Keywords: Multi-temporal SAR images, InSAR coherence image, Classification, Fuzzy c-mean
clustering, Possibility c-mean clustering, Simulated annealing, Adaptive neighborhood
model
Abstract: A classification algorithm for multi-temporal SAR images and InSAR coherence
images is developed. This is done by minimizing an energy function which is defined by the sum
of (1) the difference between the pixel value and the cluster center (mean value of a class) and
(2) the difference between the pixel label (class) and its neighborhood. The global minimization
of the energy function of the whole image is achieved by a simulated annealing approach. The
cluster centers for different classes are calculated using fuzzy c-mean and possibility c-mean
algorithms or determined manually from the image values. In order to preserve the details of the
original images, a neighborhood structure with a 5*1 window is used to calculate the energy
function, whose orientation is determined by the local homogeneity (e.g. the variance of the
pixel values within the window) of the original images. This algorithm is used to classify three
ERS-2 SAR images over the Mekong delta region, Vietnam. By comparing visually the color
composite SAR images and the classified image, it is shown that the classification result is
reasonable. Moreover, this algorithm is also used to classify an InSAR coherence image
acquired from two JERS SAR images over south Sumatra, Indonesia. The classified InSAR
coherence image delineates the bare land and forest clearly, since the coherence of bare land is
larger than that of forest.
1. Introduction
Multi-temporal ERS-1/2 synthetic aperture radar (SAR) images show not only the radar
backscattering properties of objects within one image but also the time evolution of radar
backscattering. Interferometric SAR (InSAR) images generated from two repeat-pass single-complex
SAR images give coherence properties of radar backscattering between the two SAR
images. The information contained in multi-temporal SAR images and InSAR coherence images
has been used successfully to monitor forest cover and rice fields (Liew, et. al, 1998).
Classification of objects is an important step in many applications. This is carried out by (1)
determining the cluster statistical characteristics of different classes, e. g., the mean value of
classes; (2) classifying every pixel according to the clustering result and other conditions, for
example, smooth homogeneous regions and at the same time preservation of the fine structural
details. It often happens for SAR images that mixed-up classes occur within a homogeneous
region due to noise. The preservation of fine structures is often required when utilizing SAR
data for cartography, urban planning, and analysis of agricultural sites, especially, detecting
roads.
In this paper we apply fuzzy c-mean (FCM) and possibility c-mean (PCM) clustering algorithms
to cluster images (Cherkassky and Mulier, 1998; Wong and Posner, 1993). The results of these
two algorithms are compared. Then, we use a classification algorithm which is based on the
adaptive neighborhood model (Garzelli, 1999) and the simulated annealing technique (Hegarat-Mascle
and Vidal-Madjar, 1996), to obtain smooth homogeneous regions but preserve fine
structures.
2.Clustering Algorithms
The goal of clustering is to partition an image set into a small number of groups or
representative clusters. The fuzzy c-mean clustering algorithm seeks to find fuzzy partitioning
by minimizing the following loss function:
where x
i denotes the data vector (i=1, . . . ,n), n the total number of pixels, c
j the center of a fuzzy
cluster (j=1, . . . ,m), m the number of fuzzy clusters assumed to be known, µ
j(x
i) the fuzzy
membership of xi to cluster j. The parameter b>1 is a fixed value specified a priori. Typically b
is chosen around 2. The necessary conditions for an optimal solution are
Performing differentiation and applying the constraint
leads to
Here d
ji denotes the Euclidean distance between the data vector and the cluster center.
The system of nonlinear equations can be solved by an iterative process, which is known as the
FCM algorithm
1) Set number of clusters m and parameter b
2) Initialize cluster centers cj
3) Repeat:
Update membership values µ j(xi) via (4) using current estimates of cj
and update cluster centers cj via (5) using current estimates of µ j(xi)
until the membership values stabilize;
In FCM algorithm the noise and outliers in the data set create many spurious local minima and
distort the solution that corresponds to the global minimum. Thus, a possibility c-mean (PCM)
clustering algorithm was proposed by adding a term to the loss function
where n
j denotes suitable positive numbers. Similar to the FCM algorithm the optimal solution
can be achieved by iteration, using
This is done by alternating between the estimation of the cluster membership values (for the
given values of cluster centers) and the estimation of the cluster centers (for the given
membership values).
