=Paper=
{{Paper
|id=None
|storemode=property
|title=Three-Dimensional Catheter Tip Tracking from Asynchronous Biplane X-Ray Image Sequences using Non-Linear State Filtering
|pdfUrl=https://ceur-ws.org/Vol-715/bvm2011_49.pdf
|volume=Vol-715
}}
==Three-Dimensional Catheter Tip Tracking from Asynchronous Biplane X-Ray Image Sequences using Non-Linear State Filtering==
https://ceur-ws.org/Vol-715/bvm2011_49.pdf
Three-Dimensional Catheter Tip Tracking from
Asynchronous Biplane X-Ray Image Sequences
using Non-Linear State Filtering
Marcel Schenderlein1 , Volker Rasche2 , Klaus Dietmayer1
1
Institute of Measurement, Control, and Microtechnology, University of Ulm
2
Department of Internal Medicine II, University Hospital of Ulm
marcel.schenderlein@uni-ulm.de
Abstract. Image-based three-dimensional (3D) catheter tracking has
the potential provide enhanced visualization and documentation means
for cardiac catheter navigation purposes. However, if the biplane X-ray
image sequences are acquired asynchronously, common stereo-geometric
constraints are violated and simple 3D reconstruction introduces posi-
tion errors. The presented work introduces an algorithm based on the
unscented Kalman filter, which explicitly models this image acquisition
situation. It updates the 3D catheter tip position and orientation with
single-plane two-dimensional catheter tip and electrode position mea-
surements. These measurements are derived from X-ray images, acquired
alternately from two different orientations. In this manner, the proposed
approach allows for 3D catheter tip tracking with a promising position
accuracy.
1 Introduction
Catheter ablation of cardiac arrhythmia is commonly carried out under guidance
of fluoroscopic X-ray sequences. During the intervention, electro-physiological
catheters, comprising cylindrical metal electrodes on the tip (Fig. 1d), are nav-
igated inside the heart chambers. In order to infer the three-dimensional (3D)
positions and orientations of the catheters, two image sequences from almost
orthogonal orientation are acquired (Fig. 1a). In this biplane setting, the image
sequence is generated by means of asynchronous acquisition in order to reduce
the X-ray dose as well as cross-scattering effects (Fig. 1b). Such interlaced acqui-
sition introduces errors into common reconstruction approaches which assume
a stereo-geometric image pair. Instead, 3D positions have to be reconstructed
from a set of asynchronous images, while dealing with the object motion between
the acquisitions.
In [1, 2] the interlacing is dealt with by reconstructing from an image triplet
instead of an image pair. The drawback of these approaches is, that the re-
construction is always delayed one time step. This in turn results in a tracking
delay if applied in a real-time environment. Interlaced acquisition has also been
mentioned by De Buck et al. [3] but not been dealt with. They reconstructed the
3D Catheter Tip Tracking 235
catheter tip from image pairs as if they were being acquired synchronously, ac-
cepting the introduced errors. De Buck et al. also used a state filter for catheter
tip tracking. They applied two independent standard Kalman filters for each
image plane and reconstructed the 3D tip position from the two filter results.
However, the independent filters may drift apart and loose correspondence.
The main contribution of our presented work is a catheter tip tracking
scheme, which uses the unscented Kalman filter (UKF) [4] to solve the delay
problem and still provides good reconstruction accuracy.
2 Materials and Methods
2.1 Catheter Tip Measurement
The catheter tip position is measured in the images by means of a masked
normalized cross-correlation (MNCC) of tip templates within an image region
of interest (ROI) around the previous tip position. The term masked denotes
that not the whole rectangular template is correlated with the ROI, but only
the pixels of the actual catheter image and a margin around it (Fig. 1c). This
way, the sensitivity to background clutter is reduced. A set of multiple oriented
templates is created by ray-casting the catheter model onto the image plane
similar to [3]. Their correlation with the ROI leads to a set of potential 2D
catheter tip positions with respective 2D orientations.
Since the 3D orientation can not be fully inferred from the 2D orientation,
the next electrode along the catheter is searched for. Together with its known
3D distance to the catheter tip its 3D position and thus the 3D tip orientation
can be estimated. To this end, a search region is defined around the expected
electrode position and again MNCC now with an electrode template is applied.
The best correlation maxima are stored as electrode hypotheses.
Out of the catheter tip hypotheses and its corresponding electrode hypotheses
a set of measurements is created for the association with the UKF.
IA (t) IB (t)
t
(a) (b) (c) (d)
Fig. 1. (a) Schematic of the biplane x-ray system with the two image acquisition
channels. (b) The asynchronous image (IA , IB ) acquisition scheme. Dashed rectangles
depict the non-existing images. (c) A masked template. Only the pixels of the template
which are inside the dashed contour are correlated. (d) Two views of a catheter from
both orientations with tip position (◦) and next electrodes position (×) overlaid.
236 Schenderlein, Rasche& Dietmayer
2.2 The Unscented Kalman Filter
The unscented Kalman filter [4] is a recursive state estimator just as much as the
ordinary Kalman filter (KF). It uses a prediction phase to forecast its inner state
by a state transition model and corrects this prediction by comparing an actual
measurement to the predicted measurement in the update phase. In contrast
to the KF the state transition model and the measurement model of the UKF
may be non-linear functions. This fact is utilized in the proposed approach to
apply the perspective projection formula as the measurement function. The
UKF was preferred to the commonly used extended KF because of its simpler
implementation and its higher accuracy.
2.3 Catheter Tip Tracking
Since the 3D position and orientation of the catheter tip is to be tracked, the
state vector of the UKF is defined as
[ ]
x = x, y, z, ẋ, ẏ, ż, θ, ϕ, θ̇, ϕ̇, r (1)
where (x, y, z) is the 3D position and (ẋ, ẏ, ż) is the 3D velocity of the tip. The
relative position of the next electrode to the catheter tip is characterized by the
spherical angles θ, ϕ and the distance from the tip r. The angular velocities
θ̇,ϕ̇ are also modeled. The prediction of the state is computed by a constant
tip velocity and constant angular velocity model (CV) and a unit transform
for r. However, the CV only approximates the complex catheter motion. The
non-linear measurement model function is denoted by the two projections
(u, v)tip = Pi (x, y, z)with i ∈ {A, B} (2)
(u, v)elec = Pi (T (x, y, z, θ, ϕ, r)) (3)
where (u, v)tip and (u, v)elec are the 2D positions of the catheter tip and the next
electrode and T is a function, which transforms the spherical coordinates of the
next electrode into Cartesian coordinates. The perspective projection function
Pi alternates between the known acquisition geometries A, B for each time step.
In the update phase of the UKF, a measurement of the catheter tip and
the next electrode position is passed to the filter. This measurement is chosen
from the multiple actually measured hypotheses as the one with the smallest
Mahalanobis distance to the current predicted measurement.
While the image frames from the two orientations are alternately processed in
the prediction and update loop, the UKF implicitly reconstructs the 3D position
(x, y, z) and orientation (θ, ϕ) of the catheter tip.
2.4 Experimental Setup
In order to evaluate, if the proposed approach is able to track a 3D catheter tip
and orientation, the following experiment is conducted. The X-ray images are
3D Catheter Tip Tracking 237
Table 1. Inter-frame min/mean/max 2D position and orientation changes.
fps 25.0 8.3 5.0 3.6
∆ pos. 2D [px] 0.0/7.5/67.1 0.0/17.6/156.2 0.2/24.1/162.7 0.4/29.0/195.6
∆ orient. 2D [◦ ] 0.0/3.6/79.0 0.0/8.5/107.2 0.0/12.0/107.3 0.0/15.0/111.4
acquired at a resolution of 512 × 512 pixels with a pixel size of 0.36 mm. They
are acquired alternately with an orientation difference of 70◦ and at a rate of 25
frames per second (fps) in total. The sequences were also subsampled in order to
evaluate the algorithm performance with lower frame rates of effectively 8.3 fps,
5.0fps and 3.6fps. The UKF is initialized as follows: The process noise is set by a
CV noise gain with a standard deviation (SD) of the tip position acceleration of
1500 mm/s2 and a SD of the angular acceleration of 35 rad/s2 . These values are
derived from an analysis of labeled catheter motion data. The measurement noise
is set by an assumed SD of 3 px and 10 px for the 2D position of the tip and the
next electrode. The initial tip and electrode position is inferred from a manual
labeling step and transformed accordingly into the initial state vector. The
velocities are set to zero. The initial state variances are set by choosing ten times
the process noise variances. No covariance is preset. We evaluate the tracking
in four different patient sequences comprising a total of 936 frames (Tab. 1).
The sequences contain active motion applied to the catheter by the physician
beside the anatomical motion. A manual labeling of the catheter position in
the 2D images serves as ground truth. Linear interpolation between consecutive
label data of the same orientation provides the means for reconstructing the 3D
ground truth.
Although the process noise parameters were adapted accordingly, the ever
higher inter-frame dynamics present in the 8.3 fps, 5.0 fps and 3.6 fps sequences
caused several hypotheses association errors. This in turn led to temporarily
longer mis-estimations of the UKF state. Thus we present only the results for
the 25 fps sequences.
3 Results
Fig. 2 shows the results of the 25fps sequences evaluation in the form of box plots
with whiskers with a maximum length of 1.5 IQR. The median 3D tip position
errors are 1.3mm, 1.6mm, 1.1mm, and 1.2mm, leading to a total of 1.2mm. The
median 3D tip orientation errors are 28.1◦ , 13.1◦ , 30.0◦ , and 8.7◦ , leading to a
total of 18.6◦ . Outliers are mainly caused by the algorithm temporarily loosing
the catheter which leads to chaotic filter behavior and arbitrary maximum error
values. For better illustration the plots do not show the outlier values. The
outlier rates for e3D 3D
tip are 15 %, 6 %, 8 %, and 7 %. The outlier rates for eor are
0 %, 0 %, 2 %, and 3 %. The 2D error plots serve as a reference for the tip and
electrode detection accuracy.
238 Schenderlein, Rasche& Dietmayer
Fig. 2. The 2D and 3D tip position error e2D 3D 2D 3D
tip , etip and orientation error eor , eor .
5
100
10
60
80 4
8
tip [mm]
tip [px]
or [ ]
or [ ]
◦
3
◦
6 60 40
e3D
e2D
e2D
e3D
4 40 2
20
2 20 1
0 0 0 0
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
sequence # sequence # sequence # sequence #
4 Discussion
The decreased orientation accuracy and the outliers mainly caused by hypothe-
ses association errors remain a challenge. One reason seems to be inaccurate
measurements which occur in extremal cases like e.g. the 3D catheter pointing
perpendicular to the image plane or due to bad contrast in general. Another
reason is an insufficient approximation of the complex catheter motion by the
CV process model. This fact becomes even more evident in the evaluated se-
quences of lower frame rates. Nevertheless, our experience with these sequences
is, that if the hypotheses association is correct, tracking remains possible. The
accuracy decreases, but stays in acceptable ranges at least for the 8.3 fps and
5.0fps sequences. The results regarding the 3D catheter tip position accuracy for
the 25 fps sequences are in the range of published results of other reconstruction
approaches [2, 3]. Hence, if the detection did not substantially fail, our implicit
reconstruction approach is able to provide clinically acceptable accuracy for the
tip position. We have contributed an approach which explicitly models the ac-
quisition situation and provides promising accuracy results for the catheter tip
tracking. It has the potential to provide enhanced visualization and documenta-
tion means for cardiac catheter navigation purposes. Motivated by the discussed
challenges, future work includes the investigation of more accurate state filter
modeling and higher electrode detection accuracy.
References
1. Sarry L, Boire JY. Three-dimensional tracking of coronary arteries from biplane
angiographic sequences using parametrically deformable models. IEEE Trans Med
Imaging. 2001;20(12):1341–51.
2. Schenderlein M, Stierlin S, Manzke R, et al. Catheter tracking in asynchronous
biplane fluoroscopy images by 3D b-snakes. In: Proc SPIE; 2010. p. 76251U.
3. De Buck S, Ector J, La Gerche A, et al. Toward image-based catheter tip tracking
for treatment of atrial fibrillation. In: Proc MICCAI Workshop Cardiovasc Interv
Imaging Biophys Modell; 2009.
4. Wan EA, Van Der Merwe R. The unscented Kalman filter for nonlinear estimation.
In: Proc IEEE Adapt Syst Sig Process Comm Contr Symp; 2000. p. 153–58.