Pixel classification among overlapping land cover regions in remote sensing imagery is a challenging task. Detection of uncertainty and vagueness are always key features for classifying mixed pixels. This chapter proposes an approach for pixel classification using hybrid approach of Fuzzy C-Means and Particle Swarm Optimization methods. This new unsupervised algorithm is able to identify clusters utilizing particle swarm optimization based on fuzzy membership values. This approach addresses overlapping regions in remote sensing images by uncertainties using fuzzy set membership values. PSO is a population-based stochastic optimization technique inspired from the social behavior of bird flocks. The authors demonstrate the algorithm for segmenting a LANDSAT image of Shanghai. The newly developed algorithm is compared with FCM and K-Means algorithms. The new algorithm-generated clustered regions are verified with the available ground truth knowledge. The validity and statistical analysis are performed to demonstrate the superior performance of the new algorithm with K-Means and FCM algorithms.
TopIntroduction
Remote sensing is defined as the art and science of obtaining information about an object without being in direct physical contact with the object by Cogalton and Green in 1999 (Cogalton, 1999). Several methods exist for classifying pixels into known classes (for example, an urban area or turbid water) in remote sensing images. Mathematically, a remote sensing image can be defined as a set,
(1) of
information units for pixels, where
is the set of spectral band values for
n bands associated with the pixel of coordinate
(i,j). In order to find homogeneous regions in the image we model this image by fuzzy sets, that considers both the spatial image objects and the imprecision attached to them.
Let us denote the space on which the remote sensing image is defined by 
(usually 
or 
). We denote the points of 
(pixels or voxels) as the spatial variables 
. Let 
denotes the spatial distance between two pixels 
. In several earlier works on remote sensing, 
is taken as the Euclidean distance on 
(Maulik, 2012)(Bandyopadhyay, 2005).
A crisp object 
in the remote sensing image is a subset of 
. Henceforth, a fuzzy object is defined as a fuzzy subset 
of 
. This fuzzy object 
is defined bi-univoquely by its membership function, 
. 
is known as the membership function, which represents the membership degree of the point 
to the fuzzy set
. When the value of 
is closer to 1, the degree of membership of x in 
will be higher. Such a representation allows for a direct mapping of mixed pixels in overlapping land cover regions in remote sensing images. Let 
denotes the set of all fuzzy sets defined on 
. For any two pixels
, we denote by 
as their distance in fuzzy perspective. The definition of a new method utilizing the particle swarm movements over fuzzy membership matrix is the scope of this chapter.