Optimisation-Based Image Grid Smoothing for SST Images - Advanced Concepts for Intelligent Vision Systems - page 233

CX

≤ 0

(27)

CY ≤ 0

Another type of constraint could be to limit the movement of the points. In this
case, the constraint could be express as
⎧
⎨

X

X − ≤

Y

(28)

Y − ≤

⎩

0 ≤ ≤ 0 . 5 ∗ step

with step being the step of the initial grid.

5 Simulation Results

The image dataset used in the experimentsisoriginatedfromby Meteosat satel-
lite. The SST images result from an average of the sea surface temperature
collected over a month. The first set of experiments aims at investigating the
effect of the neighbouring order and the constraints in the grid smoothing while
the second set exposes the results of the complete image processing chain (SOWA
followed by grid smoothing). The non-linear optimization method used in both
SOWA and grid smoothing is the conjugate gradient. The typical convergence
time is around 1 second for a 100 pixels

× 100 pixels image.

50 km ) including
a thermal front. As explained previously, a front characterizes the transition
between two regions of homogeneous temperature and may be interpreted as
an edge. The two homogeneous regions depict small variance, while the front
itself is characterized by a large variance. It may be observed in the results that
the grid smoothing has no or little effect on the homogeneous region (the grid
stays quasi-uniform) while the front itself depicts a larger number of points. In
the grid smoothing process, the edges act like attractors for the points in the
grid. When the optimisation process is unconstrained, the dimensions of the
new grid do not match the initial boundaries of the image, which may lead to
geometrical issues while reconstructing the image. However, it may be observed
that constraining the grid is leading to a loss of accuracy in the boundary regions.
Comparing the two orders of grid smoothing, it may be observed that a greater
shrinkage of the image is seen in the second order compared to the first order
smoothing. The grid is also denser in the second order in the regions where the
temperature is changing. As the second order smoothing uses a second order
neighbourhood between the points, the presence of an edge not only attracts its
direct neighbours but also further points in the grid. The computational cost of
the second order compared to the first order is, however, a major drawback. A
trade-off between the accuracy and the computing time is to be found according
to the application.

Figure 1 focuses on a detail of an SST image (50 km ×