Classification Methods for Remotely Sensed Data, Second Edition

Page 50

It can be inferred from Equation (1.53) that, in a homogeneous area where indicating that (see Equation (1.45)), the Kuan filter outputs which is the same value as that output by the Lee filter. However, in an area of high contrast, , which indicates that (see Equation (1.45)). When , the estimate becomes:

indicating that, in a textured area, the Kuan filter still involves average term weighted by (note that it is larger than in Equation (1.48)) to perform the estimation. By comparing Equations (1.48) and (1.54), it may be concluded that, in theory, the Lee filter is more successful than the Kuan filter in preserving texture information (Baraldi and Parmiggiani, 1995b).

1.8.3.4 The Frost filter

Based on the multiplicative noise assumption as shown in Equation (1.36), the Frost filter tries to minimise the mean square error ² (Frost et al., 1982):

where is the spatial co-ordinate, and m_t is called the impulse response, and is given by:

with

where K₁ is a normalising constant. After some simplifications, the parameter a in Equation (1.57) is eliminated, and the final formulation is:

where K₂ is the filter parameter, and σ_z and μ_z are obtained from local