Optimisation-Based Image Grid Smoothing for SST Images - Advanced Concepts for Intelligent Vision Systems - page 227

strength of the wind is also affecting the measurement of the SST by the satellite
sensor. These reasons lead to a non-uniform repartition of the noise properties in
the image. The spatial resolution of the SST images are typically 4km by 4km.
Knowing that the difference in temperature may peak up in certain region of
the world to 2 degrees per km, the shape of the structures are not conserved
in the image. Various methods have been used to filter the SST images includ-
ing low-pass filter [4], contextual filter [1], adaptive filtering [5] and others [6].
Some of the methods try to address the non-uniformity of the noise while the
other are focusing on the shape of the structures. This paper presents a common
framework to tackle both issues at the same time using a common formulation
of the problem and mathematical tools to solve it. Previous work on the grid
smoothing or interpolation can be found in [7] where the image is modelled as
a non-resistive of resistive power grid, in [8] where strong constraints on the
shape of the object are assumed, and in [9], where hierarchical grid construction
is introduced. Previous interesting work on interpolation of large dataset using
optimisation techniques may be found in [10] and [11] where a weighting factor
between the model and the data terms is introduced. The framework presented
in the present paper is twofold. In the first step, the SOWA algorithm introduced
in [12] is applied to the image to remove the noise. The SOWA algorithm uses
the mesh representation of an image and a quadratic cost function is defined
with the gray levels present in the image. The minimisation of the cost function
leads to a new set of gray levels preserving the shape of the objects in the image
while reducing the level of noise. The second step, called grid smoothing, tackles
the issue of the low resolution of the SST images. Using the mesh representation
of the image and non-linear programming, the initial uniform grid on which the
image is sampled is modified to fit the content. The result of the grid smooth-
ing is a non-uniform grid exposing more points in the region of large variance.
Section 2 introduces the mesh representation of the image used in the present
paper. Section 3 reviews the optimisation-based approach to mesh smoothing
(SOWA) while Section 4 introduces the grid smoothing framework. The results
arepresentedanddiscussedinSection5. Section 6 summarizes the contribution
of the present paper and discusses recommendations and the future works.

2 Graph-Based Image Representation

2.1 First Order Node-Edge Matrix

Our input data is a graph G =( V, E ), embedded in the 3D Euclidian space.
Each edge e in E is an ordered pair ( s, r ) of vertices, where s (resp. r) is the
sending (resp. receiving) end vertex of e .Toeachvertex v is associated a triplet
of real coordinates x v ,y v ,z v

[12]. Let C be the node-edge incidence matrix of

the graph G , defined as:

⎧
⎨

1 if v is the sending end of edge
− C = 1 if v is the receiving end of edge e

0otherwise

(1)

⎩