computationally intensive, thus are not suitable to support operational usage. This
chapter therefore aims to explore sea ice segmentation technique that is both
efficient and accurate.
6.5 Proposed Method
6.5.1 Bayesian Segmentation of SAR Sea Ice Imagery
In this chapter, we denote the discrete lattice spanned by SAR sea ice imagery by N,
and a site in the lattice by t 2 N. We represent the image patch centered at site t by
y t , a p-dimensional random vector taking on different grayscale values, and the
label of site t by l t , a random variable taking on a class {1, . . . ,K}. Then a SAR sea
ice image can be denoted as Y ¼ y t
t 2 N
È
É
, and the labels of this image as
l ¼ l t
t 2 N
È
É
. For automated segmentation of SAR sea ice imagery, we are trying
to infer l based on Y, which, in the Bayesian framework, can be achieved by
maximizing the posterior distribution of l t given y t , i.e.,
p l t
y t
À
Á
p y t
l t
À
Á
p l t
ð Þ
ð6:1Þ
where p y t
l t
À
Á
denotes the probability distribution of patch variable y t conditioned
on l t , which allows the modeling of textural information, and p(l t ) is the a priori
probability of labels, which allows the modeling of label correlation effect. The
maximum a posterior (MAP) estimation of the labels can be expressed as:
b l ¼ arg max l
Y
t2N
p l t
y t
À
Á
ð6:2Þ
or
b l ¼ arg min l
X
t2N
Àlogp y t
l t
À
Á À logp l t
ð Þ
Â
Ã
ð6:3Þ
In this letter, p y t
l t
À
Á
is approached by kernel principal component analysis
(KPCA) to mine the most discriminative textural information, whereas p(l t ) is
implemented by the MRF-based multiple logistic (MLL) prior to modeling the
label correlation effect. The maximum a priori (MAP) problem is solved by the
graph-cut-based α-expansion algorithm.
6.5.1.1 Likelihood Implementation
Since image patches y t characterize the spatial relationship of local pixels, using
image patches instead of individual pixels would allow better representation of
6 Mapping Sea Ice from Satellite SAR Imagery
119
chapter therefore aims to explore sea ice segmentation technique that is both
efficient and accurate.
6.5 Proposed Method
6.5.1 Bayesian Segmentation of SAR Sea Ice Imagery
In this chapter, we denote the discrete lattice spanned by SAR sea ice imagery by N,
and a site in the lattice by t 2 N. We represent the image patch centered at site t by
y t , a p-dimensional random vector taking on different grayscale values, and the
label of site t by l t , a random variable taking on a class {1, . . . ,K}. Then a SAR sea
ice image can be denoted as Y ¼ y t
t 2 N
È
É
, and the labels of this image as
l ¼ l t
t 2 N
È
É
. For automated segmentation of SAR sea ice imagery, we are trying
to infer l based on Y, which, in the Bayesian framework, can be achieved by
maximizing the posterior distribution of l t given y t , i.e.,
p l t
y t
À
Á
p y t
l t
À
Á
p l t
ð Þ
ð6:1Þ
where p y t
l t
À
Á
denotes the probability distribution of patch variable y t conditioned
on l t , which allows the modeling of textural information, and p(l t ) is the a priori
probability of labels, which allows the modeling of label correlation effect. The
maximum a posterior (MAP) estimation of the labels can be expressed as:
b l ¼ arg max l
Y
t2N
p l t
y t
À
Á
ð6:2Þ
or
b l ¼ arg min l
X
t2N
Àlogp y t
l t
À
Á À logp l t
ð Þ
Â
Ã
ð6:3Þ
In this letter, p y t
l t
À
Á
is approached by kernel principal component analysis
(KPCA) to mine the most discriminative textural information, whereas p(l t ) is
implemented by the MRF-based multiple logistic (MLL) prior to modeling the
label correlation effect. The maximum a priori (MAP) problem is solved by the
graph-cut-based α-expansion algorithm.
6.5.1.1 Likelihood Implementation
Since image patches y t characterize the spatial relationship of local pixels, using
image patches instead of individual pixels would allow better representation of
6 Mapping Sea Ice from Satellite SAR Imagery
119