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7th GRACM International Congress on Computational Mechanics
Athens, 30 June – 2 July 2011
MULTISCALE BLOCK MATCHING FOR CAROTID ARTERY WALL MOTION
ESTIMATION FROM B-MODE ULTRASOUND
Aimilia Gastounioti1, Nikolaos N. Tsiaparas1, Spyretta Golemati2 and Konstantina S. Nikita1
1Biomedical Simulations & Imaging Laboratory, Department of Electrical & Computer Engineering
National Technical University of Athens
Athens, GR-15780, Greece
e-mails: gaimilia@biosim.ntua.gr, ntsiapar@biosim.ntua.gr, knikita@ece.ntua.gr
2First Intensive Care Unit, Medical School
National & Kapodistrian University of Athens
Athens, GR-10676, Greece
e-mail: sgolemati@med.uoa.gr
Keywords: multiscale block matching, Kalman filter, motion analysis, ultrasound, carotid artery.
Abstract. Block matching (BM) has been previously used to study carotid artery wall motion from B-mode
ultrasound image sequences. This paper proposes the combination of BM with multiscale analysis based on the
decomposition of images using a 2D discrete wavelet transform (DWT). Multiscale BM (MBM) exploits the
information obtained with BM from the approximation sub-images at different spatial resolution scales of the
images, obtained by the DWT. Kalman filtering was selected to compose the radial and longitudinal motion
estimation of a region of interest (ROI) as a nonlinear combination of motion estimates between successive
approximation sub-images. The repetition of MBM nine times by estimating a ROI’s position at the highest
decomposition level of the first image of a sequence within a 3×3 window, followed by mean or median filtering
of the results, created two additional methods, namely MEANMBM and MEDMBM. All methods were optimized
and evaluated on noise-free and noisy synthetic image sequences through the calculation of the warping index.
MBM, MEANMBM and MEDMBM enhanced the accuracy of motion analysis of the arterial wall, yielding
average error reductions of 63%, 69% and 70%, respectively, for total displacements compared to BM.
MEDMBM was the most effective in terms of the warping index and could be considered as a reliable
computational tool for arterial wall motion estimation from B-mode ultrasound.
1 INTRODUCTION
B-mode ultrasound is widely used in the imaging of major branches of the human arteries and in the
diagnosis of arterial disease, because it allows noninvasive assessment of arterial wall morphology. Arterial wall
motion during the cardiac cycle can also be estimated from B-mode ultrasound by recording image sequences
and subsequently applying a motion estimation algorithm.
Block matching (BM) is the most popular method for estimating carotid artery wall motion from B-mode
ultrasound [1], [2]. The method relies on the use of a reference block of pixels in the first image of the sequence
and the identification, in each subsequent image, of a block that shows the highest similarity to the reference
block. Examples of applications of BM in carotid artery wall motion include the estimation of (a) the vessel
diameter in systole and diastole [1], (b) arterial wall distensibility in the radial and longitudinal directions [1], (c)
the average motion amplitude [2], and (d) the shear strain within the wall [2]. The method was also used by Bang
et al. [3] to study motion dynamics of carotid atheromatous plaque.
Wavelet-based multiscale image analysis has recently emerged as a promising method for several image
processing tasks due to its flexibility in providing a unifying framework for decomposing images into their
elementary constituents across scale and its ability to adapt to changing local image statistics and high
background noise. This approach has been efficiently used for texture classification of atherosclerotic tissue from
B-mode ultrasound, revealing the potential of multiscale analysis in the identification of texture properties of the
arterial wall [4]. Multiscale image analysis has also been combined with BM to improve video compression
through the optimization of the motion estimation process [5]. The proposed coding system not only enhanced
video compression in terms of quality and computational cost, but also provided accurate motion tracking
results.
Based on the above, this work investigated the combination of BM with wavelet-based multiscale image
analysis, in an attempt to create an accurate computational tool for arterial wall motion estimation. More
specifically, the proposed scheme, which will be referred to as multiscale BM (MBM), is based on the
decomposition of the images of a sequence using a two-dimensional (2D) discrete wavelet transform (DWT) and
it exploits the information obtained with BM from different resolution scales of the images to produce an
Aimilia Gastounioti, Nikolaos N. Tsiaparas, Spyretta Golemati and Konstantina S. Nikita.
accurate estimation about the radial and longitudinal displacements of selected regions of interest (ROIs). Noise-
free and noisy synthetic image sequences of the common carotid artery were used for the optimization and the
evaluation of different approaches of the MBM scheme. The most effective MBM algorithm was subsequently
applied to real ultrasound image sequences of the carotid artery.
2 BLOCK MATCHING & KALMAN-FILTER-BASED MULTISCALE BLOCK MATCHING
2.1 Block matching
BM consists in finding a block (best-matched block) in an image that shows the highest similarity to the
reference block which is chosen by the user in the first image [6]. The search for the best-matched block is
performed in a limited image region, called search window, centered around the best-matched block of the
previous image.
The performance of the algorithm is affected by the similarity measure, the size and the location of the
reference block, and the size of the search window. A relatively large reference block usually improves the
performance because it enhances the uniqueness of the block, but if it is too large and the algorithm deviates
from real motion, the accumulation of errors gradually deters the finding of a similar block. In terms of the
reference block, the heterogeneity of the interrogated area improves the performance. Finally the search window
should be large enough so as to include the expected motion without entailing high computational cost.
However, even when the factors mentioned above are optimized, the performance of BM is limited by its
basic assumptions, which include mere translation between subsequent images, noiseless environment and
constant appearance of the target. Therefore, adaptive methods might be useful in cases where these assumptions
are not valid.
2.2 Kalman-filter-based multiscale block matching
MBM was inspired by the multiresolution motion estimation (MRME) scheme proposed by Zhang and Zafar
[5]. In a MRME scheme, motion is first estimated at the lowest spatial resolution and the obtained information is
then manipulated as the prediction at finer spatial resolutions. MBM does not overcome the basic assumptions of
BM, but it attempts to compensate for incorrect or inaccurate estimates of motion, taking into consideration that
the motion activities for a particular image at different resolutions are highly correlated, because they actually
specify the same motion structure at different scales [5]. Kalman filtering (KF), which has been successfully
incorporated in BM-based motion analysis [7], was used to compose motion estimation as a nonlinear
combination of motion estimates at successive resolution levels. In the following, the basic principles of DWT-
based image decomposition and KF are briefly described, and the proposed motion estimation scheme of MBM
is then presented.
A) Discrete wavelet transform. The DWT of a signal is defined as its convolution with a set of lowpass H[n] and
highpass G[n] half-band filters, where G[n]=(-1)1-nH[1-n] satisfy the following conditions among scaled versions
of the functions φj,n and ψj,n, :
n
njtj tnH ,,1 ]2[
(1)
n
njtj tnG ,,1 ]2[
(2)
The functions φj,t and ψj,t consist of versions of the prototype scaling φ and wavelet ψ functions, discretized at
level j and at translation t. They form an orthonormal set of vectors, a combination of which can completely
define the signal allowing its analysis in a multiresolution scheme [8]. The outputs of the convolution with H
downsampled by two are called approximation coefficients Aj, whereas the outputs of the convolution with G
downsampled by two are called detail coefficients Dj. At each level of decomposition the time resolution is
halved, whereas frequency resolution is doubled. The parameters of DWT include both the total number of levels
L, which depends on the length N of the signal (the maximum value of L is equal to log2N), and the selected
scaling and wavelet functions. Among a large number of wavelet families (Haar, Daubechies, symlets, coiflets
and biorthogonal) Haar was used in this study due to its orthogonality and symmetry properties. Orthogonal
filters conserve energy and maintain the same amount of energy noise at each level of decomposition. Symmetric
filters are also important because they do not affect the output of the signal.
The 2D DWT of an image is defined as two successive DWTs, firstly on the rows of the image and then on
the columns of the resulted image. The decomposition of the image yields four sub-images at the first level (j=1),
namely an approximation sub-image Aj and the detail sub-images Dhj, Dvj and Ddj (Fig.1). At the next, and each
subsequent, level, only the approximation sub-image is further decomposed into new four sub-images. Each sub-
image is the result of a convolution with two half-band filters; two lowpass filters for Aj, a lowpass and a
highpass for Dhj, a highpass and a lowpass for Dvj and two highpass filters for Ddj. The total number of levels in
the 2D DWT depends on the number of rows N and columns M of the original image; the maximum value of L is
Aimilia Gastounioti, Nikolaos N. Tsiaparas, Spyretta Golemati and Konstantina S. Nikita.
equal to min (log2N, log2M).
B) Basic principles of Kalman filtering. KF is an efficient recursive filter that estimates the current state of a
linear dynamic system from a series of noisy measurements [9]. It assumes that the true state of the system at
time k is related to the state at time (k-1) according to the process-model:
kkkk wDuBxx 1
(3)
where xk is the state at time k, B is the state transition matrix applied to the previous state xk-1, D is the control-
input matrix applied to the control vector uk and wk is the process noise with a zero mean normal distribution
described by the covariance matrix Q. At time k an observation, or measurement, zk of the true state xk is made
according to the measurement-model:
kkk vFxz
(4)
where F is the observation matrix that relates the measurement of the true state with the true state and vk is the
observation noise the distribution of which is described by the covariance matrix C. KF is a recursive estimator
and the distribution of its error at time k is represented by the covariance matrix Pk. Through successive
prediction and update phases [7] KF uses the current measurement and the estimated state and filter‟s error from
the previous time step, and it computes the state and the filter‟s error for the current time step.
To use KF one should model the process according to eqs (3) and (4). The performance of KF depends on the
covariance matrices Q and C, as well as the initialization (P0) of the covariance matrix Pk.
Figure 1. Schematic diagram of the 2D DWT decomposition scheme for a given level of analysis. Note that, for
j=0, A0 is the original image. Hr, Hc, Gr, Gc are the lowpass and highpass filters on the rows and columns of
each subimage. The symbols „2↓1‟ and „1↓2‟ denote the downsampling procedure on the columns and rows,
respectively.
C) Kalman-filter-based multiscale block matching. The algorithm proposed in our study is illustrated in the
block diagram of Fig. 2 and it consists of the following steps.
Figure 2. Block diagram of MBM.
1. DWT at L levels: The images of a sequence are decomposed up to L levels using a 2D DWT. The lowest
decomposition level corresponds to the highest spatial resolution level (original images), whereas the highest
decomposition level corresponds to the lowest spatial resolution level (Fig. 3).
2. ROI selection: A ROI is selected in the first image of the sequence of original images. The initial position of
the selected ROI at the lowest spatial resolution level is computed as follows: Considering that the size of the
sub-images at level j is twice the size of sub-images at level (j+1), the position of a ROI at level L can be found
by scaling its position in the original image by a factor of 2-L and rounding the result.
Aimilia Gastounioti, Nikolaos N. Tsiaparas, Spyretta Golemati and Konstantina S. Nikita.
Figure 3. The pyramid structure of DWT image decomposition.
Steps (3)-(5) are repeated for every subsequent image of the sequence:
3. BM at level j=L: BM is initially performed at the highest decomposition level L and the radial, rad0, and
longitudinal, long0, positions of the ROI are estimated.
4. Coarse-to-fine transition: For every lower decomposition level j, with 0≤ j<L, it is assumed that the positions
of the target, radk and longk, with k=
Lj
, are related to the estimated positions, radk-1 and longk-1, at the
previous (higher decomposition) level according to eqn (5). Afterwards, measurements of radk and longk, namely
zradk and zlongk (eqn (6)), are obtained by performing BM at level j within a search window around the positions
radk-1 and longk-1 scaled by a factor of two. KF combines the defined process- and the measurement-models to
produce the estimates for radk and longk.
k
k
k
k
k
long
rad
long
rad w
1
1
20
02
(5)
k
k
k
k
k
long
rad
zlong
zrad v
10
01
(6)
This step finally, i.e. when j=0, leads to radL and longL which correspond to the final motion estimates at the
lowest decomposition level of the current image.
5. Update level L: Following the procedure described in step (2), the initial motion estimates rad0 and long0 are
updated by appropriately scaling the positions radL and longL. This step is necessary for the implementation of
step (3) for the next image, because the search for the best-matched block is performed around the best-matched
block of the previous image.
The algorithm described above estimates motion in a coarse-to-fine manner, and its performance depends on
the parameters of BM (similarity measure, size of the reference block and size of the search window), DWT (L)
and KF (Q, C and P0).
3 SYNTHETIC IMAGE DATA EXPERIMENTS
3.1 Synthetic image data
BM and MBM were optimized and evaluated by applying them to four synthetic 87-image sequences of the
common carotid artery, corresponding to three cardiac cycles. The first synthetic sequence (S0) was created by
distorting a real ultrasonic B-mode image according to a mathematical motion model [10]. Two additional
sequences, S25 and S15, were created by corrupting the first sequence with Gaussian noise with signal-to-noise
ratios equal to 25 dB and 15 dB, respectively. The fourth synthetic sequence (SF) was constructed from a
sequence of scattering strength maps according to the procedures described in [10], using the Field II software
package [11] and the same mathematical motion model. Fig. 4 presents the first images of the four synthetic
sequences along with the corresponding first level approximation sub-images. The approximation sub-images
look very similar to the original images although they are 1/4th of the original image size. However, considering
that they are produced from the convolution with lowpass filters and that Gaussian noise is a high-frequency type
of noise, the noise levels in the approximation sub-images of S25 and S15 are probably reduced, even if this is not
readily obvious at visual inspection.
Performance was assessed by means of the warping index (w) defined by eqs (7), (8) and (9), separately for
the longitudinal (wlong), radial (wrad) and total (wtotal) displacements, respectively.
mr
illongillong
w
m
l
r
i
1 1
2
estreal
long
)),(),((
(7)
mr
ilradilrad
w
m
l
r
i
1 1
2
estreal
rad
)),(),((
(8)
rad
2
long
2
total www
(9)
where longreal and radreal are the real longitudinal and radial positions, respectively, longest and radest are the
longitudinal and radial positions, respectively, estimated by the algorithms, m is the number of selected ROIs,
Aimilia Gastounioti, Nikolaos N. Tsiaparas, Spyretta Golemati and Konstantina S. Nikita.
and r is the number of images of each sequence. Accordingly, w represents an overall estimate of the error for all
interrogated ROIs and all images of the sequence.
The warping index was computed by choosing 176 ROIs for sequences S0, S25 and S15, and 196 ROIs for the
sequence SF. Fig. 4 (a, g) shows examples of the selected ROIs in the synthetic image sequences.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Figure 4. Examples of images of the common carotid artery wall in synthetic sequences (a) S0, (c) S25, (e) S15,
and (g) SF. The white marks represent the centers of the selected ROIs. (b, d, f, h) First level approximation sub-
images of the synthetic images.
3.2 Optimization of BM and MBM
Following the comments in section 2.1, BM was implemented using (a) the correlation coefficient as the
similarity measure, (b) 25×17 pixels reference blocks selected in the first frame, and (c) 21×21 pixels search
windows. These three parameters also affect the performance of MBM. The choice for the similarity measure
was the same as in BM. With regard to the size of the reference block, a variable block size scheme, which takes
into account motion activities for small objects, has been proposed in [5] and has been supported by more recent
studies [12], [13]. The popularity of this choice along with the fact that a variable block size requires fewer
computations, led to the use of (25·2-j)×(17·2-j) pixels reference blocks for the jth level sub-images. The
selection of the appropriate size for the search window was also based in related studies [5], [12], [13], where
constant search windows were preferred. Experimentation with different s×s search windows, with s varying
between 1 and 7, showed that MBM maximized its performance for s=3.
The optimization of the algorithm in terms of the DWT parameter is equally important. As a consequence,
the optimization procedure included the experimentation with different values of L and best results were
achieved for L=1. Moreover, MBM could be implemented in two distinct scenarios: performing BM (a) in all
sub-images, and (b) in one type of sub-images of each level. In the first case the best-matched block was
determined as that block for which the total similarity measure was maximized [14]. In the noise-free sequences
errors were minimized by the first scenario, which, however, produced considerably higher errors, compared
with the second scenario, for the noisy sequences. On the other hand, the second scenario with the approximation
sub-images minimized motion tracking errors for the noisy sequences and was effective enough for the noise-
free sequences. As a result the second approach, i.e. when BM was performed only on the approximation sub-
images, was selected as more suitable to our study.
MBM‟s performance also depends on the efficiency of KF. In our study matrices Q, C and P0 were
considered proportional to the identity (Q=qI, C=cI, P0=poI) [15] and MBM was optimized in terms of the
multiplication factors q, c and po. Experimentation with these parameters showed that performance was
maximized when c≤q for S0, S25 and SF and c>q for S15. This observation showed that the error was generally
minimized when the refinement at finer spatial resolutions was considered less reliable than the initial estimates
at the coarsest spatial resolution. Additionally, higher levels of noise required lower values of p0, which
corresponds to higher confidence to the filter‟s estimate. Although the optimal KF parameter values are different
for each sequence (table 1), they need to be held constant across data sets. Therefore, MBM was applied to all
sequences using the four sets of parameter values of table 1, and it was investigated which set produced the
lowest mean warping index for total displacements. The results showed that the first set, i.e. q=4.9, c=1.1 and
p0=1.3, was generally the most suitable choice and as a result, it was selected for both the evaluation procedure
and the real data experiments.
Aimilia Gastounioti, Nikolaos N. Tsiaparas, Spyretta Golemati and Konstantina S. Nikita.
S0
S25
S15
SF
q
4.9
0.1
2.7
5.1
c
1.1
0.1
5.1
1.1
p0
1.3
0.7
0.1
1.2
Table 1 : Optimal KF parameter values for the sequences S0, S25, S15, and SF
A drawback of MBM is the crucial role of the initial estimates conducted at the lowest spatial resolution
level, because when a false motion vector is generated, it is propagated to higher spatial resolution levels. Those
false initial estimates could be associated with the rounding process at the estimation of a ROI‟s initial position
at the coarsest spatial resolution (step (2)). In our work, it was examined whether this factor could be addressed
by considering a one-to-nine mapping between the initial positions at the lowest and the highest decomposition
level [12], [16]. To this end, MBM, as described in Section 2.2 and optimized above, was repeated nine times by
considering that a ROI‟s position at the highest decomposition level could be found within a 3×3 window
centered on the result of step (2). The final motion information was computed by median (MEDMBM) or mean
(MEANMBM) filtering the motion results estimated by the nine repetitions of MBM. Both MEDMBM and
MEANMBM are compared with BM and MBM in the next section.
3.3 Performance evaluation of BM and MBM methods
Table 2 shows the warping indices for each synthetic sequence when motion was estimated by BM, MBM,
MEDMBM and MEANMBM. As expected, the warping indices increased with increasing noise levels for all
methods. In most cases errors in the longitudinal direction were larger than in the radial one, which was more
obvious in the cases of the noisy sequences S25, S15.
S0
S25
Algorithm
wtotal
wrad
wlong
Algorithm
wtotal
wrad
wlong
BM
1.35
1.09
0.80
BM
4.96
1.11
4.83
MBM
1.14
0.54
1.00
MBM
1.31
0.56
1.19
MEDMBM
0.82
0.46
0.69
MEDMBM
1.26
0.47
1.16
MEANMBM
0.91
0.46
0.78
MEANMBM
1.28
0.47
1.19
S15
SF
Algorithm
wtotal
wrad
wlong
Algorithm
wtotal
wrad
wlong
BM
18.59
4.67
17.99
BM
4.07
1.06
3.93
MBM
3.06
0.87
2.93
MBM
0.93
0.68
0.64
MEDMBM
2.63
0.71
2.53
MEDMBM
0.67
0.42
0.53
MEANMBM
2.74
0.80
2.62
MEANMBM
0.70
0.42
0.56
Table 2 : Warping indices, in pixels, for BM, MBM, MEDMBM, and MEANMBM for the sequences S0, S25,
S15, and SF. Boldface characters indicate minimum warping indices for total displacements for each sequence.
MBM produced considerably lower warping indices than BM, especially in noisy environments, where
MBM yielded error reductions of 74% and 84% for total displacements, compared to BM, for the sequences S25
and S15, respectively. At this point the contribution of KF in the effectiveness of MBM and the importance of its
role in the coarse-to-fine transition were investigated, by replacing KF at step (4) with a linear combination using
equal weights. In this case, radk and longk were estimated as:
k
k
k
k
k
k
zlong
zrad
long
rad
long
rad *5.0*2*5.0 1
1
(10)
This approach produced total warping indices of 1.20, 1.31, 3.25, 1.11 pixels for the sequences S0, S25, S15, and
SF, respectively. The results demonstrated that although KF was not the main source of the increased
performance of the method, it was still necessary for its optimization.
The employment of the one-to-nine mapping between the initial positions at the highest and the lowest spatial
resolution levels further enhanced the performance of multiscale motion estimation, because both MEDMBM
and MEANMBM outperformed MBM. Among all presented methods, MEDMBM minimized motion tracking
errors for all sequences. Specifically, MEDMBM yielded error reductions of 39%, 75%, 86%, and 84% for total
displacements, compared to BM, for the sequences S0, S25, S15, and SF, respectively.
In terms of the computational cost, tracking one block in an 87-image sequence required 10 s for BM, 8 s for
MBM and 51 s for MEDMBM and MEANMBM, using a Pentium(R) Dual-Core CPU T4400. The basic MBM
scheme achieved a 20% speed-up factor in motion tracking process with respect to BM. Although MEDMBM‟s
Aimilia Gastounioti, Nikolaos N. Tsiaparas, Spyretta Golemati and Konstantina S. Nikita.
computational cost was somewhat increased, the considerable minimization of motion tracking errors led to the
selection of MEDMBM as the most effective method.
Fig. 5 shows examples of radial and longitudinal positions of a ROI located in the posterior wall-lumen
interface in the first image of the synthetic sequences S15 and SF, using BM and MEDMBM. In both cases
MEDMBM produced radial and longitudinal displacements that were closer to real motion. In the longitudinal
direction, in particular, MEDMBM resulted in smoother, less spiky waveforms, than BM. Fig. 6 illustrates
examples of motion vector maps for several ROIs of the same synthetic sequences, using BM and MEDMBM.
Each vector corresponds to the resultant of the radial and longitudinal displacements of a ROI from end diastole
to end systole and points towards its position in end diastole. All vectors were magnified four times and they
were superimposed in frames corresponding to end systole. The motion vector maps of MEDMBM were closer
to those of real motion and they generally demonstrated a uniform motion pattern in both directions. However,
BM produced nonuniform motion vector maps for the noisy sequence, with the vectors varying in both
amplitude and direction.
Figure 5. Examples of radial (RP) and longitudinal (LP) positions of a ROI located in the posterior wall-lumen
interface in the first image of the synthetic sequences S15 (top row) and SF (bottom row), using BM and
MEDMBM. Different ranges were used for the y-axes for each sequence because of higher motion tracking
errors in the presence of noise.
(a)
(b)
(c)
(d)
(e)
(f)
Figure 6. Examples of motion vector maps for several ROIs of the sequences S15 (top row) and SF (bottom row),
corresponding to (a, d) real motion, (b, e) BM and (c, f) MEDMBM.
4 REAL IMAGE DATA EXPERIMENTS
The selected MBM methodology, namely MEDMBM, was applied to two real ultrasound image sequences
of the carotid artery; one of a young normal subject and one of an elderly patient with an atherosclerotic plaque
on the posterior wall. The sequences were recorded with an ATL (Advanced Technology Laboratory) Ultramark
4 Duplex scanner and a high resolution 7.5 MHz linear scan head. Scanner settings were as follows: dynamic
range 60dB, 2D grey map, persistence low, frame rate high. The sequences were recorded at a rate of 25 frames/s
for approximately 4 s (2-3 cardiac cycles). The first frame of each sequence is shown in Fig. 7 (a, d).
Fig. 8 shows examples of radial and longitudinal displacements of two blocks („ANT‟ and „POST‟), located
Aimilia Gastounioti, Nikolaos N. Tsiaparas, Spyretta Golemati and Konstantina S. Nikita.
in opposite wall-lumen interfaces (Fig. 7 (a, d)), using MEDMBM. The displacements in each direction were
calculated by subtracting the positions of the ROI at end diastole, which for the real sequences was identified
from the minimum radial distance between ANT and POST. The waveforms produced using MEDMBM
demonstrated the expected periodicity in motion, especially in the radial direction, which enhanced the reliability
of the algorithm.
Fig. 7 (b-c, e-f) illustrates examples of motion vector maps for several ROIs of the real sequences, produced
with BM and MEDMBM in the same way as in section 3.3. The fact that MEDMBM maintained the uniformity
of motion vector maps in real sequences, suggesting uniform motion of the arterial wall, further reinforced the
reliability of the method.
(a)
(b)
(c)
(d)
(e)
(f)
Figure 7. The first frame of an ultrasound image sequence of (a) a young normal subject and (d) an elderly
patient with an atherosclerotic plaque on the posterior wall. Examples of motion vector maps for several ROIs of
the first (b, c) and the second (e, f) sequence, using BM (b, e) and MEDMBM (c, f).
Figure 8. Examples of radial (RD) and longitudinal (LD) displacements of ANT and POST for the young normal
subject (top row) and the elderly patient (bottom row), using MEDMBM.
5 DISCUSSION
This study investigated the effect of the combination of multiscale image analysis with motion estimation on
the accuracy of motion tracking of the arterial wall from B-mode ultrasound. MBM was presented as a
multiscale motion estimation scheme and it was combined with a one-to-nine mapping scheme between the
initial positions of a ROI at the highest and the lowest spatial resolution levels, resulting in two additional
methods referred to as MEANMBM and MEDMBM. The latter minimized motion tracking errors in synthetic
data experiments and it behaved well in real data experiments. Therefore MEDMBM was proposed as the most
reliable method for arterial wall motion estimation.
The application of the investigated methods to synthetic data showed that in all cases the error increased
when noise was added to the synthetic sequences. This may be due to the fact that noise reduces the image
contrast and causes undesirable spatiotemporal changes in image intensities, thus preventing BM from finding
the best-matched block. In most cases errors were greater in the longitudinal direction probably because
Aimilia Gastounioti, Nikolaos N. Tsiaparas, Spyretta Golemati and Konstantina S. Nikita.
ultrasound imaging of the arterial wall shows higher homogeneity in that direction.
When the parameter of the DWT was examined, it was shown that the performance of MBM was maximized
when the images were decomposed up to one level. This might be associated with the limitation (at that level) of
the shift-variant property of the DWT, where shifted versions of an image may not correspond to shifted wavelet
coefficients. The DWT is not shift-invariant because of the decimation process (lowpass filtering followed by
downsampling). Additionally, the optimization process revealed that only the approximation sub-images could
be used in MBM, especially for noisy sequences. The approximation sub-images contain a large percentage of
the total energy of the original image and as a result, they maintain a large amount of the information which is
necessary for the BM process. Moreover, the fact that they result from the convolution with lowpass filters
probably leads to the reduction of noise levels. The opposite occurs with the detail sub-images (Dhj, Dvj and
Ddj), which lack information and often maintain the noisy characteristics of the original image. However, it
should be noted that the choice of sub-images is subject to the application. For example, if one needs to extract
fine texture from the original image, the detail sub-images should be kept. In this case, the approximation sub-
images only capture the intensity variations induced by lighting [4]. On the contrary, for compression or motion
estimation purposes the energy compaction property of the DWT, energy localization into successively smaller
approximation sub-images, is needed.
Previous attempts have been made to improve the performance of BM through its combination with KF [7].
However, they produced slightly improved warping indices and the accuracy in arterial wall motion estimation,
especially for the noisy sequences, remained dissatisfactory. Contrarily, in this work the combination of BM
with multiscale image analysis and KF produced encouraging results in both noise-free and noisy sequences. The
optimization process for the MBM scheme in terms of the KF parameters showed that errors were generally
minimized when measurements at finer spatial resolutions were considered less reliable than the initial estimates
at the lowest spatial resolution level. The investigation for the necessity of KF proved that the use of a linear
transform in the coarse-to-fine transition would not be sufficient enough, which verified the initial choice of KF.
The investigation mentioned above also revealed that the main reason for MBM being considerably more
accurate than BM was wavelet-based image decomposition, which provides information about motion structures
at different resolutions and scales. The resolution is linked to frequency content, whereas scale to mapping of
large or small objects of the image. As the level of decomposition increases the original image passes through a
series of low-pass and high-pass filters and its resolution is reduced. However, scale is increased due to
downsampling. Thus, increased levels of decomposition refer to sub-images where objects are relative large
(large scale) and their motion can be detected. The impressive results of MBM specifically in noisy
environments were probably due to the fact that the noisy characteristics were removed from the approximation
sub-images. This, however, may also imply that the decomposition of images generally increased the accuracy in
motion measurements because ultrasound images contain other types of noise, for example speckle noise.
Consequently, image decomposition creates less noisy image intensities and real motion can be more easily
tracked through the BM process.
Both MEDMBM and MEANMBM enhanced motion tracking, because they reduced the propagation of false
motion vectors to higher spatial resolution levels which are caused by the rounding process of step (2) of the
algorithm. However, MEDMBM was the most effective method probably because, unlike mean filtering, median
filtering tends not to be affected by outliers, which may be due to increased local noise.
MEDMBM also produced the expected periodic motion waveforms when applied to real ultrasound image
sequences of the carotid artery, a finding which reinforced its reliability. The method displayed uniform motion
of the arterial wall, which was an additional argument in favor of the successful application of MEDMBM under
real conditions.
Wavelet-based multiscale image decomposition has proved to be an effective computational tool for both
motion estimation and texture feature extraction [4] from B-mode ultrasound images of the arterial wall. Taking
into consideration the synthetic and real data experiments, MEDMBM could be proposed as an alternative
algorithm for motion tracking of the arterial wall. It would be of great interest to investigate the impact of
additional wavelet families in combination with alternative shift-invariant wavelet decomposition schemes on
the performance of MEDMBM. An additional future extension of our study would also include experimentation
with different motion estimation algorithms, such as affine optical flow and adaptive BM, which overcome the
basic assumptions of mere translation between subsequent images and constant appearance of the target,
respectively, and could result in higher accuracy in motion tracking.
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ACKNOWLEDGEMENTS
The work of A. Gastounioti was supported in part by the Hellenic State Scholarships Foundation.
