmented x-ray image by a scale and translation invariant measure
computed in the frequency domain. After selecting the optimal rotations, all rigid-
10-16
Vascular and Intravascular Imaging Trends, Analysis, and Challenges, Volume 1
https://t.me/medicina_free
body parameters were iteratively optimized through minimization of the overlap
between the best matching pair of segmented DRR and the x-ray image. Despite
promising results, the estimation of the out-of-plane translation in monoplane
3D–2D registration was not addressed adequately in any of the above methods.
10.5.3 Regression-based methods
Regression-based approaches directly relate features of images to the spatial transformation parameters by a linear or a nonlinear function, hence, iterative optimization procedures are not employed during the registration process. The function is
trained usually with simulated 2D images before being applied to real intrainterventional images. Gouveia et al [56] have evaluated seven regression methods
for 3D–2D registration. Input features consisted of first and second order moments
and PCA of the 2D image intensities, while the outputs are the registration
parameters. Multivariate regression estimates the regression coefficients of a linear
and polynomial equation of input features with a least squares method. The K
nearest neighbor generates predictions by averaging output responses of k nearest
input points in the training set. Multilayer perceptrons (MLP) are a popular choice
for nonlinear regression due to their capability of approximating arbitrary functions.
In the training phase, synaptic weights are optimized such that the difference
between true and actual outputs is minimized by conjugate gradients and Levenberg—
Marquart optimization algorithms. Their activation function is typically a hyperbolic tangent function. The radial basis function (RBF) network has a similar
structure to the MLP except that a Gaussian function was used as the activation
function. Support vector machine regression (SVR) maps input data to a higher
dimensional space by the RBF kernel function and compute the output by a
weighted linear combination of the kernels. The results of Gouveia et al [56] show
that MLP with Levenberg Marquart optimization and RBF are robust to large
initial alignment offsets and yield the most accurate results with lower variance, but
are slightly less accurate than traditional iterative registration approaches.
10.6 Validation procedures
Before a 3D–2D image registration can be incorporated into a clinical imageguidance system it must undergo extensive and objective validation. Although
several 3D–2D image registration methods [11] were developed for image-guidance
systems, i.e. for 3D roadmapping [16, 57], their translation into clinical use is limited
because these methods generally lack an extensive and objective validation.
Performing such a validation is difficult due to the wide range of materials,
methods and definitions that are required, namely: (i) a large number of patient
image datasets needs to be acquired in the clinical context of image-guided
intervention; (ii) a corresponding reference or gold standard registration, which
has to be accurate and reliable, needs to be established on these datasets;
(iii) a procedure for validating 3D–2D image registration along with the definition
of performance metrics needs to be specified. Standard procedures and performance
10-17
Vascular and Intravascular Imaging Trends, Analysis, and Challenges, Volume 1
https://t.me/medicina_free
metrics for validation of 3D–2D registration in general were introduced by Van der
Kraats et al [58] and later revised by Markelj et al [59].
Unfortunately, the creation of validation datasets has received little attention in
the literature. There are currently four publicly available validation datasets of
3D–2D registration, one of a cadaveric spine segment [60], one of a cadaveric
swine head [61], one of a spine and a pelvis generated from a visible human dataset
[59] and one of cerebral angiograms [7]. There was another dataset of a cadaveric
spine segment created by Van der Kraats et al [58], but it seems to be no longer
publicly available. The clinical context associated with the aforementioned image
datasets is spine surgery [58–60], radiotherapy of the head [61] and endovascular
image-guided neurosurgery [7]. Hence, the dataset of cerebral angiograms [7], to
the best of our knowledge, is the only dataset available to objectively validate and
compare the performance of methods for 3D–2D registration of vascular
structures.
In the following subsections, the approaches toward gold standard creation,
measures of registration error and procedures for evaluating the performance of 3D–
2D registration methods are reviewed and discussed.
10.6.1 Gold standard creation
The main challenge of using the 3D and 2D patient images for objective and
quantitative validation of 3D–2D registration method(s) is how to obtain an
accurate and reliable gold standard. Two tasks need to be carried out: (i) calibrate
projection geometry of the 2D image acquisition device and (ii) devise materials and
methods to find the optimal spatial transformation of the 3D image.
Most existing C-arm systems do not provide accurate parameters of the
projection view (PA, SA, SOD, SID and
), therefore, these parameters
u
,)
v
00
have to be calibrated for each C-arm pose. A common parameterization of the 2D
imaging system on C-arm is given in [4]. For some C-arm systems the deviations
from ideal geometry and pose are reproducible and may be compensated by prior
calibration of the C-arm [16, 62, 63]. Depending on the mechanical design of the
C-arm system, however, the deviations from ideal geometry and pose might not be
reproducible and such a C-arm has to be calibrated on-line during image-guided
intervention. For such situations, Otake et al [19] used a robust tracking fiducial
made of ball bearings and steel wire shaped as an ellipse and lines that provided
C-arm calibration directly from a single 2D fluoroscopy image.
The optimal spatial transformation of a 3D image can be established in several
ways that mainly differ in the complexity of materials and methods used and,
possibly, require a different protocol of image acquisition that may be more or less
compatible with the workflow during image-guided interventions. Van de Kraats
et al [58] used a calibrated C-arm to acquire 2D x-rays from several projection views
and performed reconstruction of a 3DRX image. The gold standard registration of
CT and MR volumes was obtained through alignment to the 3DRX by intensitybased 3D–3D image registration [58]. In most clinical contexts, however, using more
than one or two 2D x-rays for establishing the gold standard may raise ethical
10-18
Vascular and Intravascular Imaging Trends, Analysis, and Challenges, Volume 1
https://t.me/medicina_free
concerns due to excessive irradiation of the patient. Markelj et al [59]defined the 2D
image projection geometry so as to create synthetic 2D projection images from the
3D images, hence, the gold standard is inherently given. However, such a simple
approach to gold standard creation does not capture the conditions, e.g. image
noise, occlusions, geometric deformations, etc, encountered on real 2D images
acquired during the intervention and is therefore not appropriate for objective
validation.
For patient images acquired during an image-guided intervention the gold
standard may be obtained by manual alignment, i.e. by perturbing the transformation of the 3D image until its projection overlaps with the 2D image [64]orby
a reference registration method based on manually co-locating prominent anatomical landmarks such as bifurcations and vessel curves on 2D and 3D images or based
on manual or semi-automated segmentation of vessels in 3D and 2D [8, 35].
Currently these are the approaches used to establish the gold standard in deformable
3D–2D registration, e.g. for the liver [8] and acquisitions of cardiac vasculatures not
gated to electrocardiography signal [6]. However, it is difficult to establish such a
gold standard in a consistent manner across a large patient image dataset due to
subjective and unreliable manual input and, in cases such as the the liver vasculature,
also due to insufficient complexity of the vessel network. Hence, the accuracy of the
gold standard may vary substantially between different patient image datasets and,
therefore, such a gold standard cannot be used to objectively and reliably validate
the 3D–2D registration methods.
By attaching fiducial markers to the patient one can recover both the 2D image
acquisition geometry and the optimal spatial transformation of the 3D image [7, 60,
61]. Therefore, this approach seems most promising for the creation of a gold
standard on patient image datasets. Tomaževič et al [60] and Pawiro et al [61] used
cadaver-implanted fiducial markers, which is clearly too invasive to perform on
(live) patients. Mitrović et al [7] used an elastic headband with integrated steel balls
as fiducial markers. The elastic headband can be easily attached to a patient’s head
during the image-guided endovascular neurosurgery, during which both 3D and 2D
images are usually acquired by the C-arm. To acquire the gold standard on
vasculature other than the cerebral vasculature, the fiducial marker carrier device
needs to be redesigned. The gold standard is based on the registration of the position
of fiducial markers extracted from 3D and 2D images, whereas two 2D projection
images need to be acquired to calibrate the C-arm in the two corresponding
projection views (figure 10.5). The advantage of such an approach is the possibility
of automating all the steps to obtain the gold standard, i.e. extraction and
correspondence of fiducial markers in 3D and 2D, retrospective C-arm calibration
and marker co-registration [65]. Furthermore, for rigid-body 3D–2D registration,
the accuracy of a gold standard based on
fiducial marker co-registration can be
assessed with the methodology presented by Fitzpatrick et al [66]. For instance, on
ten patient image datasets of cerebral angiograms Madan et al [65] reported the
accuracy of the fiducial-based gold standard from 0.1 to 0.2 mm, which is at least
twice better than the level of accuracy expected from 3D–2D registration methods
and, therefore, seems suitable for objective validation of the methods.
10-19
Vascular and Intravascular Imaging Trends, Analysis, and Challenges, Volume 1
https://t.me/medicina_free
Figure 10.5. Gold standard 3D–2D registration
extracted from 3D and 2D images [
7].
established by aligning the positions of fiducial markers
T
gs
10.6.2 Registration error
Various measures of registration error are used depending on the task of 3D–2D
registration [58]. For instance, 3D roadmapping [57], in which the 3D image is
projected and overlayed onto the 2D angiogram, requires a good overlap between
vessels in the 2D projection, therefore, the registration error should be measured in
2D. On the other hand, during image-guided biopsy or delivery of treatment devices
their exact placement in 3D patient space is important, hence, to guide or position
these tools and devices the registration error should be measured in 3D.
Registration errors can be measured by the distance between positions of 3D or
2D image features (e.g. fiducials, anatomical landmarks, object contours or surfaces)
after the 3D–2D registration and their positions in the gold standard registration.
Common image features are (target) points
on angiograms
are usually the centerline points of a 3D vessel tree [7], which can
i
that lie on the structures of interest, i.e.
i
be extracted from a segmentation of the vessels. A possible approach to extract the
vessel centerlines is to perform interactive thresholding of the 3D angiogram and
obtain centerlines by Lee’s thinning algorithm [67], followed by removal of short,
spurious and possibly incorrect centerlines and vessel branches whose length is less
than twice the corresponding vessel diameter [68].
A widely used performance measure in 3D is the target registration error (TRE),
while the mean over all target points K is used to compute the registration error:
where
and
T
reg
T
the gold standard, respectively.
1
=∣∣ −∣∣
∑
K
=
iK1
denote the transformation obtained by 3D–2D registration and
gs
ttmTRE
() (), (10.3)
TT
iireg gs
10-20
)
Vascular and Intravascular Imaging Trends, Analysis, and Challenges, Volume 1
https://t.me/medicina_free
A straightforward performance measure in 2D is the projection distance (PD)
computed as the distance between the registered and gold standard locations of
target points in the 2D image space. Since target points
space they need to be projected into 2D using the forward projection operator
which translates the points
from the x-ray source
from 3D to the 2D imaging plane along rays emanating
i
. The 2D registration error is computed as mean PD:
s
1
PtPtmPD
=∥ − ∥
∑
K
=
iK1
( ) ( ) . (10.4)
TT
FiFireg gs
are defined in 3D image
i
F
The value of mPD depends on the distance of target points to the 2D image plane.
Instead, several researchers use the reprojection distance (RPD) defined as the
minimum distance between the line
the 3D target point in the registered position
target point in the gold standard position
, which passes through the x-ray sourcesand
L
i
t(
T
igs
, and the corresponding 3D
t()
T
ireg
. Hence, the 2D registration error
that is independent of the distance to the 2D image plane is computed as mean RPD:
,
where
1
=
∑
K
iK1
denotes the minimum distance between a line and point. A geometric
·
[]
min
⎡
LT T
d rt tmRPD
=
( , ( )), ( ) , (10.5)
⎣
is i imin reg gs
⎤
⎦
representation of the TRE, RPD and PD registration errors is shown in figure 10.6.
10.6.3 Performance evaluation
The evaluation methodology of van de Kraats et al [58] and Markelj et al [59]
involves creation of synthetic transformations or deformations of the 3D image with
respect to gold standard registration, which represent the starting positions for
3D–2D registration. The starting positions are generated according to initial
misregistrations of the 3D image from the gold standard in some range of mTRE
(e.g. 0–20 mm). The mTRE is usually uniformly distributed in the specified range
Figure 10.6. Geometric representation of TRE, RPD and PD registration errors.
10-21
Vascular and Intravascular Imaging Trends, Analysis, and Challenges, Volume 1
https://t.me/medicina_free
and the number of starting positions per 1 mm mTRE subinterval is also determined. Typically there are 20 starting positions per interval and thus a total of 400
starting positions per dataset.
For 3D and 2D images both acquired on a C-arm system, one could also use the
machine-based registration obtained from DICOM-accessible C-arm parameters as
more realistic starting positions [64]. However, the number of such starting positions
is proportional to the number of datasets, which is usually low, while such an
approach is also limited to certain clinical contexts.
Common metrics of registration performance involve registration accuracy,
failure criteria, success rate, capture range and execution time. The standardized
evaluation methodology proposed by van de Kraats et al [58], and later revised by
Markelj et al [59], employs the mTRE, mRPD and mPD as measures of registration
accuracy. The most general measure is the mTRE, however, as noted previously, the
mPD and mRPD may suffice in certain clinical applications [16, 57] and are
typically reported if the registration is performed between a 3D and a single 2D
image.
In the methodology by van de Kraats et al [58], a registration failure criterion is
specified by the minimum acceptable level of registration error and depends on the
clinical application. On cerebral angiograms, Mitrović et al [7] established that
mTRE or mRPD below 2 mm is sufficient for the purpose of 3D roadmapping and
3D–2D image fusion. Other metrics are then based on the failure criterion, i.e. the
success rate measures the percentage of successful registration trials and the capture
range is defined as the initial misregistration, at which some high-enough success
rate, e.g. 95% [58], is achieved.
The selection of failure criteria may bias the performance evaluation, since
trimming the distribution of registration errors through rejection of failed registration trials directly impacts the assessment of registration accuracy, success rate and
capture range. To avoid the use of failure criteria, Markelj et al [59] employ
accumulative subintervals of initial misregistration, e.g. 0–4, 0–8, 0–12, 0–16, and
0–20 mm, in which the initial mTREs are uniformly distributed. In each of the
subintervals they capture the distribution of registration error and then determine
the accuracy as a percentile (50% and 95%) of the estimated distribution.
10.7 Validation of 3D–2D registration on cerebral angiograms
The current state-of-the-art and challenges in 3D–2D image registration are best
observed by rigorous and extensive validation on datasets with established gold
standard registration. The following experiments involved ten patient image
datasets, which are publicly available
grams [7], namely 3D and 2D digitally subtracted angiograms or 3D- and
2D-DSAs, respectively. The 2D-DSAs were acquired in the anterior–posterior
(AP) and lateral (LAT) projection views, thus forming 20 pairs of 3D and 2D
1
URL: http://lit.fe.uni-lj.si/tools.php?lang=eng.
1
and contain 3D and 2D cerebral angio-
10-22
Vascular and Intravascular Imaging Trends, Analysis, and Challenges, Volume 1
https://t.me/medicina_free
images. The gold standard 3D–2D registrations were established by co-registration
of fiducial markers [7].
The experiments involved 3D and 2D image registration trials using two recent
methods, the first based on stratified 3D rigid-body parameter optimization for
matching rotation templates and vessel tree features [35] and the second based on
iterative BOBYQA optimization and image similarity computed by comparing 3D
and 2D gradient covariances [43]. We refer to the two methods as stratified and
iterative, respectively. While the first is expected to be robust to high initial
registration errors, the second is expected to yield accurate 3D–2D registration if
initialized close to the optimal registration. Running these two methods sequentially
should, therefore, result in a registration that is robust to initial error and a
registration that is highly accurate. To verify this hypothesis, the third method
consists of a sequential execution of the stratified and iterative method and was
referred to as combined.
In the following subsection we first describe the experimental set-up and then
present validation results according to two validation methodologies [58, 59], one
with and one without the use of failure a criterion.
10.7.1 Experimental set-up
Registration errors were measured by mTRE and mRPD based on the initial and
final alignment of 3D targets with respect to their gold standard position. The 3D
targets were the vessels’ centerlines, extracted from 3D-DSA in each of the ten
datasets [7]. The initial starting positions of 3D images were defined in terms of
mTRE, generated in the range 0–100 mm with respect to the gold standard position
by randomly sampling rigid-body transformations.
Translations were randomly sampled in the range [−100, 100] mm, while
rotations were sampled in the range [−5, 5] degrees, such that the desired initial
mTRE was achieved. The following ranges of translations and rotations correspond
to the initial misalignment of the pre-operative 3D and intra-operative 2D images
that is expected in a typical interventional C-arm suite [62, 63] and may be due to the
use of uncalibrated C-arm pose or patient movement. For each 3D–2D image pair,
one set of rigid-body parameters was randomly generated in each 1 mm subinterval
of mTRE, hence, in total 100 per pair. Since there were 20 pairs of 3D- and 2DDSAs and 100 initial rigid-body parameters per each image pair and three
registration methods were tested, we altogether performed 6000 3D–2D
registrations.
10.7.2 Evaluation based on failure criteria
The methodology of van de Kraats et al [58] requires setting a threshold on
registration error, which delineates between a successful and failed registration trial.
As proposed by Mitrović et al [7] for cerebral angiograms, the registration failure
criterion was set to 2 mm for both mTRE and mRPD registration error metrics.
Hence, a 3D
–2D registration was considered successful if mTRE or mRPD was less
than 2 mm. The overall registration accuracy was defined as MEAN ± STD of
10-23
Vascular and Intravascular Imaging Trends, Analysis, and Challenges, Volume 1
https://t.me/medicina_free
mRPD of all successful registrations and the overall success rate (SR) was defined as
the percentage of successful registrations. Capture range (CR) was defined as the
first mTRE or mRPD subinterval of length 1 mm, in which more than one
registration out of 20 failed. This setting corresponded to a 95% confidence level
for the CR estimate.
Evaluation results for the three methods are shown in tables 10.3 and 10.4 for the
mTRE and mRPD metric, respectively. The stratified method achieved a higher SR
than the iterative method, but was generally less accurate. The sequentially
combined methods were the most accurate and had the highest SR and CR.
According to the mRPD metric (table 10.4) the obtained results are generally
satisfactory for the clinical application of 3D roadmapping [16, 57], while the results
for the mTRE metric fall below expectations, since the best SR is 48% and the best
CR is 1 mm. Examples of final registrations according to mTRE and mRPD metrics
are shown in figure 10.7.
For additional insight into registration performance, figure 10.8 shows a
cumulative success rate (cSR) computed with respect to the initial mTRE such
that the cumulative number of successful registration trials was divided by the
Table 10.3. Results of 3D–2D registrations on ten pairs of cerebral angiograms [44]. Registration accuracy is
reported as MEAN ± STD of mTRE of successful registrations (mTRE < 2 mm), success rate (SR) and
capture range (CR) across 1000 registrations of 3D- and 2D-DSA image pairs.
View Method MEAN ± STD [mm] SR [%] CR [mm]
AP Stratified 1.34 ± 0.41 28.0 1.0
Iterative 0.95 ± 0.54 7.4 3.0
Combined 1.12 ± 0.51 45.6 1.0
LAT Stratified 1.34 ± 0.42 17.1 1.0
Iterative — 0.0 1.0
Combined 0.95 ± 0.48 48.1 1.0
Table 10.4. Results of 3D–2D registrations on ten pairs of cerebral angiograms [44]. Registration accuracy is
reported as MEAN ± STD of mRPD of successful registrations (mRPD < 2 mm), success rate (SR) and
capture range (CR) across 1000 registrations of 3D- and 2D-DSA image pairs.
View Method MEAN ± STD [mm] SR [%] CR [mm]
AP Stratified 0.99 ± 0.48 64.8 3.0
Iterative 0.62 ± 0.41 33.1 11.0
Combined 0.39 ± 0.23 95.8 49.0
LAT Stratified 1.03 ± 0.47 75.2 3.0
Iterative 0.74 ± 0.44 34.0 9.0
Combined 0.40 ± 0.20 98.9 91.0
10-24
Vascular and Intravascular Imaging Trends, Analysis, and Challenges, Volume 1
https://t.me/medicina_free
Figure 10.7. Final alignment of cerebral angiograms in AP and LAT views with respect to mTRE and mRPD
shown as a superposition of 2D-DSA (grayscale) and a DRR (red) of 3D-DSA after 3D–2D registration.
Figure 10.8. Cumulative SRs for a failure criterion of 2 mm (final mTRE, mRPD) shown with respect to initial
mTRE across ten AP and LAT datasets of cerebral angiograms [
number of all registration trials up to some initial mTRE. When the initial mTRE
was less than 20 mm, the iterative method achieved a higher SR than the stratified
method, however, the SR then decreased drastically. Clearly, the iterative method
requires a good initial starting position for the registration to succeed. On the other
7].
10-25
Соседние файлы в папке Библиотека им академика М.И. Перельмана