of heterogeneous intensity, but are highly sensitive
to noise. Region-based are usually more robust to
noise and initialization, but they assume that the
intensities of each region to be constant, which
makes them not suitable for heterogeneous cases
which we often find in ultrasound images. Localizing
region-based active contours are proposed with the
objective of allying the advantages of both categories
while suppressing their drawbacks. Foreground
and background can be described in terms of small
regions; thus, heterogeneity of the image is not a
problem. A disk kernel (B) moves along each point
of the initial contour, computing exterior and interior
energies, as represented in Figure 7. The total energy
is given by:
E(φ) =
Z
Ω
x
δφ(x)
Z
Ω
y
B(x,y).F(I(y),φ(y))dydx
+λ
Z
Ω
x
δφ(x)
∆φ(x)
dx
(4)
Where I denotes the input image at the domain Ω,
δφ(x) is the portion of contour centred at x and B is the
neighbourhood kernel around the point (x,y), which is
used to define the localizing area. These elements are
graphically represented by the red circle (B) and the
yellow point (x,y) in Figure 7. F is the internal energy
function. The last term refers to the continuity of the
contour line and is scaled by a factor λ.
An energy optimization algorithm will move the
point by fitting a model to the region.
Figure 7: Graphical representation of the localizing active
contour method. The red circle is the neighbourhood, B, of
the yellow point (x,y) (S. Lankton, 2008).
For this work, the internal energy function F used
was the Uniform Model, defined as:
F = H(φ(y))(I(y) −u
x
)
2
+ (1 − Hφ(y))(I(y)− v
x
)
2
(5)
Where H(φ(y)) represents the exterior of the contour
in the neighbourhood (B) and u
x
represents its mean.
While (1-Hφ(y)) represents the interior and v
x
repre-
sent its mean (S. Lankton, 2008).
For the left atrium segmentation in 2D+t echocar-
diographic sequences, we proposed the application of
localizing region-based active contours. The Doppler
pseudo-colour that is superimposed in the brightness
mode image will interfere with the active contour ad-
justment. For that reason, we use the mask obtained at
the pseudo-colour isolation step, in order to get an es-
timation of the grayscale brightness mode at the back-
ground. The pixels inside the colour mask are passed
to the active contours algorithm as low random val-
ues (below the average of intensity of the image), to
mimic the typical non-tissue speckle affected aspect
of the interior of the atrium. This assumption may
seem as a possible source of errors for the contour
adaptation, specially in cases when the colour mask
is significantly large when compared with the atrium.
However, practical results suggest this is not a signif-
icant drawback for the method. A possible reason for
the ability of adaptation of the localizing active con-
tours in these cases is the internal force term, which
limits the deformability of the contour, maintaining
its shape. The penalizing parameter for the arc-length
of the curvature (λ) must be sufficiently small so it al-
lows deformation of the contour to fit the corners of
the atrium, but high enough to prevent leakage. Four
values between 0.4 and 1.0 were tested and 0.6 was
the one that seemed to keep the best compromise be-
tween the requirements.
Minimal user interaction is required for contour
initialization: two points, one at the centre of the left
atrium and one at the endocardium (inner boundary
of the atrium). The initialization mask is a circle cen-
tred at the first point with radius equal to the distance
between the two points. The stopping condition in
this method is the number of iterations. Since the re-
gional mask will move along each point of the contour
at each iteration, the process may be computationally
heavy. The number of iterations for the first frame
was selected empirically after testing multiple values
of radius of local region and checking at which num-
ber of iterations convergence happened. Frequently
there was no further active contour adaptation or im-
provement around 100 iterations. For the following
frames, the contour initialization was given by the
previous frame contour result. Assuming that the
variation between successive frames is smaller than
the variation between the user input mask and the final
result of the first frame, the number of iterations for
convergence should be smaller. Similar experiment
was made for those frames, starting at 100 iterations
and reducing gradually. The final iterations number
was 50.
Radius of the local region mask is of great rele-
vance for the performance of the algorithm. A study
was made by the author (S. Lankton, 2008) to anal-
yse the effect of the radius on the resulting contour.
The radius should be chosen considering the scale of
A Preliminary Approach for the Segmentation of Mitral Valve Regurgitation Jet in Doppler Ecocardiography Images
51